Dynamical Effects of Anti-predator Behaviour of Adult Prey in a Predator-Prey Model with Ratio-dependent Functional Response

Prabir Panja, Shyamal Kumar Mondal, Joydev Chattopadhyay

Abstract


In this paper, a three species predator-prey model has been developed. Here we divide the prey population into two subpopulations such as $(i)$ juvenile prey and $(ii)$ adult prey population along with only one predator population. It is considered that only adult prey has the anti-predator behaviour. In this paper, two functional responses of predator due to adult and juvenile prey have been introduced on the basis of ratio-dependency. Then the existence condition and boundedness of solution of our proposed mathematical model have been discussed. Also, the different equilibrium points and the stability condition of the system around these equilibrium points have been analyzed. After that, the extinction condition of the prey and predator populations and the effect of anti-predator behaviour on the predator population have been explored. The global stability condition of the proposed system around the positive equilibrium point has been also discussed. Finally, some numerical simulations have been given to test our theoretical results.


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