The Approximate Analytical Methods in the Study of Transition to Chaotic Motion in Nonlinear Oscillators

  • W. Szemplinska-Stupnicka
Part of the International Centre for Mechanical Sciences book series (CISM, volume 319)


The chapter presents an approximate approach to the study of transition to chaotic response in forced dissipative oscillators. We show that mathematical techniques and concepts of the approximate theory of nonlinear oscillations can be useful in constructing approximate criteria for chaos, i.e. in estimating system parameter critical values, the values for which chaos can be expected. The attention is focused on the strange phenomena which are related to the escape from a potential well. Four classical oscillators are studied in detail: two-well potential system under a) dynamic harmonic load, b) combined parametric and dynamic load; the single potential system with quadratic nonlinearity, and Duffing’s softening type oscillator. The approximate criteria for chaos (or escape) are obtained in the form of simple algebraic formulae. Computer simulations confirm that the theoretical results provide us with a good estimation of the system parameter critical values where the “strange phenomena” really occur.


Stability Limit Chaotic Motion Period Doubling Parametric Excitation Unstable Region 
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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • W. Szemplinska-Stupnicka
    • 1
  1. 1.Polish Academy of ScienceWarsawPoland

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