Albert C.J. Luo's Books

Discretization and Implicit Mapping Dynamics

By: Albert C. J. Luo

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Discretization and Implicit Mapping Dynamics

By: Albert C. J. Luo

This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering.

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316

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Springer

Published Date

ISBN 10

3662472759

ISBN 13

9783662472750

Towards Analytical Chaotic Evolutions in Brusselators

By: Albert C.J. Luo,Siyu Guo

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Towards Analytical Chaotic Evolutions in Brusselators

By: Albert C.J. Luo,Siyu Guo

The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. The dynamics of the Brusselator gives an oscillating reaction mechanism for an autocatalytic, oscillating chemical reaction. The Brusselator is a slow-fast oscillating chemical reaction system. The traditional analytical methods cannot provide analytical solutions of such slow-fast oscillating reaction, and numerical simulations cannot provide a full picture of periodic evolutions in the Brusselator. In this book, the generalized harmonic balance methods are employed for analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion. The bifurcation tree of period-1 motion to chaos of the Brusselator is presented through frequency-amplitude characteristics, which be measured in frequency domains. Two main results presented in this book are: • analytical routes of periodical evolutions to chaos and • independent period-(2𝑙 + 1) evolution to chaos. This book gives a better understanding of periodic evolutions to chaos in the slow-fast varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos is clearly demonstrated, which can help one understand routes of periodic evolutions to chaos in chemical reaction oscillators. The slow-fast varying systems extensively exist in biological systems and disease dynamical systems. The methodology presented in this book can be used to investigate the slow-fast varying oscillating motions in biological systems and disease dynamical systems for a better understanding of how infectious diseases spread.

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Springer Nature

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ISBN 10

3031796616

ISBN 13

9783031796616

Bifurcation Dynamics of a Damped Parametric Pendulum

By: Yu Guo,Albert C.J. Luo

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Bifurcation Dynamics of a Damped Parametric Pendulum

By: Yu Guo,Albert C.J. Luo

The inherent complex dynamics of a parametrically excited pendulum is of great interest in nonlinear dynamics, which can help one better understand the complex world. Even though the parametrically excited pendulum is one of the simplest nonlinear systems, until now, complex motions in such a parametric pendulum cannot be achieved. In this book, the bifurcation dynamics of periodic motions to chaos in a damped, parametrically excited pendulum is discussed. Complete bifurcation trees of periodic motions to chaos in the parametrically excited pendulum include: period-1 motion (static equilibriums) to chaos, and period- motions to chaos ( = 1, 2, ···, 6, 8, ···, 12). The aforesaid bifurcation trees of periodic motions to chaos coexist in the same parameter ranges, which are very difficult to determine through traditional analysis. Harmonic frequency-amplitude characteristics of such bifurcation trees are also presented to show motion complexity and nonlinearity in such a parametrically excited pendulum system. The non-travelable and travelable periodic motions on the bifurcation trees are discovered. Through the bifurcation trees of travelable and non-travelable periodic motions, the travelable and non-travelable chaos in the parametrically excited pendulum can be achieved. Based on the traditional analysis, one cannot achieve the adequate solutions presented herein for periodic motions to chaos in the parametrically excited pendulum. The results in this book may cause one rethinking how to determine motion complexity in nonlinear dynamical systems.

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Springer Nature

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ISBN 10

3031796454

ISBN 13

9783031796456

Toward Analytical Chaos in Nonlinear Systems

By: Albert C. J. Luo

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Toward Analytical Chaos in Nonlinear Systems

By: Albert C. J. Luo

Exact analytical solutions to periodic motions in nonlinear dynamical systems are almost not possible. Since the 18th century, one has extensively used techniques such as perturbation methods to obtain approximate analytical solutions of periodic motions in nonlinear systems. However, the perturbation methods cannot provide the enough accuracy of analytical solutions of periodic motions in nonlinear dynamical systems. So the bifurcation trees of periodic motions to chaos cannot be achieved analytically. The author has developed an analytical technique that is more effective to achieve periodic motions and corresponding bifurcation trees to chaos analytically. Toward Analytical Chaos in Nonlinear Systems systematically presents a new approach to analytically determine periodic flows to chaos or quasi-periodic flows in nonlinear dynamical systems with/without time-delay. It covers the mathematical theory and includes two examples of nonlinear systems with/without time-delay in engineering and physics. From the analytical solutions, the routes from periodic motions to chaos are developed analytically rather than the incomplete numerical routes to chaos. The analytical techniques presented will provide a better understanding of regularity and complexity of periodic motions and chaos in nonlinear dynamical systems. Key features: Presents the mathematical theory of analytical solutions of periodic flows to chaos or quasieriodic flows in nonlinear dynamical systems Covers nonlinear dynamical systems and nonlinear vibration systems Presents accurate, analytical solutions of stable and unstable periodic flows for popular nonlinear systems Includes two complete sample systems Discusses time-delayed, nonlinear systems and time-delayed, nonlinear vibrational systems Includes real world examples Toward Analytical Chaos in Nonlinear Systems is a comprehensive reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.

