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Crises

  • Ying-Cheng Lai
  • Tamás Tél
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 173)

Abstract

As a system parameter is varied, sudden and qualitative changes in the chaotic attractor can occur, the so-called crises [292, 293]. These qualitative changes can be seen in bifurcation diagrams where one coordinate, say x  ∗ , of the attractor is plotted versus a system parameter, as shown in Fig. 3.1. Sudden shrinkage or enlargements of the set of x  ∗  values are visible at several parameter values, indicating the complexity of crisis events in a typical dynamical system.

Keywords

Periodic Orbit Lyapunov Exponent Unstable Manifold Chaotic Attractor Stable Manifold 
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.

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Electrical EngineeringArizona State UniversityTempeUSA
  2. 2.Department of Theoretical Physics Institute of PhysicsEötvös UniversityBudapestHungary

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