The Anishchenko–Astakhov Oscillator of Chaotic Self-Sustained Oscillations

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


In general form, self-sustained oscillatory systems with one degree of freedom are described by the equation
$$\displaystyle{ \ddot{x} +\varPhi (x,\boldsymbol{\alpha })\dot{x} +\varPsi (x,\boldsymbol{\alpha }) = 0\;, }$$
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 \((\alpha _{1},\alpha _{2},\ldots,\alpha _{n})\).


Hopf Bifurcation Bifurcation Diagram Chaotic Attractor Bifurcation Line Homoclinic Trajectory 
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  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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