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Periodic Solutions of Nonlinear Dynamical Systems

Numerical Computation, Stability, Bifurcation and Transition to Chaos

  • Conference proceedings
  • © 1991

Overview

Authors:
  1. Eduard Reithmeier
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1483)

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Table of contents (3 papers)

  1. Front Matter

    Pages I-2
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  2. Introduction

    • Eduard Reithmeier
    Pages 3-8

  3. Differentiable dynamical systems

    • Eduard Reithmeier
    Pages 9-109

  4. Differentiable dynamical systems with discontinuities

    • Eduard Reithmeier
    Pages 110-151

  5. Back Matter

    Pages 152-171
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Periodic Solutions of Nonlinear Dynamical Systems

  • Book Subtitle: Numerical Computation, Stability, Bifurcation and Transition to Chaos

  • Authors: Eduard Reithmeier

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094521

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54512-5Published: 25 September 1991

  • eBook ISBN: 978-3-540-38427-4Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 174

  • Topics: Analysis, Mathematical and Computational Engineering, Classical Mechanics

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