Using a class of stochastic Euler and Runge-Kutta methods, we numerically solve a reaction-diffusion equation with additive random excitation. By discretizing the space and the associated stochastic differential system, we present a comparison of the diffusibility behaviors between the schemes above. The model presented here consists of reaction-diffusion equations describing the evolution of t...

In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fu...

When immune cells detect foreign molecules, they secrete soluble factors that attract other immune cells to the site of the infection. In this paper, I study numerical solutions to a model of this behavior proposed by Kepler. In this model the soluble factors are governed by a system of reaction-diffusion equations with sources that are centered on the cells. The motion of the model cells is a ...