Dynamical Complexity of a Spatial Phytoplankton-Zooplankton Model with an Alternative Prey and Refuge Effect

The spatiotemporal dynamics of a phytoplankton-zooplankton model with an alternative prey and refuge effect is investigated mathematically and numerically. The stability of the equilibrium point and the traveling wave solution of the phytoplankton-zooplankton model are described based on theoretical mathematical work, which provides the basis of the numerical simulation. The numerical analysis shows that refuges have a strong effect on the spatiotemporal dynamics of the model according to the pattern formation. These results may help us to understand prey-predator interactions in water ecosystems. They are also relevant to research into phytoplankton-zooplankton ecosystems.

• Publication year

  2013

• Venue

  Journal of Applied Mathematics

• Publication date

  2013-05-09

• Fields of study

  Biology, Computer Science, Environmental Science

• Identifiers
  DOI 10.1155/2013/608073
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy

  2012cited by this paper
• Dynamics of an ecological model with impulsive control strategy and distributed time delay

  2012cited by this paper
• Complex dynamics of a reaction–diffusion epidemic model

  2012cited by this paper
• I and J

  2012cited by this paper
• Mathematical and Dynamic Analysis of a Prey-Predator Model in the Presence of Alternative Prey with Impulsive State Feedback Control

  2012cited by this paper
• Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response

  2012cited by this paper
• Numerical study of pattern formation in an extended Gray–Scott model

  2011cited by this paper
• Waves analysis and spatiotemporal pattern formation of an ecosystem model

  2011cited by this paper
• Random excitations in modelling of algal blooms in estuarine systems

  2011cited by this paper
• Spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge

  2011cited by this paper
• On the dynamics of a predator–prey model with nonconstant death rate and diffusion

  2011cited by this paper
• A detailed study of the Beddington-DeAngelis predator-prey model.

  2011cited by this paper
• Structural stability analysis of an algal bloom mathematical model in tropic interaction

  2010cited by this paper
• A focus on long-run sustainability of a harvested prey predator system in the presence of alternative prey.

  2010influential reference
• An analysis of a predator-prey model with both diffusion and migration

  2010cited by this paper
• Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay

  2009cited by this paper
• EXISTENCE OF TRAVELLING WAVES IN NONLINEAR SI EPIDEMIC MODELS

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

  2008cited by this paper
• Spatial Ecology via Reaction-Diffusion Equations: Cantrell/Diffusion

  2003cited by this paper
• How predation can slow, stop or reverse a prey invasion

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

  2001cited by this paper
• Effects of spatial grouping on the functional response of predators.

  1999cited by this paper
• RICH DYNAMICS OF GAUSE-TYPE RATIO-DEPENDENT PREDATOR-PREY SYSTEM

  1999cited by this paper
• Unusual algal blooms as excitable systems: The case of “brown-tides”

  1996cited by this paper
• Positive Indirect Effects Between Prey Species that Share Predators

  1996cited by this paper
• Ratio-Dependent Predation: An Abstraction That Works

  1995cited by this paper
• Traveling Wave Solutions of Parabolic Systems

  1994cited by this paper
• The Fallacies of "Ratio‐Dependent" Predation

  1994cited by this paper
• Partial Differential Equations in Ecology: Spatial Interactions and Population Dynamics

  1994cited by this paper
• Travelling waves in predator-prey systems

  1993cited by this paper
• Physiological Basis of Ratio-Dependent Predator-Prey Theory: The Metabolic Pool Model as a Paradigm

  1992cited by this paper
• Some Remarks on Models of Plankton Densities in Lakes

  1991cited by this paper
• Traveling waves in diffusive predator-prey equations: periodic orbits and point-to-periodic heteroclinic orbits

  1986cited by this paper
• Existence of Travelling Wave Solutions of Predator–Prey Systems via the Connection Index

  1984cited by this paper
• Deterministic mathematical models in population ecology

  1982cited by this paper
• Ordinary Differential Equations

  1982cited by this paper
• Stability and Complexity in Model Ecosystems

  1976cited 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
• The American Naturalist Vol

  year unknowncited by this paper

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