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Stability of equilibrium states of a nonlinear delay differential equation with stochastic perturbations
Author(s) -
Shaikhet Leonid
Publication year - 2016
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3605
Subject(s) - nonlinear system , mathematics , equilibrium point , stochastic differential equation , quadratic equation , differential equation , white noise , stability (learning theory) , delay differential equation , exponential function , exponential stability , control theory (sociology) , mathematical analysis , physics , computer science , statistics , geometry , control (management) , quantum mechanics , machine learning , artificial intelligence
Summary The nonlinear delay differential equation with exponential and quadratic nonlinearities is considered. It is assumed that the equation is exposed to stochastic perturbations of the white noise type, which are directly proportional to the deviation of the system state from the equilibrium point. Sufficient conditions for stability in probability of the zero and positive equilibriums of the considered system under stochastic perturbations are obtained. The research results are illustrated by numerical simulations. The proposed investigation procedure can be applied for arbitrary nonlinear stochastic delay differential equations with an order of nonlinearity higher than one. Copyright © 2016 John Wiley & Sons, Ltd.