Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation
Volume 5, Issue 3 (2018), pp. 337–351
Pub. online: 20 August 2018
Type: Research Article
Open Access
Open Access
Received
11 June 2018
11 June 2018
Revised
27 July 2018
27 July 2018
Accepted
27 July 2018
27 July 2018
Published
20 August 2018
20 August 2018
Abstract
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for exponential mean square stability of the linear part of the considered nonlinear equation also are sufficient conditions for stability in probability of the initial nonlinear equation. Some new sufficient condition of stability in probability for the zero solution of the considered nonlinear non-autonomous stochastic differential equation is obtained which can be considered as a multi-condition of stability because it allows to get for one considered equation at once several different complementary of each other sufficient stability conditions. The obtained results are illustrated with numerical simulations and figures.
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