Lyapunov Stability Analysis of a Competition Model with Crowding Eects

Abstract

The present study is connected to the analysis of a nonlinear system that covered a wide range of mathematical biology in terms of competition, cooperation, and symbiosis interactions between two species. We focus on how populations change their densities when two different species follow the non-symmetric logistic growth laws. We have investigated the stability of the corresponding densities of population, and to control the convergence of solutions by proper choice of interacting constant and periodic parameters. It shows the effect of crowding tolerance on both species. It will show that there exists an infinite number of coexistence solutions if the resource distributions are identical for both populations. If the carrying capacity of the first species exceeds the rest one, then eventually the second population drops down to extinction. The results are presented studying the Lyapunov functional, phase portraits, and in a series of numerical examples.

GANIT J. Bangladesh Math. Soc. 40.2 (2020) 95-110