Role of toxin in occurrence and control of chaos-conclusion drawn from Lesile-Gower-type tri-trophic food chain model

Abstract

In this paper, the eect of toxicant on the variable of Leslie-Gower tri-trophic food chain model is studied. Two models have been studied to visualize the variables role of top and intermediate predator in the food chain under toxicant stress. We also discuss about the existence and local stability of equilibrium points as well as permanence and impermanence of the species in the food chain. To observe the global dynamics we have perform extensive numerical simulation with respect to two important parameters toxin liberation parameter and density dependent mortality. We have observed that if increase the values of birth rate of prey species we have observed chaotic dynamics through dierent nonlinear phenomena such as limit cycle oscillation, period-doubling. In this study we have observed the role of toxin liberation and density dependent mortality. If we increase the values of toxin liberation parameter we have observed stable focus through chaos to period-doubling; period-doubling to limit cycle. We have also found that if we increase the values of density dependent parameter the system settles down into stable focus through chaos and period- doubling. So it is clear from this study that the toxin liberation and density dependent parameter are responsible for controlling chaotic dynamics.