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NOISE-INDUCED BACKWARD BIFURCATIONS OF STOCHASTIC 3D-CYCLES

I. BASHKIRTSEVA

Ural State University, Lenina, 51, 620083, Ekaterinburg, Russia

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L. RYASHKO

Ural State University, Lenina, 51, 620083, Ekaterinburg, Russia

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, and

P. STIKHIN

Ural State University, Lenina, 51, 620083, Ekaterinburg, Russia

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https://doi.org/10.1142/S0219477510000095Cited by:25 (Source: Crossref)

Abstract

We study stochastically forced multiple limit cycles of nonlinear dynamical systems in a period-doubling bifurcation zone. Noise-induced transitions between separate parts of the cycle are considered. A phenomenon of a decreasing of the stochastic cycle multiplicity with a noise intensity growth is investigated. We call it by a backward stochastic bifurcation (BSB). In this paper, for the BSB analysis we suggest a stochastic sensitivity function technique. As a result, a method for the estimation of critical values of noise intensity corresponding to BSB is proposed. The constructive possibilities of this general method for the detailed BSB analysis of the multiple stochastic cycles of the forced Roessler system are demonstrated.

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