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Periodic Solutions of Nonlinear Dynamical Systems

Numerical Computation, Stability, Bifurcation and Transition to Chaos

By: Eduard Reithmeier

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Periodic Solutions of Nonlinear Dynamical Systems

Numerical Computation, Stability, Bifurcation and Transition to Chaos

By: Eduard Reithmeier

Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations. The text addresses mathematicians interested in engineering problems as well as engineers working with nonlinear dynamics.

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Page Count

177

Publisher

Springer

Published Date

ISBN 10

3540384278

ISBN 13

9783540384274

Periodic Solutions of Nonlinear Dynamical Systems

Numerical Computation, Stability, Bifurcation and Transition to Chaos

By: Eduard Reithmeier

Write a review Read reviews Take a Quiz Solve Book Puzzle

Periodic Solutions of Nonlinear Dynamical Systems

Numerical Computation, Stability, Bifurcation and Transition to Chaos

By: Eduard Reithmeier

Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations. The text addresses mathematicians interested in engineering problems as well as engineers working with nonlinear dynamics.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

Solve jigsaw puzzle

Age

Page Count

177

Publisher

Springer

Published Date

ISBN 10

3540384278

ISBN 13

9783540384274