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A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems

  • G. A. Leonov
  • N. V. Kuznetsov
  • E. V. Kudryashova
Article

Abstract

A direct method is proposed for studying the behavior of two-dimensional dynamical systems in the critical case when the linear part of the system has two purely imaginary eigenvalues. This method allows one to construct approximations to solutions of the system and to the “turn-round” time of the trajectory in the form of a finite series in powers of the initial datum. With the help of symbolic computations and the proposed method, first approximations of a solution are constructed and expressions for the first three Lyapunov quantities of the Liénard system are written.

Keywords

Lyapunov quantities limit cycle symbolic computations 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • G. A. Leonov
    • 1
  • N. V. Kuznetsov
    • 1
  • E. V. Kudryashova
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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