Alexandr Kuznetsov

Zelenaya st., 38, Saratov, 410019, Russia
Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov Branch


Kuznetsov A. P., Shchegoleva N. A., Sataev I. R., Sedova Y. V., Turukina L. V.
From Chaos to Quasi-Periodicity
2015, vol. 20, no. 2, pp.  189-204
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, vol. 20, no. 2, pp. 189-204
Kuznetsov A. P., Sataev I. R., Sedova Y. V.
We discuss the structure of bifurcation diagram in the plane of parameters controlling period-doublings for the system of coupled logistic maps. The analysis is carried out by computing the charts of dynamical regimes and charts of Lyapunov exponents giving showy and effective illustrations. The critical point of codimension two at the border of chaos is found. It is a terminal point for the Feigenbaum critical line. The bifurcation analysis in the vicinity of this point is presented.
Keywords: criticality, universality, transition to chaos, coupled maps, bifurcation, terminal point
Citation: Kuznetsov A. P., Sataev I. R., Sedova Y. V.,  Dynamics of Coupled Non-Identical Systems with Period-Doubling Cascade, Regular and Chaotic Dynamics, 2008, vol. 13, no. 1, pp. 9-18
Kuznetsov A. P., Kuznetsov S. P., Sataev I. R.
While considering multiparameter families of nonlinear systems, types of behavior at the onset of chaos may appear which are distinct from Feigenbaum's universality. We present a review of such situations which can be met in families of one-dimensional maps and discuss a possibility of their realization and observation in nonlinear dissipative systems of more general form.
Citation: Kuznetsov A. P., Kuznetsov S. P., Sataev I. R.,  Codimension and typicity in a context of description of transition to chaos via period-doubling in dissipative dynamical systems, Regular and Chaotic Dynamics, 1997, vol. 2, nos. 3-4, pp. 90-105

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