Dynamical analysis of a Beddington–DeAngelis commensalism system with two time delays

Abstract

This study considers two time delays applied in a commensalism system with a Beddington–DeAngelis functional response. In contrast with existing literature on commensalism systems, the system considered in the present study has two time delays in one species. The local stability of the positive equilibrium and Hopf bifurcation are investigated. The linearized stability is thoroughly examined. Furthermore, the characteristic equations are investigated, and the time delays are applied as the bifurcation parameter. Eventually, the presence of Hopf bifurcation is demonstrated. The Lyapunov functional is constructed, and the system is shown to have uniform persistence. The consistent persistent domain of the system is obtained by constructing a persistent function. Numerical simulations are conducted, demonstrating the reliability of the derived results.