Export citation

Export citation

Choose format for download:

Download Citation

    Example of a Physical System with a Hyperbolic Attractor of the Smale-Williams Type

    Sergey P. Kuznetsov

    • Institute of Radio-Engineeing and Electronics of RAS, Saratov Division, Zelenaya 38 Saratov, 410019, Russia

    Phys. Rev. Lett. 95, 144101 – Published 28 September, 2005

    DOI: https://doi.org/10.1103/PhysRevLett.95.144101

    Abstract

    A simple and transparent example of a nonautonomous flow system with a hyperbolic strange attractor is suggested. The system is constructed on the 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 counterphase variation in time. In terms of stroboscopic Poincaré sections, the respective 4D mapping has a hyperbolic strange attractor of the 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 analysis of distributions of angles between stable and unstable subspaces of a chaotic trajectory is performed.

    Authorization Required

    We need you to provide your credentials before accessing this content.

    References (Subscription Required)

    Outline

    Information

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation