Allee effect in a prey–predator system

Hadjiavgousti, Despina; Ichtiaroglou, S.

doi:10.1016/j.chaos.2006.06.053

Cited by 38 publications

(13 citation statements)

References 20 publications

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“…Here, an increase in stability refers to the case that the system with Allee effect approximates to the equilibrium point much faster than that without it. Clearly, in our system, Allee effects not only stabilize but also destabilize the population dynamics, which is in disagreement with previous work [10,14,[18][19][20][21]. The impact of the Allee effect on the stability of population models shows different dynamics when the corresponding model is difference.…”

Section: Numerical Simulations and Analysiscontrasting

confidence: 86%

“…In particular, discretetime models can also provide more efficient computational models for numerical simulations and richer dynamics can be observed from them. In two previous papers [20,21], the stability of a simple discrete-time predator-prey system with Holling's type I functional response is studied, while only the prey obeys the Allee effect. However, Allee effect can occur not only on prey but also on predator populations in real ecosystems.…”

Section: Introductionmentioning

confidence: 99%

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Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System

Wang

Jiao

Chen

2013

Journal of Applied Mathematics

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A discrete-time predator-prey model is proposed with Leslie-type numerical response, and the asymmetrical influence of Allee effect on the proposed system is investigated. By mathematical analysis, locally stable conditions for the equilibrium points of the considered systems with or without Allee effect are obtained firstly. Furthermore, numerical simulation is used to verify the results and detect some new outcomes. The results show that Allee effect on predator leads the system to its stable state in much longer time. Conversely, the prey population with Allee effect makes it much faster. In particular, a large value of Allee effect on prey results in periodic dynamics of the system.

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Section: Numerical Simulations and Analysiscontrasting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System

Wang

Jiao

Chen

2013

Journal of Applied Mathematics

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“…Allee, in [16], shows that the growth rate is not always positive for small densities, and it may not be decreasing as in the logistic model either. In general, Allee effect mechanisms arise from cooperation or facilitation among individuals in the species [17]. A population is said to have an Allee effect if the growth rate per capita is initially an increasing function for the low density.…”

Section: Introductionmentioning

confidence: 99%

Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect

2020

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Allee effect is one of the important factors in ecology, and taking it into account can cause significant impacts in the system dynamics. In this paper, we study the dynamics of a two-prey one-predator system, where the growth of both prey populations is subject to Allee effects, and there is a direct competition between the two-prey species having a common predator. Two discrete time delays τ 1 and τ 2 are incorporated into the model to represent reaction time of predators. Sufficient conditions for local stability of positive interior equilibrium and existence of Hopf bifurcations in terms of threshold parameters τ * 1 and τ * 2 are obtained. A Lyapunov functional is deducted to investigate the global stability of positive interior equilibrium. Sensitivity analysis to evaluate the uncertainty of the state variables to small changes in the Allee parameters is also investigated. Presence of Allee effect and time delays in the model increases the complexity of the model and enriches the dynamics of the system. Some numerical simulations are provided to illustrate the effectiveness of the theoretical results. e model is highly sensitive to small changes in Allee parameters at the early stages and with low population densities, and this sensitivity decreases with time.Hindawi Complexity Volume 2020, Article ID 7306412, 15 pages https://doi.

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“…N (t) and P (t) can be interpreted as the densities of prey and predator populations at time t, respectively. Zhou et al first studied the stability conditions of the equilibrium point for the system and then by introducing so called Allee effect [3,6,7] in different forms, they investigated the impact of this effect on the dynamics of this predator-prey system. In system (1.1), there is no delay.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays

Lv¹,

Zhang²,

Tang³

2016

J. Nonlinear Sci. Appl.

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In this paper, we consider a ratio-dependent predator-prey system with multiple delays where the dynamics are logistic with the carrying capacity proportional to prey population. By choosing the sum τ of two delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.

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Allee effect in a prey–predator system

Cited by 38 publications

References 20 publications

Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System

Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System

Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect

Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays

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