### 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 language | English |
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Pages (from-to) | 297-333 |

Number of pages | 37 |

Journal | Journal of Mathematical Biology |

Volume | 34 |

Issue number | 3 |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Mathematical Biology*,

*34*(3), 297-333.

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

Research output: Contribution to journal › Article

*Journal of Mathematical Biology*, vol. 34, no. 3, pp. 297-333.

}

TY - JOUR

T1 - A predator-prey reaction-diffusion system with nonlocal effects

AU - Gourley, S. A.

AU - Britton, N. F.

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

KW - Predator-prey

KW - Reaction-diffusion

KW - Time delay bifurcation pattern formation

UR - http://www.scopus.com/inward/record.url?scp=0012189671&partnerID=8YFLogxK

M3 - Article

VL - 34

SP - 297

EP - 333

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 3

ER -