Bistable synchronization of coupled random network of cubic maps

Abstract

The spatiotemporal behavior of coupled cubic maps over a dynamic network having randomness in coupling connections is investigated here. Due to the bistable nature of cubic map the synchronization behavior is dependent on the initial conditions. The network can stabilize to any one of the nonzero unstable fixed point of the map depending on the initial conditions. Linear stability analysis of synchronized fixed point gives the value of coupling at which onset of synchronization occurs. The critical coupling strength depends on the randomness in rewiring, properties of the local map, but it is independent of lattice size. Numerical simulation results match very well with predictions from theoretical analysis. Behaviors of the network for synchronized initial conditions are pointed out. Looking at the case of stability in a network with static rewiring, it is found that, the range of synchronization of fixed point becomes shorter than the dynamical random one. Contribution of delay in the synchronization phenomenon is studied both analytically and numerically and the range of synchronized period-2 orbit is found to be quite similar in both the cases. Multistable nature of the delay coupled network is shown numerically.

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