Delay-induced effects on isola type of steady state pattern in a coupled optical bistable chain

Abstract

This study shows that delay may not destabilize a steady state which is surrounded by unstable steady states. This is in a sharp contrast to a well-known concept, i.e. “delay will induce instability”. An example is shown within the isolas' bifurcation structure and three types of steady state patterns are classified. Type I and II patterns form the isolas while type III pattern is the symmetrical solution. It is shown that the unstable type I pattern survives delay. This is the basic requirement for further development of isola chaos. However, type II and III patterns are not recovered by delay. Isola chaos will be terminated via crisis and merge to full-scale chaos. We investigate the origin of this full-scale chaos. A phenomenon related to “sensitivity of parameters” is shown. Finally we discuss the possibility of observation.