Modelling effect of toxicant in a three-species food-chain system incorporating delay in toxicant uptake process by prey

Abstract

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.

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays

“…Based on a discrete plant virus disease model with drilling and replanting, Luo et al showed that the basic reproduction number acts as a threshold parameter in determining the global dynamics of the model [40]. Using a mathematical model, a three-species food chain system incorporating delay of toxicant uptake by prey populations has been analyzed [41]. There has been extensive research on epidemics models for plant diseases (see [42][43][44][45][46]).…”