Loss of synchronization in coupled Rossler systems

This paper considers the loss of synchronization for a system of two coupled Rossler oscillators. Bifurcation curves for the transverse destabilization of low-periodic orbits embedded in the synchronized chaotic state are obtained, and we show that desynchronization for a pair of symmetrically coupled, identical Rossler systems is associated with different orbits undergoing transverse pitchfork or period-doubling bifurcations. The transverse destabilization of the period-1 orbit is examined in detail, and we follow the sequence of bifurcations that the asynchronous periodic cycles undergo. In the presence of an asymmetry in the coupling, the transverse period-doubling bifurcation remains essentially the same. The transverse pitchfork bifurcation, on the other hand, is transformed into a transcritical riddling bifurcation. If the interacting Rossler oscillators have different parameter values, the non-generic character of the pitchfork bifurcation leads it to be replaced by a saddle-node bifurcation occurring off the symmetric sub-space. Finally, we show how the transverse stability properties of the equilibrium point can be used to obtain approximative analytical results for the transverse stability of the coupled chaotic oscillators. (C) 2001 Elsevier Science B.V. All rights reserved.