Seasonal effects on a Beddington-DeAngelis type predator-prey system with impulsive perturbations
type: Item
instance of: scholarly article
title: Seasonal effects on a Beddington-DeAngelis type predator-prey system with impulsive perturbations
zbMATH Open document ID: 1187.34058
DOI: 10.1155/2009/695121
author: Young-hae Do
author: Hun Ki Baek
published in: Abstract and Applied Analysis
publication date: 2009-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/45654
review text: The authors consider the following periodical impulsive differential equations which represent a predator-prey system \[ \begin{gathered} x'(t)= rx(t)\Biggl(1- {x(t)\over k}\Biggr)- {ax(t) y(t)\over by(t)+ x(t)+c}+\lambda x(t)\sin(\omega t),\\ y'(t)= -dy(t)+ {eax(t) y(t)\over by(t)+ x(t)+c},\quad t\neq n\tau,\\ x(t^+)= (1- p_1) x(t),\;t= n\tau,\;y(t^+)= (1- p_2) y(t)+ q,\;(x(0^+), y(0^+))= (x_0, y_0),\end{gathered}\tag{1} \] where \(\tau\) is the period of impulsive immigration or stock of the predator, \(0\leq p_1\), \(p_2< 1\) and \(x(t)\), \(y(t)\) represent the population densities of prey and predator, respectively. The authors perform a numerical analysis of (1) for the case without of impulses, i.e. \(p_1= p_2= 0\). Sufficient conditions for the local asymptotic stability of (1) are derived. For the periodic solution \((0,y^*(t))\) sufficient conditions for its local asymptotic stability are found. A numerical analysis of seasonal effect and impulsive perturbations is performed.
reviewed by: S. Kostadinov
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5627605
zbMATH Keywords: pedator-prey sytem
zbMATH Keywords: impulse perturbation
zbMATH Keywords: Floquet theory
zbMATH Keywords: chaotic phenomena
zbMATH Keywords: numerical simulations
zbMATH Keywords: local and global stability
Wikidata QID: Q58646651
MaRDI profile type: Publication
OpenAlex ID: W1990864240
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description: scientific article; zbMATH DE number 5627605