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270

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John Wiley & Sons

Published Date

ISBN 10

1118658612

ISBN 13

9781118658611

Analytical Routes to Chaos in Nonlinear Engineering

By: Albert C. J. Luo

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Analytical Routes to Chaos in Nonlinear Engineering

By: Albert C. J. Luo

Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. This works well up to some accuracy and some range for the input values, but some interesting phenomena such as chaos and singularities are hidden by linearization and perturbation analysis. It follows that some aspects of the behavior of a nonlinear system appear commonly to be chaotic, unpredictable or counterintuitive. Although such a chaotic behavior may resemble a random behavior, it is absolutely deterministic. Analytical Routes to Chaos in Nonlinear Engineering discusses analytical solutions of periodic motions to chaos or quasi-periodic motions in nonlinear dynamical systems in engineering and considers engineering applications, design, and control. It systematically discusses complex nonlinear phenomena in engineering nonlinear systems, including the periodically forced Duffing oscillator, nonlinear self-excited systems, nonlinear parametric systems and nonlinear rotor systems. Nonlinear models used in engineering are also presented and a brief history of the topic is provided. Key features: Considers engineering applications, design and control Presents analytical techniques to show how to find the periodic motions to chaos in nonlinear dynamical systems Systematically discusses complex nonlinear phenomena in engineering nonlinear systems Presents extensively used nonlinear models in engineering Analytical Routes to Chaos in Nonlinear Engineering is a practical reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.

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433

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John Wiley & Sons

Published Date

ISBN 10

1118883926

ISBN 13

9781118883921

Vibro-impact Dynamics

By: Albert C. J. Luo,Yu Guo

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Vibro-impact Dynamics

By: Albert C. J. Luo,Yu Guo

Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysis Comprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools viable for properly characterizing grazing bifurcation. The authors establish vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications. Vibro-impact Dynamics presents an original theoretical way of analyzing the behavior of vibro-impact dynamics that can be extended to discontinuous dynamics. All topics are logically integrated to allow for vibro-impact dynamics, the central theme, to be presented. It provides a unified treatment on the topic with a sound theoretical base that is applicable to both continuous and discrete systems Vibro-impact Dynamics: Presents mapping dynamics to determine bifurcation and chaos in vibro-impact systems Offers two simple vibro-impact systems with comprehensive physical interpretation of complex motions Uses the theory for discontinuous dynamical systems on time-varying domains, to investigate the Fermi-oscillator Essential reading for graduate students, university professors, researchers and scientists in mechanical engineering.

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269

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John Wiley & Sons

Published Date

ISBN 10

1118402901

ISBN 13

9781118402900

Polynomial Functional Dynamical Systems

By: Albert Luo

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Polynomial Functional Dynamical Systems

By: Albert Luo

The book is about the global stability and bifurcation of equilibriums in polynomial functional systems. Appearing and switching bifurcations of simple and higher-order equilibriums in the polynomial functional systems are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The third-order sink and source bifurcations for simple equilibriums are presented in the polynomial functional systems. The third-order sink and source switching bifurcations for saddle and nodes are also presented, and the fourth-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for two second-order upper-saddles and two second-order lower-saddles, respectively. In general, the (2 + 1)th-order sink and source switching bifurcations for (2)th-order saddles and (2 +1)-order nodes are also presented, and the (2)th-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for (2)th-order upper-saddles and (2)th-order lower-saddles (, = 1,2,...). The vector fields in nonlinear dynamical systems are polynomial functional. Complex dynamical systems can be constructed with polynomial algebraic structures, and the corresponding singularity and motion complexity can be easily determined.

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151

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Springer Nature

Published Date

ISBN 10

3031797094

ISBN 13

9783031797095

Memorized Discrete Systems and Time-delay

By: Albert C. J. Luo

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Memorized Discrete Systems and Time-delay

By: Albert C. J. Luo

This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.

