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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2006, Volume 2, Number 3, Pages 307–331
(Mi nd172)
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This article is cited in 7 scientific papers (total in 7 papers)
Transition to a synchronous chaos regime in a system of coupled non-autonomous oscillators presented in terms of amplitude equations
P. V. Kuptsov, S. P. Kuznetsova a Saratov Branch of Institute of Radio-engineering and Electronics, Russian Academy of Sciences
Abstract:
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:
P. V. Kuptsov, S. P. Kuznetsov, “Transition to a synchronous chaos regime in a system of coupled non-autonomous oscillators presented in terms of amplitude equations”, Nelin. Dinam., 2:3 (2006), 307–331
Linking options:
https://www.mathnet.ru/eng/nd172 https://www.mathnet.ru/eng/nd/v2/i3/p307
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