Abstract
In this paper, we study the effect of the behavior of predators on prey-predator interaction. We assume that there is one prey population that suffers from the fear of predators which could force it to move in to the refuge; and three are two predator populations, one of them is aggressive in its attack and the other one using sit-and-wait procedure, which is less aggressive. All the model’s equilibrium points have been found and their stability was established. The possibility of transcritical and Hopf bifurcation was also investigated and numerical simulations were given. The effect of prey refuge and fear also are detected. The cost of them is to allow the model to reach to double transcritical point. The effect of the competition between prey populations is to convert the model from the stable limit cycle to a spiral stable equilibrium point of afraid prey with predator. When it becomes large it converts the model to the stable trivial solution.
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