Stability Analysis of Prey-Predator Mathematical Model with Delay and Control of the Prey

Abstract

Dynamics of interacting biological species has been studied in the past few decades from various angles. Many species become extinct and many others are at the verge of extinction due to several reasons like, over exploitation, over predation, environmental pollution, mismanagement of natural resources etc. Establishing the conditions for the stability of ecosystems and for stable coexistence of interacting populations is a problem of the highest priority in mathematical ecology. Bearing this in mind, in this study the stability of prey predator in the absence of delay was clearly stated. The minimum cutoff value at which the system loses its stability was also pointed out. Furthermore, the existence of global stability without linearizing the model was proved with an appropriate condition. Finally, non-existence of limit cycle at positive equilibrium was proved by Dulac’s criterion.