Global properties of a general predator-prey model with non-symmetric attack and consumption rate
type: Item
instance of: scholarly article
title: Global properties of a general predator-prey model with non-symmetric attack and consumption rate
zbMATH Open document ID: 1225.34054
author: A. Korobeinikov
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2010-12-16T00:00:00Z
review text: The paper focuses on deriving conditions which ensure the global stability of a predator-prey (consumer-supplier) type of model under the assumption that the resource is partially wasted by the predator (consumer). The paper begins with a discussion about the study of population stability and oscillations. Unlike many previous studies, this paper considers more generally ecosystem-stability which is not based on a specific choice of functional response. The model under consideration, in which the consumption rate is not proportional to the attack rate, is introduced in section 2. The existence of a globally asymptotic stable equilibrium state under 13 given hypotheses is stated and proved in theorem 3.1. Global neutral stability and global asymptotic stability, both under weaker hypotheses, are proved in theorems 3.2 and 3.3. The author concludes that, in general, wastage increases the rate of convergence of solutions to the equilibrium state.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 5827362
zbMATH Keywords: predator-prey model
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: partially wasted resource
zbMATH Keywords: direct Lyapunov method
zbMATH Keywords: consumer-supplier model
zbMATH Keywords: ecosystem stability
zbMATH Keywords: unspecified response function
reviewed by: Pat Lumb
MaRDI profile type: Publication
full work available at URL: dcdsb.2010.14.1095
OpenAlex ID: W2019484821
DOI: 10.3934/DCDSB.2010.14.1095
description: scientific article; zbMATH DE number 5827362