A host–parasitoid interaction with Allee effects on the host

Jang, Sophia R.‐J.; Diamond, Sandra L.

doi:10.1016/j.camwa.2006.12.013

Cited by 37 publications

(34 citation statements)

References 22 publications

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“…Although this kind of model has been investigated by many scholars, little research has been carried out on discrete systems [9][10][11][12][13]. In this study, the discrete host-parasitoid system (1.1) is further investigated in detail.…”

Section: P(t + 1) = H(t)[1 -Exp(-abp(t) 1+ah(t)mentioning

confidence: 99%

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Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

2018

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In this paper, a discrete-time biological model and its dynamical behaviors are studied in detail. The existence and stability of the equilibria of the model are qualitatively discussed. More precisely, the conditions for the existence of a flip bifurcation and a Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Numerical simulations are presented not only to validate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors. We also analyze the dynamic characteristics of the system in a two-dimensional parameter space. Numerical results indicate that we can more clearly and directly observe the chaotic phenomenon, period-doubling and period-adding, and the optimal parameters matching interval can also be found easily.

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Section: P(t + 1) = H(t)[1 -Exp(-abp(t) 1+ah(t)mentioning

confidence: 99%

“…In order to discuss the stability of the equilibrium E 1 , we also need the following lemma, which can be easily proved by the relationship between roots and coefficients of a quadratic equation [9]. Then we have the following theorem on the stability of a positive fixed point of system (1.2).…”

Section: Stability Of Equilibriamentioning

confidence: 99%

Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

2018

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“…In recent years, there are fair amount of mathematical modelling work in studying the dynamics of host-parasitoid systems subject to Allee effects based on the modified discrete-time NicholsonBailey model (see, e.g. [3,25,26,30,31,34]) in addition to the approaches of the differential equations (e.g. see the work of Hilker et al [21], Morozov et al [38], Petrovskii et al [42]).…”

Section: Introductionmentioning

confidence: 99%

“…The study of Jang and Diamond [26] considered host-parasitoid system with Allee effects on host where host's density-dependent growth regulation is modelled by overcompensatory Ricker model. They observed that, the Allee effect has a negative impact on the coexistence of both host and parasitoid populations.…”

Section: Introductionmentioning

confidence: 99%

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

Kang

Sasmal

Bhowmick

et al. 2014

Journal of Biological Dynamics

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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.

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“…Therefore, their interactions can be modeled by discrete differences [15][16][17][18]. In 1929, Thompson [1] introduced a host-parasitoid model with a set of biological assumption.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of a host–parasitoid ecological model with the beddington-deangelis functional response

Agrawal

2014

Global Journal of Mathematical Analysis

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A host–parasitoid interaction with Allee effects on the host

Cited by 37 publications

References 22 publications

Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

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

Bifurcation analysis of a host–parasitoid ecological model with the beddington-deangelis functional response

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