Exact solutions of systems of nonlinear differential equations describing the evolution of interacting populations

TL;DR

This paper extends the simplest equation method to find exact solutions for systems of nonlinear differential equations modeling the evolution of two interacting populations, considering different critical density scenarios.

Contribution

It introduces a generalized method for solving such systems and provides explicit solutions for specific population interaction cases.

Findings

Exact solutions for systems with low critical density in both populations.

Solutions for systems where only one population has low critical density.

Method applicable to various population interaction models.

Abstract

The generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented. The exact solutions of NDE systems describing the evolution of two interacting populations in two cases (both populations have the low critical density or low critical density is typical for only one of populations) are obtained.