An Alternative Food for the Predator and Constant Harvesting of Both the Species

Abstract

The present paper is devoted to an analytical investigation of a two species prey-predator model. Predator is provided with a limited resource of food in addition to the prey and a cover to prey proportionate to its population to get protection from the predator. Both the prey and predator are harvested at a constant rate. The model is characterized by couple of first order non-linear ordinary differential equations. The lone equilibrium point of the model is identified and its stability criteria is discussed. The Global stability of linearized equations is discussed by constructing a suitable Liapunov’s function. A threshold theorem is stated and results are discussed.

Keywords: Equilibrium point, Normal Study State, Prey, Predator, Stability, Threshold Diagrams, and Threshold Theorems.

2000 Mathematics Subject Classification. 37C75