On difference equations with asymptotically stable 2-cycles perturbed by a decaying noise

Authors:
E. Braverman;A. Rodkina
Affiliations:
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N. W., Calgary, AB T2N 1N4, Canada;Department of Mathematics, The University of the West Indies, Mona Campus, Kingston, Jamaica
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

The results stating that the stability of a 2-cycle is preserved (almost surely) under an eventually decaying stochastic perturbation are obtained in the case when the system is in the range of the parameters immediately following the Hopf bifurcation and preceding the next period doubling bifurcation. Several examples of systems and types of noise are presented.