Qualitative analysis of a ratio-dependent predator–prey system with diffusion

No abstract is available for this paper.

• Publication year

  2003

• Venue

  Proceedings of the Royal Society of Edinburgh: Section A Mathematics

• Publication date

  2003-08-01

• Fields of study

  Biology, Mathematics, Environmental Science

• Identifiers
  DOI 10.1017/S0308210500002742
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Steady states of a strongly coupled prey-predator model

  2005cited by this paper
• Non‐Constant Positive Steady States of a Predator‐Prey System with Non‐Monotonic Functional Response and Diffusion

  2004cited by this paper
• Non-constant positive steady states of the Sel'kov model ☆

  2003cited by this paper
• Global Qualitative Analysis for a Ratio-Dependent Predator–Prey Model with Delay☆☆☆

  2002cited by this paper
• Parametric analysis of the ratio-dependent predator–prey model

  2001cited by this paper
• Global analysis of the Michaelis–Menten-type ratio-dependent predator-prey system

  2001cited by this paper
• Rich dynamics of a ratio-dependent one-prey two-predators model

  2001cited by this paper
• Predator migration in response to prey density: What are the consequences?

  2001cited by this paper
• On the Symbiotic Lotka–Volterra Model with Diffusion and Transport Effects

  2000cited by this paper
• Existence and Instability of Neumann Layer Solutions for a 3-component Lotka-Volterra Model with Diffusion

  2000cited by this paper
• Effects of spatial grouping on the functional response of predators.

  1999cited by this paper
• Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics

  1998cited by this paper
• Global qualitative analysis of a ratio-dependent predator–prey system

  1998cited by this paper
• Some uniqueness and exact multiplicity results for a predator-prey model

  1997cited by this paper
• Practical persistence in ecological models via comparison methods

  1996cited by this paper
• A counterexample on competing species equations

  1996cited by this paper
• Empirical Evidence of the Role of Heterogeneity in Ratio‐Dependent Consumption

  1993cited by this paper
• Coexistence in a simple food chain with diffusion

  1992cited by this paper
• The biological control paradox.

  1991cited by this paper
• Coupling in predator-prey dynamics: Ratio-Dependence

  1989cited by this paper
• Geometric Theory of Semilinear Parabolic Equations

  1989cited by this paper
• Large amplitude stationary solutions to a chemotaxis system

  1988cited by this paper
• Coexistence theorems of steady states for predator-prey interacting systems

  1988cited by this paper
• Topics in nonlinear functional analysis

  1967cited by this paper

• Analysis of nonconstant steady states in a cross-diffusive predator-prey system with Allee effect and generalized Holling IV response

  2026cites this paper
• Bifurcation and numerical investigations of diffusive predator-prey model in two space dimension

  2025cites this paper
• Spatio-temporal pattern formation under varying functional response parametrizations

  2025cites this paper
• Impacts of predator-taxis on a spatiotemporal predator-prey model

  2025cites this paper
• Dynamic complexity of Holling-Tanner predator-prey system with predator cannibalism

  2025cites this paper
• Steady States of a Diffusive Population-Toxicant Model with Negative Toxicant-Taxis

  2024cites this paper
• Dynamic analysis and pattern formation in a Generalized Klausmeier-Gray-Scott Model

  2024cites this paper
• Dynamics of a prey–predator model with reproductive Allee effect for prey and generalist predator

  2024cites this paper
• Parameter estimation for network-organized Turing system based on convolution neural networks

  2023cites this paper
• Well-posedness and qualitative analysis of a SEIR model with spatial diffusion for COVID-19 spreading

  2023cites this paper
• Asymptotic profiles of positive steady states for a diffusive predator–prey model with predator interference

  2023cites this paper
• Stability and bifurcation of a delayed diffusive predator-prey model affected by toxins

  2023cites this paper
• Predation-induced dispersal toward fitness for predator invasion in predator–prey models

  2023cites this paper
• Dynamical behavior in a reaction-diffusion system with prey-taxis

  2022cites this paper
• Hunting cooperation among slowly diffusing specialist predators can induce stationary Turing patterns

  2022cites this paper
• A Quasilinear Predator-Prey Model with Indirect Prey-Taxis

  2021cites this paper
• Consequences of refuge and diffusion in a spatiotemporal predator–prey model

  2021cites this paper
• Coexistence States of a Ratio-Dependent Predator-Prey Model with Nonlinear Diffusion

