Spatiotemporal Synchronization of Diffusively Coupled Modified Logistic Map Under Complex Network

摘要

We study spatiotemporal synchronization under complex network of diffusively coupled chaotic modified logistic map. In modified logistic map a new parameter is introduced such that nonlinear term is in fractional power. The complex network is dynamic whose coupling connections change stochastically in time. Here we investigate the spatiotemporal dynamics of coupled modified logistic maps whose coupling connections are rewired randomly, and we determine (1) the effects of variation of newly induced parameter beta, (2) the effects of variation of low and high rewiring probability, (3) the effects of variation of growth rate r and (4) the effects of variation of different randomness and linear stability analysis of the synchronized steady-state solution. We have calculated analytically the critical coupling coefficient for the transition to spatiotemporal regularity of the lattice. The analytical results match well with the numerical simulation results. The variation of the basin size with respect to coupling strength and rewiring probability with various randomness and coupling is plotted. The simulation results do not change significantly with the variation of lattice sizes.