A Density-Dependent Host-parasitoid Model with Stability, Bifurcation and Chaos Control (original) (raw)
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We study the comprehensive dynamics of a density-dependent host-parasitoid system with the Hassell growth function for the host population. Particularly, we investigate the dynamical properties related to boundedness, local asymptotic stability of boundary equilibrium, existence and uniqueness of positive equilibrium point and global asymptotic stability of the positive equilibrium point of this modified host-parasitoid model. Moreover, it is also proved both populations endure period-doubling bifurcation and Neimark-Sacker bifurcation at positive steady-state with suitable choice of parametric values. OGY method is implemented in order to controlling chaos in host-parasitoid model. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behavior in the model.
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We investigate qualitative behaviour of a density-dependent discrete-time host-parasitoid model. Particularly, we study boundedness of solutions, existence and uniqueness of positive steady-state, local and global asymptotic stability of the unique positive equilibrium point and rate of convergence of modified hostparasitoid model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation with the help of bifurcation theory. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behaviour over a broad range of parameters. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behaviour in the model.
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The interaction between prey and predator is well-known within natural ecosystems. Due to their multifariousness and strong link population dynamics, predators contain distinct features of ecological communities. Keeping in view the Nicholson-Bailey framework for host-parasitoid interaction, a discrete-time predator–prey system is formulated and studied with implementation of type-II functional response and logistic prey growth in form of the Beverton-Holt map. Persistence of solutions and existence of equilibria are discussed. Moreover, stability analysis of equilibria is carried out for predator–prey model. With implementation of bifurcation theory of normal forms and center manifold theorem, it is proved that system undergoes transcritical bifurcation around its boundary equilibrium. On the other hand, if growth rate of consumers is taken as bifurcation parameter, then system undergoes Neimark-Sacker bifurcation around its positive equilibrium point. Methods of chaos control are ...
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of concern in the paper is the stability of populations which change their size according to the Hassell growth function, not only in isolation, but also under external effects such as migration. The mathematical model developed is applied to a host-parasite system and the dynamics of the resulting system are studied analytically. The numerical simulations demonstrate the inherent instabilities in the single-species system, which manifest itself in the form of period-doubling bifurcations and chaos. It is found that the effect of migration is to suppress such an unstable behaviour. (~)
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Eco-epidemiological models are now receiving much attention to the researchers. In the present article we re-visit the model of Holling-Tanner which is recently modified by Haque and Venturino 1 with the introduction of disease in prey population. Density dependent disease-induced predator mortality function is an important consideration of such systems. We extend the model of Haque and Venturino 1 with density dependent disease-induced predator mortality function. The existence and local stability of the equilibrium points and the conditions for the permanence and impermanence of the system are worked out. The system shows different dynamical behaviour including chaos for different values of the rate of infection. The model considered by Haque and Venturino 1 also exhibits chaotic nature but they did not shed any light in this direction. Our analysis reveals that by controlling disease-induced mortality of predator due to ingested infected prey may prevent the occurrence of chaos.