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307

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Springer

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ISBN 10

3319427784

ISBN 13

9783319427782

Nonlinear Vibration Reduction

An Electromagnetically Tuned Mass Damper System

By: Albert C. J. Luo,Chuan Guo

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Nonlinear Vibration Reduction

An Electromagnetically Tuned Mass Damper System

By: Albert C. J. Luo,Chuan Guo

The tuned mass damper is one of the classic dynamic vibration absorbers with effective devices for energy dissipation and vibration reduction. The electromagnetically tuned mass damper system is extensively used for vibration reduction in engineering. A better understanding of the nonlinear dynamics of the electromagnetically tuned mass damper system is very important to optimize the parameters of such systems for vibration reduction. However, until now, one cannot fully understand complex periodic motions in such a nonlinear, electromagnetically tuned mass damper system. In this book, the semi-analytical solutions of periodic motions are presented through period-1, period-3, period-9, and period-12 motions. The corresponding stability and bifurcations of periodic motions are determined. The frequency-amplitude characteristics for bifurcation routes of such higher-order periodic motions are presented. This book helps people better understand the dynamical behaviors of an electromagnetically tuned mass damper system for the new development and design of vibration reduction and energy harvesting systems.

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104

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Springer Nature

Published Date

ISBN 10

3031174992

ISBN 13

9783031174995

Bifurcation and Stability in Nonlinear Discrete Systems

By: Albert C. J. Luo

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Bifurcation and Stability in Nonlinear Discrete Systems

By: Albert C. J. Luo

This book focuses on bifurcation and stability in nonlinear discrete systems, including monotonic and oscillatory stability. It presents the local monotonic and oscillatory stability and bifurcation of period-1 fixed-points on a specific eigenvector direction, and discusses the corresponding higher-order singularity of fixed-points. Further, it explores the global analysis of monotonic and oscillatory stability of fixed-points in 1-dimensional discrete systems through 1-dimensional polynomial discrete systems. Based on the Yin-Yang theory of nonlinear discrete systems, the book also addresses the dynamics of forward and backward nonlinear discrete systems, and the existence conditions of fixed-points in said systems. Lastly, in the context of local analysis, it describes the normal forms of nonlinear discrete systems and infinite-fixed-point discrete systems. Examining nonlinear discrete systems from various perspectives, the book helps readers gain a better understanding of the nonlinear dynamics of such systems.

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313

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Springer Nature

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ISBN 10

9811552126

ISBN 13

9789811552120

Two-Dimensional Quadratic Nonlinear Systems

Volume I: Univariate Vector Fields

By: Albert C. J. Luo

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Two-Dimensional Quadratic Nonlinear Systems

Volume I: Univariate Vector Fields

By: Albert C. J. Luo

This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert’s sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering.

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692

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Springer Nature

Published Date

ISBN 10

9811678731

ISBN 13

9789811678738

Periodic Flows to Chaos in Time-delay Systems

By: Albert C. J. Luo

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Periodic Flows to Chaos in Time-delay Systems

By: Albert C. J. Luo

This book for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems.

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203

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Springer

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ISBN 10

3319426648

ISBN 13

9783319426648

Regularity and Complexity in Dynamical Systems

By: Albert C. J. Luo

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Regularity and Complexity in Dynamical Systems

By: Albert C. J. Luo

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

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500

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Springer Science & Business Media

Published Date

ISBN 10

1461415233

ISBN 13

9781461415237

Discontinuous Dynamical Systems on Time-varying Domains

By: Albert C. J. Luo

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Discontinuous Dynamical Systems on Time-varying Domains

By: Albert C. J. Luo

Discontinuous Dynamical Systems on Time-varying Domains" is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains, this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory, principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers, advanced undergraduate and graduate students in mathematics, physics and mechanics. Dr. Albert C. J. Luo is a professor at Southern Illinois University Edwardsville, USA. His research is involved in the nonlinear theory of dynamical systems. His main contributions are in the following aspects: a stochastic and resonant layer theory in nonlinear Hamiltonian systems, singularity on discontinuous dynamical systems, and approximate nonlinear theories for a deformable-body.

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234

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Springer Science & Business Media

Published Date

ISBN 10

3642002536

ISBN 13

9783642002533

Nonlinear Deformable-body Dynamics

By: Albert C. J. Luo

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Nonlinear Deformable-body Dynamics

By: Albert C. J. Luo

Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of nonlinear dynamics in dynamical systems and deformable solids.

