An example of physical system with hyperbolic attractor of Smale - Williams type

Details An example of physical system with hyperbolic attractor of Smale - Williams type An example of physical system with hyperbolic attractor of Smale - Williams type

2005-03-18

arxiv.org/abs/nlin/0503041v1

Nonlinear Sciences

Chaotic Dynamics

7 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.95.144101

A simple and transparent example of a non-autonomous flow system, with hyperbolic strange attractor is suggested. The system is constructed on a basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and the parameters controlling generation in both oscillators undergo a slow periodic counter-phase variation in time. In terms of stroboscopic Poincar\'{e} section, the respective four-dimensional mapping has a hyperbolic strange attractor of Smale - Williams type. Qualitative reasoning and quantitative data of numerical computations are presented and discussed, e.g. Lyapunov exponents and their parameter dependencies. A special test for hyperbolicity based on statistical analysis of distributions of angles between stable and unstable subspaces of a chaotic trajectory has been performed. Perspectives of further comparative studies of hyperbolic and non-hyperbolic chaotic dynamics in physical aspect are outlined.

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