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Stability and bifurcation analysis of a three species competitive food chain model system incorporating prey refuge

Nijamuddin Ali, Santabrata Chakravarty

Abstract


The present article deals with a constant proportion of prey refuge in presence of both the inter specific competition and the intra-specific competition among predator populations of a prey-dependent three component food chain model consisting of two competitive predators sharing one prey species as their food. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. Boundedness and dissipativeness of the system are established. The stability analysis including local and global stability of the equilibria has been carried out in order to examine the behaviour of the system. The present model system experiences Hopf-Andronov bifurcation for suitable choice of the parameter values. The influences of the prey refuge parameters on the dynamical behaviour of the system are exhibited through several plots and discussed at some equilibrium positions. It is worth-noting that prey refuge has stabilization effect in some selected situations which may be of some use for biological control. Numerical simulations are performed to illustrate and to support the analytical findings so as to validate the applicability of the model under consideration.

Keywords


Food chain; Inter and intra-specific competition; Prey refuge; Stability; Hopf-Andronov bifurcations; Lyapunov function.

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