  2021cites this paper
• Global structure research of a class of predator-prey model with cross-diffusions and refuge

  2021cites this paper
• A diffusive two predators–one prey model on periodically evolving domains

  2021cites this paper
• Interactive Simulation of Disease Contagion in Dynamic Crowds

  2021cites this paper
• Qualitative analysis of the Oregonator model

  2020cites this paper
• Global well-posedness and stability analysis of prey-predator model with indirect prey-taxis

  2020cites this paper
• Diffusive Epidemiological Predator–Prey Models with Ratio-Dependent Functional Responses and Nonlinear Incidence Rate

  2020cites this paper
• Asymptotic dynamics and spatial patterns of a ratio-dependent predator–prey system with prey-taxis

  2020cites this paper
• Stationary Pattern of a Reaction–Diffusion Mussel–Algae Model

  2020cites this paper
• Spatiotemporal dynamics of a diffusive predator-prey model with generalist predator

  2020influential citation
• Positive Solutions of a Predator-Prey Model with Additive Allee Effect

  2020cites this paper
• Optimality for a diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge

  2020cites this paper
• Qualitative Analysis of a Predator-prey Systemwith Ratio-dependent and Modified Leslie-GowerFunctional Response

  2020cites this paper
• Diffusive Epidemiological Predator–Prey Models with Ratio-Dependent Functional Responses and Nonlinear Incidence Rate

  2020cites this paper
• Fixed Point Theory and Positive Solutions for a Ratio-Dependent Elliptic System

  2019cites this paper
• Global structure of positive steady-state solutions for a class of predator-prey model with cross-diffusion

  2019cites this paper
• Dynamic analysis of a reaction–diffusion impulsive hybrid system

  2019cites this paper
• Hopf bifurcation and steady-state bifurcation for a Leslie-Gower prey-predator model with strong Allee effect in prey

  2019cites this paper
• Spatial patterns in a cannibalistic eco-epidemiological model

  2019cites this paper
• Complex dynamics of a diffusive predator–prey model with strong Allee effect and threshold harvesting

  2019cites this paper
• Global attractors of some predator–prey reaction–diffusion systems with density-dependent diffusion and time-delays

  2018cites this paper
• Qualitative analysis of a strongly coupled predator–prey system with modified Holling–Tanner functional response

  2018cites this paper
• Permanence, stability, and coexistence of a diffusive predator–prey model with modified Leslie–Gower and B–D functional response

  2018influential citation
• Qualitative analysis of a Belousov–Zhabotinskii reaction model

  2018cites this paper
• Spatio-temporal complexity of a delayed diffusive model for plant invasion

  2018cites this paper
• Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator–prey system with the crowing term and the weak growth

  2018cites this paper
• Effect of the protection zone on coexistence of the species for a ratio-dependent predator-prey model

  2018cites this paper
• Stationary patterns of a ratio-dependent prey-predator model with cross-diffusion

  2017cites this paper
• Hopf and steady state bifurcation analysis in a ratio-dependent predator-prey model

  2017cites this paper
• Pattern formation of a diffusive eco-epidemiological model with predator-prey interaction

  2017cites this paper
• A stochastic prey-predator model with time-dependent delays

  2017cites this paper
• Steady states of a Sel'kov-Schnakenberg reaction-diffusion system

  2017cites this paper
• Qualitative analysis of a Belousov–Zhabotinskii reaction model

  2017cites this paper
• A spatially heterogeneous predator-prey model

  2017cites this paper
• Stationary patterns of a ratio-dependent prey-predator model with cross-diffusion

  2017cites this paper
• Dynamics of a diffusive prey-predator system with strong Allee effect growth rate and a protection zone for the prey

  2017cites this paper
• STEADY STATES OF A SEL’KOV-SCHNAKENBERG REACTION-DIFFUSION SYSTEM

  2017cites this paper
• Asymptotic behavior of a diffusive eco-epidemiological model with an infected prey population

  2017cites this paper
• Turing patterns in a reaction–diffusion epidemic model

  2017cites this paper
• PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIO- DEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION

  2016cites this paper
• The complex dynamics of a diffusive prey-predator model with an Allee effect in prey

  2016influential citation
• Qualitative analysis for a diffusive predator-prey model with a transmissible disease in the prey population

  2016cites this paper
• Positive Coexistence of Steady States for a Diffusive Ratio-Dependent Predator-Prey Model with an Infected Prey

