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The Anishchenko–Astakhov Oscillator of Chaotic Self-Sustained Oscillations

  • Vadim S. Anishchenko
  • Tatyana E. Vadivasova
  • Galina I. Strelkova
Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

In general form, self-sustained oscillatory systems with one degree of freedom are described by the equation
$$\displaystyle{ \ddot{x} +\varPhi (x,\boldsymbol{\alpha })\dot{x} +\varPsi (x,\boldsymbol{\alpha }) = 0\;, }$$
(11.1)
where x is a variable oscillating periodically, \(\varPhi (x,\boldsymbol{\alpha })\) and \(\varPsi (x,\boldsymbol{\alpha })\) are nonlinear functions characterizing the action of forces providing periodic self-sustained oscillations, and \(\boldsymbol{\alpha }\) is a vector of parameters \((\alpha _{1},\alpha _{2},\ldots,\alpha _{n})\).

Keywords

Hopf Bifurcation Bifurcation Diagram Chaotic Attractor Bifurcation Line Homoclinic Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Anishchenko, V.S.: Dynamical Chaos – Models and Experiments. World Scientific, Singapore (1995)Google Scholar
  2. 2.
    Anishchenko, V.S., Astakhov, V.V., Neiman, A.B., Vadivasova, T.E., Schimansky-Geier, L.: Nonlinear Dynamics of Chaotic and Stochastic Systems. Springer, Berlin (2002)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Vadim S. Anishchenko
    • 1
  • Tatyana E. Vadivasova
    • 1
  • Galina I. Strelkova
    • 1
  1. 1.Department of Physics Instiute of Nonlinear DynamicsSaratov State UniversitySaratovRussia

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