Effects of Scale-Free Topological Properties on Dynamical Synchronization and Control in Coupled Map Lattices

In the paper, we study effects of scale-free (SF) topology on dynamical synchronization and control in coupled map lattices (CML). Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as ε is increased linearly. The CML with SF loses synchronization and intermittency occurs if γ>γc. Numerical examples are presented to demonstrate all results.