A predator-prey reaction-diffusion system with nonlocal effects

S. A. Gourley, N. F. Britton

Research output: Contribution to journalArticle

118 Citations (Scopus)

Abstract

We consider a predator-prey system in the form of a coupled system of reaction-diffusion equations with an integral term representing a weighted average of the values of the prey density function, both in past time and space. In a limiting case the system reduces to the Lotka Volterra diffusion system with logistic growth of the prey. We investigate the linear stability of the coexistence steady state and bifurcations occurring from it, and expressions for some of the bifurcating solutions are constructed. None of these bifurcations can occur in the degenerate case when the nonlocal term is in fact local.

Original languageEnglish
Pages (from-to)297-333
Number of pages37
JournalJournal of Mathematical Biology
Volume34
Issue number3
Publication statusPublished - 1996

Fingerprint

Prey-predator System
Nonlocal Effects
Prey
Reaction-diffusion System
Bifurcation
Predator prey systems
Logistic Growth
predators
Lotka-Volterra
Predator-prey System
Weighted Average
Linear Stability
Term
Reaction-diffusion Equations
Density Function
Coexistence
space and time
Coupled System
Probability density function
Logistics

Keywords

  • Predator-prey
  • Reaction-diffusion
  • Time delay bifurcation pattern formation

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

A predator-prey reaction-diffusion system with nonlocal effects. / Gourley, S. A.; Britton, N. F.

In: Journal of Mathematical Biology, Vol. 34, No. 3, 1996, p. 297-333.

Research output: Contribution to journalArticle

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