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


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.


Periodic Orbit Lyapunov Exponent Unstable Manifold Chaotic Attractor Stable Manifold 
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© 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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