A Host-parasitoid Dynamics with Allee and Refuge effects (original) (raw)

Global Behavior and Bifurcation in a Class of Host–Parasitoid Models with a Constant Host Refuge

Qualitative Theory of Dynamical Systems, 2020

In this paper, by using the analytical approach, we investigate the global behavior and bifurcation in a class of host-parasitoid models when a constant number of the hosts are safe from parasitism. We find the conditions for the existence and stability of the equilibria. We detect the existence of the Neimark-Sacker bifurcation under certain conditions. We explicitly derived the approximation of the limit curve depending on the parameters that appear in the model. We show that a locally asymptotically stable equilibrium can never be transformed into unstable by increasing a constant number of hosts that are using a refuge. Specially, we consider the effect of constant host refuge in (S), (HV), and (PP) models.The obtained results show that the constant number of hosts in refuge affects the qualitative behavior of these models in comparison to the same models without refuge. The theory is confirmed and illustrated numerically.

Stability of a certain class of a host–parasitoid models with a spatial refuge effect

Journal of Biological Dynamics, 2019

A certain class of a host-parasitoid models, where some host are completely free from parasitism within a spatial refuge is studied. In this paper, we assume that a constant portion of host population may find a refuge and be safe from attack by parasitoids. We investigate the effect of the presence of refuge on the local stability and bifurcation of models. We give the reduction to the normal form and computation of the coefficients of the Neimark-Sacker bifurcation and the asymptotic approximation of the invariant curve. Then we apply theory to the three well-known host-parasitoid models, but now with refuge effect. In one of these models Chenciner bifurcation occurs. By using package Mathematica, we plot bifurcation diagrams, trajectories and the regions of stability and instability for each of these models.

Stability analysis of a host-parasitoid model with logistic growth using allee effect

Applied Mathematical Sciences, 2015

Allee effect and parasitism are common biological phenomena observed in nature. In this paper, we consider a discrete-time Host-Parasitiod model with and without Allee effect. We list all the possible equilibrium points of our Host-Parasitoid model. And we analyze the conditions under which our model is stable or unstable in both the cases.

A discrete-time host–parasitoid model with an Allee effect

Journal of Biological Dynamics, 2014

We introduce a discrete-time host-parasitoid model with a strong Allee effect on the host. We adapt the Nicholson-Bailey model to have a positive density dependent factor due to the presence of an Allee effect, and a negative density dependence factor due to intraspecific competition. It is shown that there are two scenarios, the first with no interior fixed points and the second with one interior fixed point. In the first scenario, we show that either both host and parasitoid will go to extinction or there are two regions, an extinction region where both species go to extinction and an exclusion region in which the host survives and tends to its carrying capacity. In the second scenario, we show that either both host and parasitoid will go to extinction or there are two regions, an extinction region where both species go to extinction and a coexistence region where both species survive.

An Analytical Study in Dynamics of Host Parasitoid Model with Allee Effect

In this paper, a discrete time host parasitoid model is investigated. The fixed points in the stability are analyzed. Two biological phenomena, the Allee effect of host population aggregation of the parasitism are considered in our mathematical model. The population dynamics are compressed when Allee effect is added, the sensitivity to the initial conditions for the host parasitoid system decreased after adding Allee effect. Finally various mathematical study were discussed.

Host-Parasitoid Systems with Predation-Driven Allee effects in Host

Allee effects and parasitism are common biological phenomena observed in nature, which are believed to have significant impacts in ecological conservation programs. In this article, we investigate the population dynamics of host-parasitoid systems with Allee effects induced by predation satiation in host to study the effects of Allee effects and parasitism as well as the timing of parasite's attacking. The interactions of Allee effects and parasitism can lead to extremely complicated dynamics that include but are not limited to extinction of both species due to Allee effects at their low population density, multiple attractors, strange interior attractors and even crisis of strange attractor due to high parasitism. We perform 1) the local analysis to study the number of equilibria and their stability; and 2) the global analysis to study the extinction and permanence of host-parasitoid systems with Allee effects, for both parasitism attacking before and after the growth phase of host. The theoretical and numerical results suggest that i) Allee effects can generate and destroy interior equilibrium; ii) The timing of parasite's attacking does not affect the boundary equilibria and their stability as well as the permanence condition; iii) The combination of strong Allee effects and parasitism may promote the coexistence of both host and parasite at their hight population density. These results may have potential useful biological importance for biological conservation.

A host–parasitoid system with predation-driven component Allee effects in host population

Journal of Biological Dynamics, 2014

Allee effects and parasitism are common biological phenomena observed in nature, which are believed to have significant impacts in ecological conservation programmes. In this article, we investigate population dynamics of a discrete-time host-parasitoid system with component Allee effects induced by predation satiation in host to study the synergy effects of Allee effects and parasitism. Our model assumes that parasitism attacks the host after the density dependence of the host. The interactions of component Allee effects and parasitism can lead to extremely rich dynamics that include but are not limited to extinction of both species due to Allee effects at their low population density, multiple attractors, strange interior attractors and even crisis of strange attractor due to high parasitism. We perform local and global analysis to study the number of equilibria and their stability; and study the extinction and permanence of our hostparasitoid system. One of the most interesting results shows that the combination of strong Allee effects and parasitism may promote the coexistence of both host and parasite at their high population density. In addition, component Allee effects may destroy interior equilibrium under different values of parameters' ranges.

Global stability and Neimark-Sacker bifurcation of a host-parasitoid model

International Journal of Systems Science, 2016

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.

A Density-Dependent Host-parasitoid Model with Stability, Bifurcation and Chaos Control

Mathematics

The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton–Holt growth function for a host population and Hassell–Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability are investigated. On the other hand, it is demonstrated that the model endures Hopf bifurcation about its positive steady-state when the growth rate of the consumer is selected as a bifurcation parameter. Bifurcating and chaotic behaviors are controlled through the implementation of chaos control strategies. In the end, all mathematical discussion, especially Hopf bifurcation, methods related to the control of chaos and global asymptotic stability for a positive steady-state, is supported with suitable numerical simulations.

Dynamics of a class of host–parasitoid models with external stocking upon parasitoids

Advances in Difference Equations, 2021

This paper is motivated by the series of research papers that consider parasitoids’ external input upon the host–parasitoid interactions. We explore a class of host–parasitoid models with variable release and constant release of parasitoids. We assume that the host population has a constant rate of increase, but we do not assume any density dependence regulation other than parasitism acting on the host population. We compare the obtained results for constant stocking with the results for proportional stocking. We observe that under a specific condition, the release of a constant number of parasitoids can eventually drive the host population (pests) to extinction. There is always a boundary equilibrium where the host population extinct occurs, and the parasitoid population is stabilized at the constant stocking level. The constant and variable stocking can decrease the host population level in the unique interior equilibrium point; on the other hand, the parasitoid population level s...