An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag

Abstract

This paper deals with an approach to obtaining the numerical solution of the Lotka–Volterra predator-prey models with discrete delay using Euler polynomials connected with Bernoulli ones. By using the Euler polynomials connected with Bernoulli ones and collocation points, this method transforms the predator-prey model into a matrix equation. The main characteristic of this approach is that it reduces the predator-prey model to a system of algebraic equations, which greatly simplifies the problem. For these models, the explicit formula determining the stability and the direction is given. Numerical examples illustrate the reliability and efficiency of the proposed scheme.

Application of the Generalized Backstepping Control Method for Lotka-Volterra Prey-Predator System with Constant Time Delay

“…Finally,  describes the rivalry among predator species and  is the species at which successful predation contributes to the predator population. This shows that the prey species in system (1) is governed by the well-known logistic equation in the absence of predator species, whilst the predator species will be decreased in the absence of prey species [1,2,12].…”