DERIVING NON-NEGATIVE SOLUTION FOR LOTKA-VOLTERRA MODEL WITH CROSS-DIFFUSION USING PERSISTENT DEFORMING ANALYSIS METHOD.

In this article, firstly we examine the essential circumstances for the existence of non-negative solutions for the several species Lotka-Volterra systems (cross-diffusion) by employing Sobolev embedding theorems and probe the coexistence region in the plane of argument. Secondly, we apply the persistent deforming analysis method (PDAM) to investigate the change of state brought about by the passage of time on the several species Lotka-Volterra models. Based on these investigations, we provide the right and most appropriate persistent solution for the several nonlinear species Lotka-Volterra system. This solution’s accuracy is equivalent to the accuracy of the solution obtained by a purely numerical fourth-order method.