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395

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Springer Science & Business Media

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ISBN 10

3642121365

ISBN 13

9783642121364

Periodic Motions to Chaos in a Spring-Pendulum System

By: Yu Guo,Albert C. J. Luo

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Periodic Motions to Chaos in a Spring-Pendulum System

By: Yu Guo,Albert C. J. Luo

This book builds on the fundamental understandings, learned in undergraduate engineering and physics in principles of dynamics and control of mechanical systems. The design of real-world mechanical systems and devices becomes far more complex than the spring-pendulum system to which most engineers have been exposed. The authors provide one of the simplest models of nonlinear dynamical systems for learning complex nonlinear dynamical systems. The book addresses the complex challenges of the necessary modeling for the design of machines. The book addresses the methods to create a mechanical system with stable and unstable motions in environments influenced by an array of motion complexity including varied excitation frequencies ranging from periodic motions to chaos. Periodic motions to chaos, in a periodically forced nonlinear spring pendulum system, are presented through the discrete mapping method, and the corresponding stability and bifurcations of periodic motions on the bifurcation trees are presented. Developed semi-analytical solutions of periodical motions to chaos help the reader to understand complex nonlinear dynamical behaviors in nonlinear dynamical systems. Especially, one can use unstable motions rather than stable motions only.

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110

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Springer Nature

Published Date

ISBN 10

3031178831

ISBN 13

9783031178832

Bifurcation Dynamics in Polynomial Discrete Systems

By: Albert C. J. Luo

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Bifurcation Dynamics in Polynomial Discrete Systems

By: Albert C. J. Luo

This is the first book focusing on bifurcation dynamics in 1-dimensional polynomial nonlinear discrete systems. It comprehensively discusses the general mathematical conditions of bifurcations in polynomial nonlinear discrete systems, as well as appearing and switching bifurcations for simple and higher-order singularity period-1 fixed-points in the 1-dimensional polynomial discrete systems. Further, it analyzes the bifurcation trees of period-1 to chaos generated by period-doubling, and monotonic saddle-node bifurcations. Lastly, the book presents methods for period-2 and period-doubling renormalization for polynomial discrete systems, and describes the appearing mechanism and period-doublization of period-n fixed-points on bifurcation trees for the first time, offering readers fascinating insights into recent research results in nonlinear discrete systems.

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440

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Springer Nature

Published Date

ISBN 10

9811552088

ISBN 13

9789811552083

Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems

By: Siyuan Xing,Albert C.J. Luo

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Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems

By: Siyuan Xing,Albert C.J. Luo

In this book, the global sequential scenario of bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is presented for a better understanding of global behaviors and motion transitions for one periodic motion to another one. A 1-dimensional (1-D), time-delayed, nonlinear dynamical system is considered as an example to show how to determine the global sequential scenarios of the bifurcation trees of periodic motions to chaos. All stable and unstable periodic motions on the bifurcation trees can be determined. Especially, the unstable periodic motions on the bifurcation trees cannot be achieved from the traditional analytical methods, and such unstable periodic motions and chaos can be obtained through a specific control strategy. The sequential periodic motions in such a 1-D time-delayed system are achieved semi-analytically, and the corresponding stability and bifurcations are determined by eigenvalue analysis. Each bifurcation tree of a specific periodic motion to chaos are presented in detail. The bifurcation tree appearance and vanishing are determined by the saddle-node bifurcation, and the cascaded period-doubled periodic solutions are determined by the period-doubling bifurcation. From finite Fourier series, harmonic amplitude and harmonic phases for periodic motions on the global bifurcation tree are obtained for frequency analysis. Numerical illustrations of periodic motions are given for complex periodic motions in global bifurcation trees. The rich dynamics of the 1-D, delayed, nonlinear dynamical system is presented. Such global sequential periodic motions to chaos exist in nonlinear dynamical systems. The frequency-amplitude analysis can be used for re-construction of analytical expression of periodic motions, which can be used for motion control in dynamical systems.

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Springer Nature

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ISBN 10

3031796691

ISBN 13

9783031796692

Singularity and Dynamics on Discontinuous Vector Fields

By: Albert C.J. Luo

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Singularity and Dynamics on Discontinuous Vector Fields

By: Albert C.J. Luo

This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones' thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics. - Challenging continuous Newton's dynamics - Original theory and seeds of new researches in the field - Wide spectrum of applications in science and engineering - Systematic presentation and clear illustrations

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311

Publisher

Elsevier

Published Date

ISBN 10

0080480934

ISBN 13

9780080480930

Nonlinear and Complex Dynamics

Applications in Physical, Biological, and Financial Systems

By: José António Tenreiro Machado,Dumitru Baleanu,Albert C. J. Luo

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Nonlinear and Complex Dynamics

Applications in Physical, Biological, and Financial Systems

By: José António Tenreiro Machado,Dumitru Baleanu,Albert C. J. Luo

Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.

