Geodesic
Transition to a synchronous chaos regime in a system of coupled non-autonomous oscillators presented in terms of amplitude equations
Russian journal of nonlinear dynamics, Tome 2 (2006) no. 3, pp. 307-331.

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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
Mots-clés : amplitude equations. 
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     author = {P. V. Kuptsov and S. P. Kuznetsov},
     title = {Transition to a synchronous chaos regime in a system of coupled non-autonomous oscillators presented in terms of amplitude equations},
     journal = {Russian journal of nonlinear dynamics},
     pages = {307--331},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2006_2_3_a4/}
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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. Russian journal of nonlinear dynamics, Tome 2 (2006) no. 3, pp. 307-331. http://geodesic.mathdoc.fr/item/ND_2006_2_3_a4/