A Single Species Model with Impulsive Diffusion

A Single Species Model with Impulsive Diffusion In most models of population dynamics, diffusion between patches is assumed to be continuous or discrete, but in practice many species diffuse only during a single period. In this paper we propose a single species model with impulsive diffusion between two patches, which provides a more natural description of population dynamics. By using the discrete dynamical system generated by a monotone, concave map for the population, we prove that the map always has a globally stable positive fixed point. This means that a single species system with impulsive diffusion always has a globally stable positive periodic solution. This result is further substantiated by numerical simulation. Under impulsive diffusion the single species survives in the two patches. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A Single Species Model with Impulsive Diffusion

A Single Species Model with Impulsive Diffusion

Acta Mathematicae Applicatae Sinica, English Series Vol. 21, No. 1 (2005) 43–48 A Single Species Model with Impulsive Diffusion 1 2 Jing Hui ,Lan-sun Chen Department of Mathematics, East China Normal University, Shanghai 200062, China & Department of Information & Computation Sciences, Guangxi University of Technology, Liuzhou 545006, China (E-mail:jinghui@amss.ac.cn) Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China (E-mail: lschen@math.ac.cn) Abstract In most models of population dynamics, diffusion between patches is assumed to be continuous or discrete, but in practice many species diffuse only during a single period. In this paper we propose a single species model with impulsive diffusion between two patches, which provides a more natural description of population dynamics. By using the discrete dynamical system generated by a monotone, concave map for the population, we prove that the map always has a globally stable positive fixed point. This means that a single species system with impulsive diffusion always has a globally stable positive periodic solution. This result is further substantiated by numerical simulation. Under impulsive diffusion the single species survives in the two patches. Keywords impulsive diffusion; stroboscopic map; boundedness; monotone concave map; positive fixed point; global stability 2000 MR Subject Classification 92B05; 34D05 1 Introduction The effect of spatial factors in population dynamics is a topic of interest (see for instances, [13,15]). In reality, dispersal between patches often occurs in ecological environments, so more realistic models should include dispersal process. In recent years, the analysis of these models [2−7,12,19] focus on the coexistence of population and local (or global) stability of equilibria ,in particular a single population was considered in [3,5,6,8-10]. Spatial factors play a fundamental role in the persistence and stability...
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Publisher
Springer-Verlag
Copyright
Copyright © 2005 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
10.1007/s10255-005-0213-3
Publisher site
See Article on Publisher Site

Abstract

In most models of population dynamics, diffusion between patches is assumed to be continuous or discrete, but in practice many species diffuse only during a single period. In this paper we propose a single species model with impulsive diffusion between two patches, which provides a more natural description of population dynamics. By using the discrete dynamical system generated by a monotone, concave map for the population, we prove that the map always has a globally stable positive fixed point. This means that a single species system with impulsive diffusion always has a globally stable positive periodic solution. This result is further substantiated by numerical simulation. Under impulsive diffusion the single species survives in the two patches.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2005

References

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