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328

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Springer Science & Business Media

Published Date

ISBN 10

146140231X

ISBN 13

9781461402312

Machine Tool Vibrations and Cutting Dynamics

By: Brandon C. Gegg,C. Steve Suh,Albert C. J. Luo

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Machine Tool Vibrations and Cutting Dynamics

By: Brandon C. Gegg,C. Steve Suh,Albert C. J. Luo

“Machine Tool Vibrations and Cutting Dynamics” covers the fundamentals of cutting dynamics from the perspective of discontinuous systems theory. It shows the reader how to use coupling, interaction, and different cutting states to mitigate machining instability and enable better machine tool design. Among the topics discussed are; underlying dynamics of cutting and interruptions in cutting motions; the operation of the machine-tool systems over a broad range of operating conditions with minimal vibration and the need for high precision, high yield micro- and nano-machining.

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187

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Springer Science & Business Media

Published Date

ISBN 10

1441998012

ISBN 13

9781441998019

Discretization and Implicit Mapping Dynamics

By: Albert C. J. Luo

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Discretization and Implicit Mapping Dynamics

By: Albert C. J. Luo

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316

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Springer

Published Date

ISBN 10

3662472759

ISBN 13

9783662472750

System Dynamics with Interaction Discontinuity

By: Albert C. J. Luo,Dennis M. O'Connor

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System Dynamics with Interaction Discontinuity

By: Albert C. J. Luo,Dennis M. O'Connor

This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

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Page Count

266

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Springer

Published Date

ISBN 10

3319174223

ISBN 13

9783319174228

Discontinuous Dynamical Systems

By: Albert C. J. Luo

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Discontinuous Dynamical Systems

By: Albert C. J. Luo

“Discontinuous Dynamical Systems” presents a theory of dynamics and flow switchability in discontinuous dynamical systems, which can be as the mathematical foundation for a new dynamics of dynamical system networks. The book includes a theory for flow barriers and passability to boundaries in discontinuous dynamical systems that will completely change traditional concepts and ideas in the field of dynamical systems. Edge dynamics and switching complexity of flows in discontinuous dynamical systems are explored in the book and provide the mathematical basis for developing the attractive network channels in dynamical systems. The theory of bouncing flows to boundaries, edges and vertexes in discontinuous dynamical systems with multi-valued vector fields is described in the book as a “billiard” theory of dynamical system networks. The theory of dynamical system interactions in discontinued dynamical systems can be used as a general principle in dynamical system networks, which is applied to dynamical system synchronization. The book represents a valuable reference work for university professors and researchers in applied mathematics, physics, mechanics, and control. Dr. Albert C.J. Luo is an internationally respected professor in nonlinear dynamics and mechanics, and he works at Southern Illinois University Edwardsville, USA.

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Page Count

700

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Springer Science & Business Media

Published Date

ISBN 10

364222461X

ISBN 13

9783642224614

Galloping Instability to Chaos of Cables

By: Albert C. J. Luo,Bo Yu

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Galloping Instability to Chaos of Cables

By: Albert C. J. Luo,Bo Yu

This book provides students and researchers with a systematic solution for fluid-induced structural vibrations, galloping instability and the chaos of cables. They will also gain a better understanding of stable and unstable periodic motions and chaos in fluid-induced structural vibrations. Further, the results presented here will help engineers effectively design and analyze fluid-induced vibrations.

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Page Count

213

Publisher

Springer

Published Date

ISBN 10

9811052425

ISBN 13

9789811052422

Global Transversality, Resonance And Chaotic Dynamics

By: Albert C J Luo

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Global Transversality, Resonance And Chaotic Dynamics

By: Albert C J Luo

This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics.

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Page Count

461

Publisher

World Scientific

Published Date

ISBN 10

9814474320

ISBN 13

9789814474320

Discontinuous Dynamical Systems

By: Albert C. J. Luo

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Discontinuous Dynamical Systems

By: Albert C. J. Luo

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Page Count

700

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364222461X

ISBN 13

9783642224614

Dynamical System Synchronization

By: Albert C. J. Luo

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Dynamical System Synchronization

By: Albert C. J. Luo

Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques.

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Page Count

245

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461450977

ISBN 13

9781461450979

Bifurcation and Stability in Nonlinear Dynamical Systems

By: Albert C. J. Luo

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Bifurcation and Stability in Nonlinear Dynamical Systems

By: Albert C. J. Luo

This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems. From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will bring us to the new era of dynamical systems and control. Presents an efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums; Discusses dynamics of infinite-equilibrium systems; Demonstrates higher-order singularity.

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Page Count

418

Publisher

Springer Nature

Published Date

ISBN 10

3030229106

ISBN 13

9783030229108

Book's by Albert C.J. Luo

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