Periodic Solutions of Nonlinear Dynamical Systems

Numerical Computation, Stability, Bifurcation and Transition to Chaos

  • Authors
  • Eduard¬†Reithmeier
Part of the Lecture Notes in Mathematics book series (LNM, volume 1483)

Table of contents

  1. Front Matter
    Pages I-2
  2. Eduard Reithmeier
    Pages 3-8
  3. Eduard Reithmeier
    Pages 9-109
  4. Back Matter
    Pages 152-171

About these proceedings

Introduction

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.

Keywords

Dynamical system Vibration algorithm algorithms chaos dynamical systems dynamische Systeme nonlinear dynamics

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0094521
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54512-5
  • Online ISBN 978-3-540-38427-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692