In this paper, the effect of toxicant on the dynamics of Leslie-Gower tritrophic food chain population model is studied. Two models have been studied to visualize the dynamical behaviour of prey and predator populations under toxicant stress. All the feasible equilibria of the systems are obtained and using stability theory the conditions are derived for the survival or extinction of species. From the analysis of the models it is observed that the effect of toxicant on predator population increases the equilibrium density of prey population. Finally, we support our analytical findings with numerical simulations.

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In this paper, a mathematical model is proposed and analyzed to study the effect of toxicant in a threespecies food-chain system incorporating delay in toxicant uptake process by prey population. The model is formulated by using the system of non linear ordinary differential equations. In the model, it is assumed that the growth rate of prey population is affected by organismal toxicant. In this paper, we have introduced distributed delay in the environmental toxicant in the model. The distributed delay differential equations, though simple in structure, possess a rich array of solutions. The models are being analyzed by using variational matrix and Liapunov functions. The conditions for local and global stability of the equilibrium points are obtained. A region of attraction is being found for global asymptotic stability of the equilibrium points. Also, a Hopf bifurcation analysis has been performed with respect to key parameters for non-trivial equilibrium points. Furthermore, we support our analytical findings with numerical simulations.

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