Analysis of two generic spatially extended predator-prey models
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Summary
An a priori estimate is provided that leads to the global well-posedness of the classical (nonnegative) solutions, given any nonnegative L 1 - initial data.
- Type
- article
- Published
- 2006-01-01
- Cited by
- 5
- References
- 39
- OpenAlex
- https://openalex.org/W24417945
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:18692569
Keywords
Mathematics, A priori and a posteriori, Applied mathematics, Galerkin method, Limit cycle
References
- Plane Wave Solutions to Reaction‐Diffusion Equations
- Iterative methods for sparse linear systems
- Dynamical Systems: An Introduction with Applications in Economics and Biology
- Some Characteristics of Simple Types of Predation and Parasitism
- Competition and dispersal in predator-prey waves.
- Critical phenomena in plankton communities: KISS model revisited
- Deterministic mathematical models in population ecology
- Spatiotemporal Complexity of Plankton and Fish Dynamics
- Generation of periodic waves by landscape features in cyclic predator–prey systems
- Oscillations and chaos behind predator–prey invasion: mathematical artifact or ecological reality?
- Introduction to Applied Nonlinear Dynamical Systems and Chaos
- The functional response of predators to prey density and its role in mimicry and population regulation.
- Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics
- Shock Waves and Reaction-Diffusion Equations
- A minimal model of pattern formation in a prey-predator system
- Experimental ecology of the feeding of fishes
- Diffusion-induced chaos in a spatial predator–prey system
- Graphical Representation and Stability Conditions of Predator-Prey Interactions
- Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics.
- FUNCTIONAL RESPONSES WITH PREDATOR INTERFERENCE: VIABLE ALTERNATIVES TO THE HOLLING TYPE II MODEL
Cited by
- Existence And Uniqueness For Optimal Control Of Oxygen Absorption In Aquatic System
- Global existence for semilinear reaction–diffusion systems on evolving domains
- Finite-Difference Schemes for Reaction–Diffusion Equations Modeling Predator–Prey Interactions in MATLAB
- A HYBRID METHOD FOR STIFF REACTION–DIFFUSION EQUATIONS
- Dynamical Behavior of Nonlinear Coupled Reaction-Diffusion Model: A Numerical Study Utilizing ADI and Staggered Grid Finite Volume Method in Matlab
- Global existence for semilinear reaction-diffusion systems on evolving domains
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