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Russia Yekaterinburg
Section  Mathematics 
Title  Noiseinduced transitions and deformations of stochastic attractors for onedimensional systems 
Author(s)  Bashkirtseva I.A.^{a}, Ryazanova T.V.^{a}, Ryashko L.B.^{a} 
Affiliations  Ural Federal University^{a} 
Abstract  The influence of additive and parametrical noise on attractors of the onedimensional system governed by the stochastic differential Ito equation is investigated. It is shown that unlike additive, parametrical disturbances lead to the shift of extrema of probability density function. For the value of this shift, a decomposition on small parameter of noise intensity is obtained. It is shown that the influence of the parametrical noise can change not only the arrangement, but also the quantity of extrema of probability density function. The corresponding noiseinduced phenomena are studied for three dynamical models in detail. An analysis of the error for the different order estimations of the shift of extrema for the probability density function is presented by the example of a linear model. Two scenarios of the transition between unimodal and bimodal forms of the stochastic attractor are investigated for systems with different types of cubic nonlinearity. 
Keywords  scalar Ito equation, stochastic attractor, parametrical noise, noiseinduced transitions 
UDC  517.925, 519.216 
MSC  34F05, 37H20, 60G07 
DOI  10.20537/vm120201 
Received  3 March 2012 
Language  Russian 
Citation  Bashkirtseva I.A., Ryazanova T.V., Ryashko L.B. Noiseinduced transitions and deformations of stochastic attractors for onedimensional systems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 2, pp. 316. 
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