Spatiotemporal Patterns of a Homogeneous Diffusive Predator–Prey System with Holling Type III Functional Response

No abstract is available for this paper.

• Publication year

  2017

• Venue

  Journal of Dynamics and Differential Equations

• Publication date

  2017-12-01

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1007/S10884-016-9517-7
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Global bifurcation analysis and pattern formation in homogeneous diffusive predator–prey systems

  2016cited by this paper
• Patterned solutions of a homogenous diffusive predator-prey system of Holling type-III

  2016cited by this paper
• Positive steady state solutions of a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion

  2014cited by this paper
• Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

  2014cited by this paper
• Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction–diffusion model

  2012cited by this paper
• Instabilities and patterns in coupled reaction-diffusion layers.

  2012cited by this paper
• Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population Genetics

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

  2011cited by this paper
• Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone

  2011cited by this paper
• Multiple Limit Cycles in a Gause Type Predator–Prey Model with Holling Type III Functional Response and Allee Effect on Prey

  2011cited by this paper
• Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩

  2009cited by this paper
• Some nonexistence results for nonconstant stationary solutions to the Gray-Scott model in a bounded domain

  2009cited by this paper
• Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system

  2009cited by this paper
• On global bifurcation for quasilinear elliptic systems on bounded domains

  2009cited by this paper
• Effect of a protection zone in the diffusive Leslie predator-prey model

  2009cited by this paper
• Traveling waves in a diffusive predator–prey model with holling type-III functional response

  2008cited by this paper
• Dynamic complexities of a predator-prey model with generalized Holling type III functional response and impulsive effects

  2008cited by this paper
• On stationary patterns of a reaction–diffusion model with autocatalysis and saturation law

  2008cited by this paper
• Diffusion-driven instability and bifurcation in the Lengyel-Epstein system

  2008cited by this paper
• Non-constant steady-state solutions for Brusselator type systems

  2008cited by this paper
• Global Dynamics of the Brusselator Equations

  2007cited by this paper
• Allee effect and bistability in a spatially heterogeneous predator-prey model

  2007cited by this paper
• A diffusive predator–prey model with a protection zone☆

  2006cited by this paper
• Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect.

  2006cited by this paper
• Strongly coupled elliptic systems and applications to Lotka–Volterra models with cross-diffusion

  2005cited by this paper
• Pattern formation in the Brusselator system

  2005cited by this paper
• Turing patterns in the Lengyel-Epstein system for the CIMA reaction

  2005cited by this paper
• Mesa-type patterns in the one-dimensional Brusselator and their stability

  2005cited by this paper
• Multiple coexistence states for a prey-predator system with cross-diffusion

  2004cited by this paper
• Stability of steady-state solutions to a prey–predator system with cross-diffusion☆

  2004cited by this paper
• Positive steady--states for two interacting species models with linear self-cross diffusions

  2003cited by this paper
• Spatial Ecology via Reaction-Diffusion Equations: Cantrell/Diffusion

  2003cited by this paper
• A predator–prey interaction model with self and cross-diffusion

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

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

  2001cited by this paper
• Topics in Nonlinear Functional Analysis

  2001cited by this paper
• S-Shaped Global Bifurcation Curve and Hopf Bifurcation of Positive Solutions to a Predator–Prey Model

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

  1997cited by this paper
• On a predator-prey system of Holling type

  1997cited by this paper
• Global Stability for a Class of Predator-Prey Systems

  1995cited by this paper
• Global bifurcation in the Brusselator system

  1995cited by this paper
• Allee Dynamics and the Spread of Invading Organisms

  1993cited by this paper
• Biotic interactions and global change.

  1993cited by this paper
• Permanence in ecological systems with spatial heterogeneity

  1993cited by this paper
• Coupling in predator-prey dynamics: Ratio-Dependence

  1989cited by this paper
• Functional Responses and Interference within and between Year Classes of a Dragonfly Population

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

  1989cited by this paper
• Dynamic optimization of combined harvesting of a two-species fishery

  1988cited by this paper
• Asymptotic Behavior of Dissipative Systems

  1988cited by this paper
• Uniqueness of limit cycles in Gause-type models of predator-prey systems

  1988cited by this paper
• Global existence and boundedness in reaction-diffusion systems

  1987cited by this paper
• The qualitative analysis of two species predator-prey model with Holling's type III functional response

  1986cited by this paper
• Deterministic mathematical models in population ecology

  1982cited by this paper
• Theory and applications of Hopf bifurcation

  1981cited by this paper
• Ecological Determinants of Functional Response

  1979cited by this paper
• Convergence to Homogeneous Equilibrium State for Generalized Volterra–Lotka Systems with Diffusion

  1979cited by this paper
• An application of the invariance principle to reaction-diffusion equations

  1979cited by this paper
• LARGE TIME BEHAVIOR OF SOLUTIONS OF SYSTEMS OF NONLINEAR REACTION-DIFFUSION EQUATIONS*

  1978cited by this paper
• A model predator-prey system with functional response

  1978cited by this paper
• A Model for Tropic Interaction

  1975cited by this paper
• A MODEL FOR TROPHIC INTERACTION

  1975cited by this paper
• Bifurcation analysis of nonlinear reaction-diffusion equations—I. Evolution equations and the steady state solutions

  1975cited by this paper
• Mutual Interference Between Parasites or Predators and its Effect on Searching Efficiency

  1975cited by this paper
• The functional response of predators to prey density and its role in mimicry and population regulation.

