A positivity preserving Lamperti transformed Euler-Maruyama method for solving the stochastic Lotka-Volterra competition model

A new positivity preserving numerical scheme is presented for a class of d-dimensional stochastic Lotka-Volterra competitive models, which are characterized by super-linear coefficients and positive solutions. The scheme, dubbed the Lamperti transformed Euler-Maruyama method, approximates the exact solution by integrating a Lampertitype transformation with an explicit Euler-Maruyama method that has the benefit of being explicit and straightforward to implement. Even though the coefficients of the transformed models grow exponentially and do not satisfy the general monotonicity condition, based on the exponential integrability of the solution, it is proved that the proposed numerical method is of 12 -order strong convergence. In particular, when matrix A of the model is a diagonal matrix, the first-order strong convergence is also obtained. Without any step size constraints, the method can preserve long-time dynamical properties such as extinction and pth moment exponential asymptotic stability. Numerical examples are given to support our theoretical conclusions. (c) 2023 Elsevier B.V. All rights reserved.