Stability of Equilibria of Stochastically Perturbed Nonlinear Mathematical Models

Abstract

The Glassy-winged Sharpshooter's known nonlinear mathematical model is taken into consideration. This model is thought to be affected by stochastic perturbations of the white noise variety, and these perturbations are thought to be exactly proportional to the system state's deviation from the positive equilibrium. We obtain a necessary and sufficient condition for the equilibrium of the linear section of the nonlinear stochastic differential equation under consideration to have asympt- otic mean square stability. This need is also a sufficient one for the probability- based stability of the equilibrium of the initial nonlinear equation. The results are shown in numerical computations and figures. It is noted that the purpose of this research is not to study the stability of a particular model. The proposed method of stability investigation can be applied to study stability of many other nonlinear equations and systems of nonlinear equations under stochastic perturbations.