About Stability of Nonlinear Stochastic Differential Equations with State-Dependent Delay

Abstract

A nonlinear stage-structured population model with a state-dependent delay under stochastic perturbations is investigated. Delay-independent and delay-dependent conditions of stability in probability for two equilibria of the considered system are obtained via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The model under consideration is not the aim of the work and was chosen only to demonstrate the proposed research method, which can be used for the study of other types of nonlinear systems with a state-dependent delay.

Exponential Stability for Second-Order Neutral Stochastic Systems Involving Impulses and State-Dependent Delay

“…The occurrence of the stochastic process in the mathematical model is unavoidable to characterize the physical structures. So, the stability analysis of stochastic nonlinear systems involving several effects was studied in [19][20][21][22][23][24]. Further, impulsive systems have been paid remarkable attention in various areas and many significant works have been attained by researchers.…”

A Method of Qualitative Analysis for Determining Monotonic Stability Regions of Particular Solutions of Differential Equations of Dynamic Systems

“…Maintaining the stability of solutions in contemporary nonlinear dynamical systems has been a major challenge in their operation [1][2][3][4]. Conventionally [5][6][7][8][9][10][11][12][13][14][15][16][17], Lyapunov's second method is used to study the stability and optimization of solutions in systems composed of ordinary differential equations. For instance, in [5], Lyapunov's stability theory is employed to establish the global asymptotic stability of the periodic solution in a recognized ecosystem model.…”