Noise Induced almost Sure Exponential Stability of a Nonlinear Delay Differential Equation with a Constant Time Lag
Donatus Ijeoma Anonwa *
Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria.
Augustine Omoghaghare Atonuje
Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study investigates the effect of multiplicative white noise on stabilizing nonlinear delay differential equation which generally appear unstable in their deterministic form. The applied technique includes Lyapunov sample exponents and stochastic perturbation methods. By applying multiplicative white noise to the deterministic system, the resulting system becomes stochastically stable in an almost sure exponential sense. It demonstrates that, under certain conditions appropriate noise intensity and small delay the system achieves almost sure exponential stability.
Keywords: Almost sure exponential stability, deterministic delay differential equation, Lyapunov sample exponent, Brownian noise, stochastic stability