Backward stochastic bifurcations of the discrete system cycles

I. A. Bashkirtseva; L. B. Ryashko; S. P. Fedotov; I. N. Tsvetkov

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Backward stochastic bifurcations of the discrete system cycles

I. A. Bashkirtseva ; L. B. Ryashko ; S. P. Fedotov ; I. N. Tsvetkov

Russian journal of nonlinear dynamics, Tome 6 (2010) no. 4, pp. 737-753

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Résumé

We study stochastically forced limit cycles of discrete dynamical systems in a period-doubling bifurcation zone. 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 Verhulst and Ricker systems are demonstrated.

Keywords: stochastic discrete systems, Verhulst system, Ricker system.
Mots-clés : bifurcations

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     author = {I. A. Bashkirtseva and L. B. Ryashko and S. P. Fedotov and I. N. Tsvetkov},
     title = {Backward stochastic bifurcations of the discrete system cycles},
     journal = {Russian journal of nonlinear dynamics},
     pages = {737--753},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2010_6_4_a2/}
}

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I. A. Bashkirtseva; L. B. Ryashko; S. P. Fedotov; I. N. Tsvetkov. Backward stochastic bifurcations of the discrete system cycles. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 4, pp. 737-753. http://geodesic.mathdoc.fr/item/ND_2010_6_4_a2/