Bifurcations of Two-Dimensional Tori and Chaos in Dissipative Systems

  • V. S. Anishchenko
  • T. E. Vadivasova
  • M. A. Safonova
Conference paper
Part of the Advances in Simulation book series (ADVS.SIMULATION, volume 1)


Transition to dynamical chaos in different distributed and multidimensional systems is often preceded by a quasiperiodic motion bifurcations. In simplest case, chaos arises via distruction of two-dimensional torus (T2) [1]. This communication represents the results of computer and physical experiments on the investigation of torus distruction regularities, mechanisms of appearance of quasiattractors (CA1) and their characteristics in different flow and diskrete systems. The following systems realising regim of quasiperiodic oscillations were investigated: driven generator with inertial nonlineority, two coupled generators and discrete system of coupled Feigenbaum maps.


Dissipative System Parameter Plane Circle Mapping Dynamical Chaos Couple Generator 
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  1. [1]
    Anishchenko V.S.: Dynamical Chaos-Basic Concepts. Teubner-Verlag, Leipzig 1987.MATHGoogle Scholar
  2. [2]
    Afraimovich V.S., Shilnikov L.P.: Invariant two-dimensional tori, their distruction and stochastisity. Methods of qualitative theory of differential equations. University Gorky, 1983, 3–25.Google Scholar
  3. [3]
    Anishchenko V.S.: Distinction of quasiperiodic osoillations and chaos in dissipative systems. Journal of Technical Physics, 56, (1986) 2, 225–237.Google Scholar

Copyright information

© Akademie-Verlag Berlin 1988

Authors and Affiliations

  • V. S. Anishchenko
  • T. E. Vadivasova
  • M. A. Safonova
    • 1
  1. 1.Departament of PhysicsSaratov State UniversitySaratovUSSR

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