Effect of asymmetry on the loss of chaos synchronization

We investigate the effect of asymmetry of coupling on the bifurcation mechanism for the loss of synchronous chaos in coupled systems. It is found that only when the symmetry-breaking pitchfork bifurcations take part in the process of the synchronization loss for the case of symmetric coupling, the asymmetry changes the bifurcation scenarios of the desynchronization. For the case of weak coupling, pitchfork bifurcations of asynchronous periodic saddles are replaced by saddle-node bifurcations, while for the case of strong coupling, pitchfork bifurcations of synchronous periodic saddles transform to transcritical bifurcations. The effects of the saddle-node and transcritical bifurcations for the weak asymmetry are similar to those of the pitchfork bifurcations for the symmetric-coupling case. However, with increasing the "degree" of the asymmetry, their effects change qualitatively, and eventually become similar to those for the extreme case of unidirectional asymmetric coupling.