Spatiotemporal Dynamics of Coupled Ikeda maps Over a Ring Networks

Abstract

In this paper, we investigate the spatiotemporal dynamics of a latticeof coupled chaotic Ikeda maps whose coupling connections are dynamically rewired torandom sites with probability p. Ikeda map is defined asxn+1 = 1 + (b(xncos(tn) ? ynsin(tn))yn+1 = b(xnsin(tn) + yncos(tn))where b is a positive constant and tn = 0.4?6/(1+x2n+y2n). Firsly, we consider a diffusivelycoupled network of Ikeda maps whose x-component can only diffuse. Bifurcation diagramof the lattice with respect to coupling strength are done. The variation of synchronizedbasin size with respect to coupling strength are shown for different values of rewiringprobability. The variation of synchronized basin size with respect to rewiring probabilityare shown for different values of coupling strength. We do not observe complete synchronizationin this type of network. In search for a network where complete synchronizationcan occur we consider a completely random network where both x and y components candiffuse. For the second type of network we observe synchronized spatiotemporal fixedpoint.