NUMERICAL INVESTIGATION OF D-BIFURCATIONS FOR A STOCHASTIC DELAY LOGISTIC EQUATION

Abstract

This paper explores the use of numerical (approximation) methods in the detection of changes in the dynamical behaviour of solutions to parameter-dependent stochastic delay differential equations. We focus on the use of approximations to Lyapunov exponents. Using three numerical methods we begin to describe the probability distributions of the local approximate Lyapunov exponents and we use this information to enable us to predict values of the parameters at which solutions bifurcate. We conclude the paper by reviewing some of the potential pitfalls of using numerical simulations to detect the dynamical behaviour of the solutions to stochastic delay differential equations.