Dynamics of Prey, Predator and Commensalism Model with Time Delay

Suryanarayana Evuri and K. Lakshmi Narayan

This paper is devoted to an analytical investigation of a three species ecosystem consisting of a prey, predator and a host where the host species is having a commensalism interaction with the prey species and also the time delay term is imposed on the prey and the predator species in this context. This food web ecosystem can be mathematically formed as a set of three first order non-linersimultaneousintegro-differential equations. The equation for the host species is non-liner but de-coupled with the prey species. In all, there will be six possible equilibrium points are observed and the stability analysis of each equilibrium point is carried out by using perturbed technique. Also the global stability at interior equilibrium is discussed by constructing a suitable Laipunov’s function. Further analytical results are supported by numerical results using Mat lab.

Volume 11 | Issue 1

Pages: 122-131