Pattern formation in a variable diffusion predator–prey model with additive Allee effect

This paper deals with a variable diffusion predator–prey model with additive Allee effect. A good understanding of the existence of steady states is gained for the case σ=0 . The result shows that the reduce problem has multiple solutions. Moreover, by applying the singular perturbation method, we give a proof of existence of large amplitude solutions when σ is sufficiently small.

• Publication year

  2019

• Venue

  Mathematical methods in the applied sciences

• Publication date

  2019-12-29

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1002/mma.6171
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Positive Solutions of a Predator-Prey Model with Additive Allee Effect

  2020cited by this paper
• Dynamics in a diffusive predator–prey system with strong Allee effect and Ivlev-type functional response

  2015cited by this paper
• Strong Allee effect in a diffusive predator–prey system with a protection zone☆

  2014cited by this paper
• NONEXISTENCE OF PERIODIC ORBITS FOR PREDATOR-PREY SYSTEM WITH STRONG ALLEE EFFECT IN PREY POPULATIONS

  2013cited by this paper
• Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey

  2011cited by this paper
• The evidence for Allee effects

  2009cited by this paper
• Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect.

  2006cited by this paper
• Allee effects driven by predation

  2004cited by this paper
• Speeds of invasion in a model with strong or weak Allee effects.

  2001cited by this paper
• How predation can slow, stop or reverse a prey invasion

  2001cited by this paper
• Inverse density dependence and the Allee effect.

  1999cited by this paper
• What Is the Allee Effect

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

  1999cited by this paper
• The Allee effect, finding mates and theoretical models

  1997influential reference
• Allee Dynamics and the Spread of Invading Organisms

  1993cited by this paper
• Singular perturbation approach to traveling waves in competing and diffusing species models

  1982cited by this paper
• Multiple Solutions of Two-Point Boundary Value Problems of Neumann Type with a Small Parameter

  1980cited by this paper
• Boundary and interior transition layer phenomena for pairs of second-order differential equations☆

  1976cited by this paper
• Animal aggregations, a study in general sociology. / by W. C. Allee.

  1931cited by this paper
• Animal Aggregations: A Study in General Sociology

  1931cited by this paper

• Bifurcation and spatiotemporal patterns of a Leslie-Gower model with diffusive

  2025cites this paper
• Stable patterns with jump-discontinuity for a phytoplankton-zooplankton system with both Allee and fear effect

  2024cites this paper
• Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator Harvesting

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

  2022cites this paper