Global properties of a general predator-prey model with non-symmetric attack and consumption rate

Andrei Korobeinikov

doi:10.3934/dcdsb.2010.14.1095

Article Contents

2010, Volume 14, Issue 3: 1095-1103. Doi: 10.3934/dcdsb.2010.14.1095

This issue Previous Article Analysis of a predator-prey model with predators impulsively diffusing between two patches Next Article Stationary patterns for an adsorbate-induced phase transition model I: Existence

Global properties of a general predator-prey model with non-symmetric attack and consumption rate

Andrei Korobeinikov^1,

1.
MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick

Received: September 30, 2009

Revised: November 30, 2009

Published: September 2010

Abstract Related Papers Cited by

Abstract

Identification of conditions for stable coexistence of interacting populations is a problem of the highest priority in mathematical biology. This problem is usually considered under specific assumptions made regarding the functional forms of non-linear feedbacks. Apparently, such an approach is lacking generality. In this paper, we consider the dynamics of two species with interaction of predator--prey (consumer-supplier) type with the assumption that a part of the resource is neglected or wasted by the predator (consumer). This model describes, for instance, killing for fun; such behaviour is typical for many predators when the prey is abundant.
We assume that the functional responses that are usually included in such models are given by unspecified functions. Using the direct Lyapunov method, we derive the conditions which ensure global asymptotic stability of this model. It is remarkable that these conditions impose much weaker constraints on the system properties than that are usually assumed.

Keywords:

Mathematics Subject Classification: Primary: 592D30; Secondary: 34D20.

Citation:

Article Metrics

HTML views() PDF downloads(91) Cited by(0)

Global properties of a general predator-prey model with non-symmetric attack and consumption rate

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Global properties of a general predator-prey model with non-symmetric attack and consumption rate

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content