Rich dynamics caused by delay in a nonchaotic Rulkov map

Abstract

In this paper, we propose a simple delayed nonchaotic Rulkov map and criteria for the existence of the critical stable boundary of the unique fixed point is analyzed for $$\tau =0, 1, 2$$ , through which the equilibrium loses its stability and there occur multiple bifurcations. Compared with $$\tau =0$$ (without delay), we find that the corresponding stable region becomes larger as delay $$\tau $$ increases and interesting phenomena are discovered, including the simultaneous occurrence of two pairs of conjugate complex eigenvalues with modulus equal to 1 and $$\lambda ^n=1$$ $$(n=2,3)$$ related to strong resonance, etc. Geometrical description of the corresponding critical eigenvalue curves is also included.