Dynamics of coupled chaotic oscillators: from chaos to quasiperiodicity

    2014, Vol. 10, No. 4, pp.  387-405

    Author(s): Kuznetsov A. P., Shchegoleva N. A., Sataev I. R., Sedova Y. V., Turukina L. V.

    Ensembles of several chaotic R¨ossler oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of invariant tori of different and sufficiently high dimension. The possibility of a quasi-periodic Hopf bifurcation and of the cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonant tori are revealed whose boundaries correspond to a saddle-node bifurcation. Within areas of resonant modes the torus-doubling bifurcations and tori destruction are observed.
    Keywords: chaos, quasiperiodic oscillations, invariant tori, Lyapunov exponents, bifurcations
    Citation: Kuznetsov A. P., Shchegoleva N. A., Sataev I. R., Sedova Y. V., Turukina L. V., Dynamics of coupled chaotic oscillators: from chaos to quasiperiodicity, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 4, pp.  387-405

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