Unconditionally positivity-preserving and stable explicit method for the stochastic delay Lotka–Volterra model

To solve the multidimensional stochastic delay Lotka–Volterra model with inherent positivity and superlinear growth coefficients while maintaining the long-time behavior of the model, this paper introduces the explicit Lamperti transformation Euler–Maruyama (LTEM) method. In scenarios where coefficients fail to meet global monotonicity conditions, we illustrate the moment boundedness of both exact and numerical solutions generated by the LTEM method for the stochastic delay Lotka–Volterra model. By employing local error and stopping time techniques, we establish the strong convergence of the LTEM method. Furthermore, regarding the preservation of long-time behavior by the numerical scheme, we prove that the proposed method can capture the extinction, moment exponential stability, and stochastically ultimate boundedness of exact solutions without the influence of additional step size constraints. Lastly, numerical experiments aligned with theoretical findings are presented.