From Chaos to Quasi-Periodicity

    2015, Volume 20, Number 2, pp.  189-204

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

    Ensembles of several Rössler chaotic oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonance tori are revealed. Boundaries of these domains correspond to the saddle-node bifurcations. Inside the domains of resonance modes, torus-doubling bifurcations and destruction of tori are observed.
    Keywords: chaos, quasi-periodic oscillation, invariant torus, Lyapunov exponent, bifurcation
    Citation: Kuznetsov A. P., Shchegoleva N. A., Sataev I. R., Sedova Y. V., Turukina L. V., From Chaos to Quasi-Periodicity, Regular and Chaotic Dynamics, 2015, Volume 20, Number 2, pp. 189-204

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