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...
Loading next page...
 
/lp/springer_journal/a-single-species-model-with-impulsive-diffusion-Dfx0nhNOLU
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

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial