Stability Analysis and Maximum Profit of One Prey-Two Predators Model under Constant Effort of Harvesting
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Abstract
In this paper we present a deterministic and continuous model for one prey-two predators population model based on the Lotka-Volterra model. The two predators are subjected to constant effort of harvesting. We study analytically the necessary conditions of harvesting to ensure existence of the equilibrium points and their stabilities. The methods used to analyse the stability are linearisation and Hurwitz stability test. The results show that there is an asymptotically stable equilibrium point in positive octane for the model without constant effort of harvesting. We found that there is an asymptotically stable equilibrium point in positive octane for the model with constant effort of harvesting. The stable equilibrium point for the model with constant effort of harvesting is then related to profit function which we found to have maximum profit. This means that the prey and predator populations can live in coexistence and give maximum profit although the two predators are harvested with constant effort of harvesting.
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