Existence of positive periodic solution of periodic time-dependent predator-prey system with impulsive effects
type: Item
instance of: scholarly article
title: Existence of positive periodic solution of periodic time-dependent predator-prey system with impulsive effects
zbMATH Open document ID: 1058.34051
author: Jing Hui
author: Lansun Chen
publication date: 2004-10-01T00:00:00Z
review text: The following impulsive problem is considered \[ \begin{aligned} \dot{N}_1& =N_1(b_1-c_{11}N_1-c_{12}N_2), \\ \dot{N}_2& =N_2(-b_2+c_{21}N_1-c_{22}N_2), \\ \Delta N_1& =c_kN_1,\quad \Delta N_2=d_kN_2,\quad t=\tau_k, \end{aligned} \] where \(b_i(t), c_{ij}(t)\) are continuous, \(T\)-periodic positive functions, \[ c_{k+q}=c_k,~d_{k+q}=d_k,~\tau_{k+q}=\tau_k+T, 1+c_k>0,~1+d_k>0. \] Under some additional assumptions, using bifurcation theory, the authors prove the existence of a positive periodic solution for this system and discuss some biological applications.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 2104900
zbMATH Keywords: predator-prey system
zbMATH Keywords: impulsive effects
zbMATH Keywords: periodic solution
reviewed by: Leonid Berezansky
MaRDI profile type: Publication
Wikidata QID: Q115606170
full work available at URL: s10114-004-0333-3
OpenAlex ID: W2015522719
cites work: A periodic prey-predator system
cites work: The periodic predator-prey Lotka-Volterra model
cites work: Some global results for nonlinear eigenvalue problems
cites work: Bifurcation from simple eigenvalues
cites work: Bifurcation, perturbation of simple eigenvalues, and linearized stability
cites work: Q4325523
cites work: Pulse vaccination strategy in the SIR epidemic model
cites work: Q4487445
cites work: Impulsive stabilization and applications to population growth models
cites work: A cell population model described by impulsive PDEs. -- Existence and numerical approximation
cites work: Impulsive control of a Lotka-Volterra system
cites work: Invasion and chaos in a periodically pulsed mass-action chemostat
cites work: Differential equations: Stability, oscillations, time lags
DOI: 10.1007/S10114-004-0333-3
Recommended article: Q3074135
Recommended article: Q5486899
Recommended article: Q3630651
Recommended article: Existence of positive periodic solution of a neutral impulsive delay predator-prey system
Recommended article: Positive periodic solutions for an impulsive predator-prey system with delay and diffusion
Recommended article: Positive periodic solutions for impulsive Gause-type predator-prey systems
Recommended article: Q3052000
Recommended article: Q3640882
Recommended article: Positive periodic solutions for impulsive predator-prey model with dispersion and time delays
Recommended article: Q5490084
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2104900