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    Transition to a synchronous chaos regime in a system of coupled non-autonomous oscillators presented in terms of amplitude equations

    2006, Vol. 2, No. 3, pp.  307-331

    Author(s): Kuptsov P. V., Kuznetsov S. P.

    Amplitude equations are obtained for a system of two coupled van der Pol oscillators that has been recently suggested as a simple system with hyperbolic chaotic attractor allowing physical realization. We demonstrate that an approximate model based on the amplitude equations preserves basic features of a hyperbolic dynamics of the initial system. For two coupled amplitude equations models having the hyperbolic attractors a transition to synchronous chaos is studied. Phenomena typically accompanying this transition, as riddling and bubbling, are shown to manifest themselves in a specific way and can be observed only in a small vicinity of a critical point. Also, a structure of many-dimensional attractor of the system is described in a region below the synchronization point.
    Keywords: hyperbolic chaos, strange Smale-Williams attractor, chaotic synchronization, amplitude equations
    Citation: Kuptsov P. V., Kuznetsov S. P., Transition to a synchronous chaos regime in a system of coupled non-autonomous oscillators presented in terms of amplitude equations, Rus. J. Nonlin. Dyn., 2006, Vol. 2, No. 3, pp.  307-331
    DOI:10.20537/nd0603005


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