  1965cited by this paper
• The Components of Predation as Revealed by a Study of Small-Mammal Predation of the European Pine Sawfly

  1959cited by this paper
• Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences is currently published by The Royal

  1951cited by this paper
• Fluctuations in the Abundance of a Species considered Mathematically

  1926cited by this paper
• Elements of Physical Biology.

  1925cited by this paper

• STABILITY OF A NONAUTONOMOUS DELAYED PERIODIC REACTION-DIFFUSION PREDATOR-PREY MODEL

  2025cites this paper
• Stability Analysis of a Nonautonomous Diffusive Predator–Prey Model with Disease in the Prey and Beddington–DeAngelis Functional Response

  2025cites this paper
• Energetic Derivation and Geometric Reduction of Reaction-Diffusion Systems with Holling-Type Functional Responses

  2025cites this paper
• Stability and Bifurcation in a Discrete Phytoplankton-Zooplankton Model with Holling-Type Toxic Effects

  2025cites this paper
• Stability, bifurcation, and chaos control in a discrete-time phytoplankton–zooplankton model with Holling type II and type III functional responses

  2025cites this paper
• GLOBAL STABILITY OF PERIODIC SOLUTION FOR A 3-SPECIES NONAUTONOMOUS RATIO-DEPENDENT DIFFUSIVE PREDATOR-PREY SYSTEM

  2024cites this paper
• Stability criterion of a nonautonomous 3-species ratio-dependent diffusive predator-prey model

  2024cites this paper
• Discrete dynamics of phytoplankton-zooplankton systems with Holling type functional responses

  2024influential citation
• Identifying numerical bifurcation structures of codimensions 1 and 2 in interacting species system

  2024cites this paper
• Pattern dynamics of a predator-prey system with Ivlev-type functional response

  2024cites this paper
• Stability and Hopf bifurcation analysis of a delayed predator–prey model with age-structure and Holling III functional response

  2023cites this paper
• Effects of B-D Functional Response and Protection Zone on a Predator-prey Model

  2023cites this paper
• On Turing-Turing bifurcation of partial functional differential equations and its induced superposition patterns

  2022cites this paper
• NEIMARK-SACKER BIFURCATION AND STABILITY ANALYSIS IN A DISCRETE PHYTOPLANKTON-ZOOPLANKTON SYSTEM WITH HOLLING TYPE II FUNCTIONAL RESPONSE

  2022cites this paper
• Spatio-Temporal Patterns of Predator-Prey Model with Allee Effect and Constant Stocking Rate for Predator

  2021cites this paper
• Spatial pattern formation in activator-inhibitor models with nonlocal dispersal

  2021cites this paper
• Hopf bifurcation in an age-structured prey-predator model with Holling Ⅲ response function.

  2021cites this paper
• Nonexistence of Nonconstant Positive SteadyStates of a Diffusive Predator-prey Model withFear Effect

  2020cites this paper
• Double zero singularity and spatiotemporal patterns in a diffusive predator-prey model with nonlocal prey competition

  2020cites this paper
• GLOBAL DYNAMICS OF TWO PHYTOPLANKTON-ZOOPLANKTON MODELS WITH TOXIC SUBSTANCES EFFECT

  2019cites this paper
• Turing–Hopf bifurcation and multi-stable spatio-temporal patterns in the Lengyel–Epstein system

  2019cites this paper
• Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay

  2018cites this paper
• Bifurcation analysis of a diffusive predator–prey system with nonmonotonic functional response

  2018cites this paper
• Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay

  2018cites this paper
• Predator-prey equations with constant harvesting and planting.

  2018cites this paper
• Spatial Nonhomogeneous Periodic Solutions Induced by Nonlocal Prey Competition in a Diffusive Predator-Prey Model

  2018cites this paper
• Stationary patterns of a diffusive predator–prey model with Crowley–Martin functional response

  2017cites this paper
• Stochastic spatiotemporal diffusive predator-prey systems

  2017cites this paper
• Nonexistence of nonconstant positive steady states of a diffusive predator-prey model

  2017cites this paper
• Dynamics of a Diffusive Predator–Prey Model: The Effect of Conversion Rate

  2016cites this paper