The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect

We study the dynamics of a delayed predator-prey model with double Allee effect. For the temporal model, we showed that there exists a threshold of time delay in predator-prey interactions; when time delay is below the threshold value, the positive equilibrium is stable. However, when time delay is above the threshold value, the positive equilibrium is unstable and period solution will emerge. For the spatiotemporal model, through numerical simulations, we show that the model dynamics exhibit rich parameter space Turing structures. The obtained results show that this system has rich dynamics; these patterns show that it is useful for a delayed predator-prey model with double Allee effect to reveal the spatial dynamics in the real model.

• Publication year

  2015

• Venue

  Discrete Dynamics in Nature and Society

• Publication date

  2015-10-04

• Fields of study

  Biology, Mathematics

• Identifiers
  DOI 10.1155/2015/102597
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Qualitative analysis of a predator–prey system with double Allee effect in prey

  2015influential reference
• Existence of Limit Cycles in the Solow Model with Delayed-Logistic Population Growth

  2014cited by this paper
• On the Dalgaard-Strulik Model with Logistic Population Growth Rate and Delayed-Carrying Capacity

  2013cited by this paper
• Pattern Dynamics in a Spatial Predator-Prey System with Allee Effect

  2013cited by this paper
• THE ROSENZWEIG-MACARTHUR PREDATION MODEL WITH DOUBLE ALLEE EFFECTS ON PREY

  2013cited by this paper
• Multiparametric bifurcations of an epidemiological model with strong Allee effect

  2012cited by this paper
• Consequences of double Allee effect on the number of limit cycles in a predator-prey model

  2011cited by this paper
• Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey

  2011cited by this paper
• Modulation of predator–prey interactions by the Allee effect

  2010cited by this paper
• Allee effect in a discrete-time predator-prey system

  2009cited by this paper
• Allee Effects in Ecology and Conservation

  2008cited by this paper
• Allee effect in a prey-predator system

  2008cited by this paper
• Multiple Allee effects and population management.

  2007cited by this paper
• Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect.

  2006cited by this paper
• Analysis of a predator–prey model with modified Leslie–Gower and Holling-type II schemes with time delay

  2006cited by this paper
• Bifurcations and chaos in a predator-prey system with the Allee effect

  2004cited by this paper
• Allee effect makes possible patchy invasion in a predator-prey system.

  2002cited by this paper
• Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment

  2000cited by this paper
• Inverse density dependence and the Allee effect.

  1999cited by this paper
• Consequences of the Allee effect for behaviour, ecology and conservation.

  1999cited by this paper

• Dynamics of a fractional order predator-prey system with double Allee effect and group defense

  2025cites this paper
• Dynamics of a Leslie–Gower predator–prey model with Allee effect in predator: stability, bifurcations, and pattern formation

  2025cites this paper
• Exploring complex dynamics in a Ricker type predator-prey model with prey refuge.

  2025cites this paper
• Theoretical and Numerical Bifurcation Analysis of a Discrete Predator–Prey System of Ricker Type with Weak Allee Effect

  2024cites this paper
• Analysis of Two Prey and One Predator Interaction Model With Discrete Time Delay

  2023cites this paper
• Qualitative Analysis of a Spatiotemporal Prey‐Predator Model with Additive Allee Effect and Fear Effect

  2022cites this paper
• Multi-stage deep learning approaches to predict boarding behaviour of bus passengers

  2021cites this paper
• On an SIR epidemic model with vaccination in a patchy environment

  2019cites this paper
• Supercritical and subcritical Hopf-bifurcations in a two-delayed prey-predator system with density-dependent mortality of predator and strong Allee effect in prey

  2019cites this paper
• A Supervised Multi-control for Monitoring the Antiviral Treatment Strategy for an SEIADR Epidemic Model

  2018cites this paper
• A switched multicontroller for an SEIADR epidemic model with monitored equilibrium points and supervised transients and vaccination costs

  2018cites this paper
• Predicting subway passenger flows under different traffic conditions

  2018cites this paper
• On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease

  2017cites this paper