Additive Allee effect of top predator in a mathematical model of three species food chain

Abstract

In the present paper, the Hastings and Powell model of three species food chain model is modified incorporating Allee effect. Additive type Allee effect has been used in order to modify the three-species food chain model. We investigate the impact of Allee in the food chain model. Dynamical behaviours such as existence of steady states and their local stability analysis, bifurcation analysis of the proposed three species model have been discussed. Numerical examples are provided to justify the analytical results. Regions of stability of different equilibrium points have been plotted which are in coherence with the results derived analytically. From this study, we find that chaos in the three species food chain can be controlled when prey is subject to the strength of the Allee effect. Bifurcation diagrams show that the model turns from stable to periodic doubling and periodic doubling to chaos due to the strength of Allee effect. We observe that this modified HP model is lesser chaotic in case of increase in severity of Allee effect.

Keywords

Additive Allee / Hastings and Powell model / Stability / Bifurcation / Chaos

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