ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations
and
Control Processes

Stochastic Sensitivity of Equilibria and Cycles for Nonlinear Stochastic Discrete Systems

Author(s):

I. A. Bashkirtseva

Russia, 620083, Ekaterinburg, Lenina av., 51
Ural State University
Docent

irina.bashkirtseva@usu.ru

L. B. Ryashko

Russia, 620083, Ekaterinburg, Lenina av., 51
Ural State University
Professor

lev.ryashko@usu.ru

I. N. Tsvetkov

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

itsvet@e1.ru

Abstract:

The sensitivity of the regular attactors (equilibria and cycles) for the multidimensional discrete systems to random disturbances is investigated. The analysis of the stochastic sensitivity is carried out with use the first approximation systems. The stochastic sensitivity function is introduced. The stationary probability density of the stochastic attactor is approximated by means of this function. Conformity the theoretical results with the data of numerical experiment is shown for system Hennon. The law of the growth of the system cycles sensitivity is revealed at the transition to chaos through period doubling bifurcation cascades.

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