An adaptive time-stepping algorithm for a stochastic Lotka–Volterra competitive model with time-dependent delays

In this paper, a variable step-size strategy is proposed for a Lotka-Volterra stochastic competitive model with time-dependent delays. In this adaptive strategy, the numerical solution proceeds with the Milstein method and the step-sizes are determined by two local error estimators based on the drift and diffusion parts of the model. Numerical results show better accuracy of the proposed strategy compared to a reference fixed step-size mechanism.