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Bifurcations of Dynamical Systems

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

Abstract

In the natural sciences, it turns out that the formulation of mathematical models leads to temporal evolution laws for state variables that depend on parameters. The values of these parameters are defined by system elements that do not change over time. When described mathematically, a wide class of physical problems lead to differential equations or maps which depend on one or several parameters. Fixing parameter values determines the type of solutions for given initial conditions, while variation of these values may result in both quantitative and qualitative changes in the nature of the solutions.

Keywords

Hopf Bifurcation Bifurcation Point Stable Cycle Stable Limit Cycle Pitchfork Bifurcation 
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.

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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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