A new numerical approach method to solve the Lotka–Volterra predator–prey models with discrete delays

This paper proposes a new approach called Extreme Learning Machine (ELM) to solve the Lotka–Volterra predator–prey models using a novel approximation form. Unlike the traditional methods that involve constructing complex algebraic systems and performing inverse matrix operations, ELM transforms the system of differential equations into a set of nonlinear equations and solves for the parameters through optimization iterations to obtain an approximate solution. Furthermore, we construct a solution form that satisfies the initial conditions, eliminating the need to handle initial conditions during the solving process, making this method more concise. Finally, by comparing with other numerical methods using two sets of models and parameters, ELM can produce high-precision results and further demonstrate the advantages of our method.