Effect of Environmental Fluctuation in the Dynamics of a Three-Species Food Chain Model with Sexually Reproductive Generalized Type Top Predator and Crowley-Martin Type Functional Response Between Predators.

The main aim of this paper is to explore the dynamical behavior of a three-species prey-predator interaction model with sexually reproductive generalized type top predator under the consideration of environmental fluctuations. Our discussion has involved a continuous tritrophic food chain model with Crowley-Martin senses and Holling type II functional responses. For the deterministic model, the existence of equilibria as well as boundedness of the solution has been established here. The feasibility and local stability of the interior and non-interior equilibrium points has been investigated. The global dynamics of the co-existence of all the three species are shown at the interior equilibrium point. To determine the direction of Hopf bifurcations under the non-hyperbolic case, the first Lyapunov number is computed using the center manifold theorem. Several bifurcation analyses are performed at the interior equilibrium point. The effect of environmental fluctuation on some of model parameters are studied here through the verification of existence of unique positive global solution, existence and persistence of stationary solution. Numerical simulation has been carried out to illustrate the theoretical findings by using the MATLAB and Maple software packages and finally some concluding remarks are given. [ABSTRACT FROM AUTHOR]