The food web prey-predator model with toxin

In this paper, a food web mathematical model consists from stage structure prey – predator model with toxin and harvesting was proposed and analyzed. Prey species is exposed directly some kind of toxic substance from environment, while first predator and top predator species exposed the toxic through the feeding; the prey follows the logistic growth law. In this model, the first predator consumes the immature and mature prey according to Holling type-II functional response, while the top predator consumes the first predator by Lotka-Volterra. The equilibrium points of this model are calculated. The conditions which guarantee the local stability are found. Lyapunov function was used for studying model global dynamics. Finally, to confirm our analytic results numerical simulations are used.