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Bashkirtseva I. A., Ryashko L. B., Fedotov S. P., Tsvetkov I. N. Backward stochastic bifurcations of the henon map. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 2, pp. 31-42. DOI: 10.18500/0869-6632-2011-19-2-31-42

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Backward stochastic bifurcations of the henon map

Bashkirtseva Irina Adolfovna, Ural Federal University named after the first President of Russia B.N.Yeltsin
Ryashko Lev Borisovich, Ural Federal University named after the first President of Russia B.N.Yeltsin
Fedotov Sergej Petrovich, School of Mathematics, University of Manchester
Tsvetkov Ivan Nikolaevich, Ural Federal University named after the first President of Russia B.N.Yeltsin

We study the 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. In this paper, for such a bifurcation analysis we suggest a stochastic sensitivity function technique. The constructive possibilities of this method are demonstrated for analysis of the two-dimensional Henon model.

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