Rich dynamics caused by delay in a nonchaotic Rulkov map

Rich dynamics caused by delay in a nonchaotic Rulkov map 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Rich dynamics caused by delay in a nonchaotic Rulkov map

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-017-3603-1
Publisher site
See Article on Publisher Site

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 $$\tau =0, 1, 2$$ 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.

Journal

Nonlinear DynamicsSpringer Journals

Published: Jul 8, 2017

References

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