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• The effect of top predator interference on the dynamics of a tritrophic food chain model is the principal goal to study general framework for three species food chain models in which intermediate and top predators are specialist and generalist types respectively where the top predator grows by sexual reproduction. • This concept is used to design five different models in this paper by five different combinations of functional responses of specialist intermediate predator (food uptake process follows either prey dependent, Holling type III/IV or prey-predator dependent, BD-functional response) and sexually reproductive generalist top predator (food uptake follows strictly prey-predator dependent, BD/CM functional response) respectively assuming the fact that the growth of intermediate predator is mediated by gestation delay. • Stability of each equilibria of the non-delayed counterpart of each model and the existence of Hopf-bifurcation for the coexisting equilibrium point of all delayed systems are established. • The delayed and non-delayed models can blow-up in finite time under sufficient conditions on the initial data. Furthermore, some dynamic behaviors of the systems are clarified by some numerical tests. The numerical simulations show that the gestation delay can act as a damping mechanism and prevent blow-up in certain critical range of gestation period. • Ecological implications of this phenomenon are discussed. Depending upon the choice of food, availability of resource and growth structure, food uptake process of higher trophic level species are significantly complicated and gives interesting dynamical impacts on community food chain. The effect of top predator interference on the dynamics of a tritrophic food chain model is the principal goal to study general framework for three species food chain models in which intermediate and top predators are specialist and generalist types respectively where the top predator grows by sexual reproduction. This concept is used to design five different models in this paper by five different combinations of functional responses of specialist intermediate predator (food uptake process follows either prey dependent, Holling type III/IV or prey-predator dependent, Beddington-DeAngelis (BD)-functional response) and sexually reproductive generalist top predator (food uptake follows strictly prey-predator dependent, BD/Crowley–Martin (CM) functional response) respectively assuming the fact that the growth of intermediate predator is mediated by gestation delay. We establish the stability of each equilibrium point of the non-delayed counterpart of each model and investigate the existence of Hopf-bifurcation for the coexistence equilibrium point of all delayed systems. We also show that both the delayed and non delayed models can blow-up in finite time under sufficient conditions on the initial data. Furthermore, some dynamic behaviors of the systems are clarified by some numerical tests. The numerical simulations show that the gestation delay can act as a damping mechanism and prevent blow-up in certain critical range of gestation period. Ecological implications of this phenomenon are discussed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the effects of top predator interference on the dynamics of a food chain model involving an intermediate and a top predator are considered. It is assumed that the interaction between the prey and intermediate predator follows the Volterra scheme, while that between the top predator and its favorite food depends on Beddington–DeAngelis type of functional response. The boundedness of the system, existence of an attracting set, local and global stability of non-negative equilibrium points are established. Number of the bifurcation and Lyapunov exponent bifurcation diagrams is established. It is observed that, the model has different types of attracting sets including chaos. Moreover, increasing the top predator interference stabilizes the system, while increasing the normalization of the residual reduction in the top predator population destabilizes the system. [Copyright &y& Elsevier]

Abstract: In this paper, a three species food chain model, consisting of a hybrid type of prey-dependent and predator-dependent functional responses, is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence conditions are established. Bifurcation diagrams are obtained for biologically feasible parameters. The results show that the system exhibits rich complexity features such as stable, periodic and chaotic dynamics. [Copyright &y& Elsevier]

We study how the dynamics of a food chain depends on the biology of the top-predator. We consider two model food chains with specialist and generalist top-predators. Both types of food chains display same type of chaotic behavior, short-term recurrent chaos; but the generating mechanisms are drastically different. Food chains with specialist top-predators are dictated by exogenous stochastic factors. On the contrary, the dynamics of those with the generalist top-predator is governed by deterministic changes in system parameters. The study also suggests that robust chaos would be a rarity. [Copyright &y& Elsevier]

An attempt has been made to identify the mechanism, which is responsible for the existence of chaos in narrow parameter range in a realistic ecological model food-chain. Analytical and numerical studies of a three species food-chain model similar to a situation likely to be seen in terrestrial ecosystems has been carried out. The study of the model food chain suggests that the existence of chaos in narrow parameter ranges is caused by the crisis-induced sudden death of chaotic attractors. Varying one of the critical parameters in its range while keeping all the others constant, one can monitor the changes in the dynamical behaviour of the system, thereby fixing the regimes in which the system exhibits chaotic dynamics. The computed bifurcation diagrams and basin boundary calculations indicate that crisis is the underlying factor which generates chaotic dynamics in this model food-chain. We investigate sudden qualitative changes in chaotic dynamical behaviour, which occur at a parameter value a1=1.7804 at which the chaotic attractor destroyed by boundary crisis with an unstable periodic orbit created by the saddle-node bifurcation. Multiple attractors with riddled basins and fractal boundaries are also observed. If ecological systems of interacting species do indeed exhibit multiple attractors etc., the long term dynamics of such systems may undergo vast qualitative changes following epidemics or environmental catastrophes due to the system being pushed into the basin of a new attractor by the perturbation. Coupled with stochasticity, such complex behaviours may render such systems practically unpredictable. [Copyright &y& Elsevier]

An attempt has been made to understand the role of top predator interference and gestation delay on the dynamics of a three species food chain model involving intermediate and top predator populations. Interaction between the prey and an intermediate predator follows the Volterra scheme (with Holling type IV functional response), while that between the top predator and its prey depends on Beddington–DeAngelis type functional response. Stability switches and Hopf-bifurcation occurs when the delay crosses some critical value. Model system exhibits irregular behavior when the interference is high or gestation period is larger than its critical value. Furthermore, the direction of Hopf-bifurcation and the stability of the bifurcating periodic solutions are determined using the center manifold theorem and normal form theory. Computer simulations have been carried out to illustrate the analytical findings. Different diagnostic tests, like, initial sensitivity, Lyapunov exponent, recurrence plot tests ensure the complex dynamical behavior of the model system. Finally, we observed the subcritical Hopf-bifurcation phenomena in the designed model system and the bifurcating periodic solution is unstable for the considered set of parameter values. [ABSTRACT FROM AUTHOR]