Stabilization of nonlinear systems via aperiodic intermittent stochastic noise driven by G-Brownian motion with application to epidemic models

Abstract

Abstract To stabilize a nonlinear system d x ( t ) = f ( t , x ( t ) ) d t $dx(t)=f(t,x(t))\,dt$ , we stochastically perturb the deterministic model by using two types of aperiodic intermittent stochastic noise driven by G-Brownian motion. We demonstrate quasi-sure exponential stability for the perturbed system and give the convergence rate, which is related to the control intensity. An application to SIS epidemic model is presented to confirm the theoretical results.

Keywords

• Stochastic differential equations
• Delay
• Integro-differential equations
• Split-step theta method
• Mean square exponential stability
• Convergence