Control of chaos due to additional predator in the Hastings–Powell food chain model

A three species Hastings and Powell (HP) food chain model involving another predator of top prey is proposed and studied. The modified food web model is analyzed to obtain the different conditions for which system exhibits stability around the biological feasible equilibrium points. The permanence is established and global stability of boundary equilibrium point Ex is discussed. It is observed through numerical simulations, that four-dimensional model may show stable dynamics in contrast to chaotic dynamics that occurred in three species food chain. Varieties of dynamical behaviors in the food web are possible depending upon the sharing of food between the two predators of the top prey. The results demonstrate that the additional predator play the crucial role in reducing the complexity in the dynamical behavior of the system.