Fast numerical test of hyperbolic chaos

Abstract

The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a distribution of a characteristic value which is bounded within the unit interval and whose zero indicate the presence of tangency between expanding and contracting subspaces. To perform the test one needs to solve several copies of equations for infinitesimal perturbations whose amount is equal to the sum of numbers of positive and zero Lyapunov exponents. Since for high-dimensional system this amount is normally much less then the full phase space dimension, this method provide the fast and memory saving way for numerical hyperbolicity test of such systems.

4 pages and 4 figures

References in corpus (3)

• Characterizing dynamics with covariant Lyapunov vectors
• Hyperbolicity and the effective dimension of spatially-extended dissipative systems
• Hyperbolic decoupling of tangent space and effective dimension of dissipative systems

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• On Hyperbolic Attractors in Complex Shimizu -- Morioka Model
• Parametric Generator of Robust Chaos: Circuit Implementation and Simulation Using the Program Product MULTISIM
• Hyperbolic chaos at blinking coupling of noisy oscillators
• Smale-Williams Solenoids in a System of Coupled Bonhoeffer-van der Pol Oscillators
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