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 $$\tau =0, 1, 2$$ τ = 0 , 1 , 2 , through which the equilibrium loses its stability and there occur multiple bifurcations. Compared with $$\tau =0$$ τ = 0 (without delay), we find that the corresponding stable region becomes larger as delay $$\tau $$ τ increases and interesting phenomena are discovered, including the simultaneous occurrence of two pairs of conjugate complex eigenvalues with modulus equal to 1 and $$\lambda ^n=1$$ λ n = 1 $$(n=2,3)$$ ( n = 2 , 3 ) related to strong resonance, etc. Geometrical description of the corresponding critical eigenvalue curves is also included.
Nonlinear Dynamics – Springer Journals
Published: Jul 8, 2017
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