Study of Dynamical Behavior of a Prey-Predator Model when the Prey Population Affected by Multifactor
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Abstract
In this work, a prey-predator model with Holling type II functional response is considered. The proposed model incorporates the cost of the fear of predators in prey, effect of environmental pollution and harvesting on prey population. Firstly, the details of model derivation of are given and then some of behaviors of the model solutions are proved, the existence criteria for each of the model equilibrium points are determined. For each of the equilibrium point, the sufficient and necessary conditions for being locally asymptotically stable are found. Via Lyapunov method, the sufficient conditions for global stability of the model equilibrium point are determined. Some numerical simulations are performed to discover the impact of the fear, harvesting population and environmental pollution on prey dynamics.
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