Transition to a synchronous chaos regime in a system of coupled non-autonomous oscillators presented in terms of amplitude equations

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.