  2015cites this paper
• A free boundary problem of the ratio-dependent prey-predator model

  2015influential citation
• Bifurcation analysis of a diffusive predator–prey system with a herd behavior and quadratic mortality

  2015cites this paper
• A stochastic predator-prey model with delays

  2015cites this paper
• Analysis of Spatiotemporal Dynamic and Bifurcation in a Wetland Ecosystem

  2015cites this paper
• Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model

  2015cites this paper
• Spatial, temporal and spatiotemporal patterns of diffusive predator-prey models with mutual interference

  2015cites this paper
• Existence and dynamics of quasilinear parabolic systems with time delays

  2015cites this paper
• Protection zone in a diffusive predator–prey model with Beddington–DeAngelis functional response

  2015cites this paper
• Wolbachia infection dynamics by reaction-diffusion equations

  2015cites this paper
• Uniqueness and stability of positive steady state solutions for a ratio-dependent predator–prey system with a crowding term in the prey equation

  2015cites this paper
• Bifurcation analysis of a diffusive ratio-dependent predator–prey model

  2014cites this paper
• Spatiotemporal complexity in a predator--prey model with weak Allee effects.

  2014influential citation
• Wolbachia infection dynamics by reaction-diffusion equations

  2014cites this paper
• Cross-diffusion induced instability and pattern formation for a Holling type-II predator-prey model

  2014cites this paper
• Spatiotemporal dynamics in a diffusive ratio-dependent predator-prey model near a Hopf-Turing bifurcation point

  2014cites this paper
• Dynamics of a diffusive predator–prey model with modified Leslie–Gower schemes and additive Allee effect

  2014cites this paper
• Persistence, Stability and Hopf Bifurcation in a Diffusive Ratio-Dependent Predator-Prey Model with Delay

  2014cites this paper
• Spatiotemporal complexity of a three-species ratio-dependent food chain model

  2014cites this paper
• Positivity and boundedness preserving semi-implicit schemes for the fractional reaction-diffusion equation

  2014cites this paper
• Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species

  2014cites this paper
• Dynamics in a diffusive plant-herbivore model with toxin-determined functional response

  2014cites this paper
• Spatiotemporal complexity of a three-species ratio-dependent food chain model

  2014cites this paper
• Bifurcation analysis of a diffusive ratio-dependent predator–prey model

  2014cites this paper
• GLOBAL ASYMPTOTIC STABILITY OF POSITIVE STEADY STATES OF AN n-DIMENSIONAL RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH DIFFUSION

  2013cites this paper
• Positivity and boundedness preserving schemes for space-time fractional predator-prey reaction-diffusion model

  2013cites this paper
• QUALITATIVE ANALYSIS OF A DIFFUSIVE FOOD WEB CONSISTING OF A PREY AND TWO PREDATORS

  2013cites this paper
• Positive Steady States of a Strongly Coupled Predator-Prey System with Holling-(n+1) Functional Response

  2013cites this paper
• Dynamics of a diffusive predator-prey model with modified Leslie-Gower and Holling-type III schemes

  2013cites this paper
• The Existence of Positive Nonconstant Steady States in a Reaction: Diffusion Epidemic Model

  2013cites this paper
• Spatial patterns of the Holling–Tanner predator–prey model with nonlinear diffusion effects

  2013cites this paper
• Positivity and boundedness preserving schemes for the fractional reaction-diffusion equation

  2013cites this paper
• A diffusive one-prey and two-competing-predator system with a ratio-dependent functional response: I, long time behavior and stability of equilibria

  2013cites this paper
• A diffusive one-prey and two-competing-predator system with a ratio-dependent functional response: II stationary pattern formation

  2013cites this paper
• Stationary patterns in a two-cell coupled isothermal chemical system with arbitrary powers of autocatalysis

  2013cites this paper
• Stationary pattern of a diffusive prey-predator model with trophic intersections of three levels

  2013cites this paper
• Traveling wave solutions of density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method

  2013cites this paper
• Dynamique spatio-temporelle et identification des diffusions non linéaires

  2013cites this paper
• Coexistence of a one-prey two-predators model with ratio-dependent functional responses

  2012cites this paper
• Positive solutions of a diffusive predator-prey model with modified Leslie-Gower and Holling-type II schemes ✩

  2012cites this paper
• Periodic Solutions of a Lotka-Volterra System with Delay and Diffusion

  2012cites this paper