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Journal of Mathematical Biology

, Volume 42, Issue 5, pp 439–454 | Cite as

The effect of dispersal on single-species nonautonomous dispersal models with delays

  • Zhidong Teng
  • Zhengyi Lu

Abstract.

In this paper, single-species nonautonomous dispersal models with delays are considered. An interesting result on the effect of dispersal for persistence and extinction is obtained. That is, if the species is persistent in a patch then it is also persistent in all other patches; if the species is permanent in a patch then it is also permanent in all other patches; if the species is extinct in a patch then it is also extinct in all other patches. Furthermore, some new sufficient conditions for the permanence and extinction of the species in a patch are established. The existence of positive periodic solutions is obtained in the periodic case by employing Teng and Chen's results on the existence of positive periodic solutions for functional differential equations.

Key words or phrases: Single-species nonautonomous model – Dispersal – Delay – Persistence – Extinction – Positive periodic solution 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Zhidong Teng
    • 1
  • Zhengyi Lu
    • 2
  1. 1.Department of Mathematics, Xinjiang University, Urumqi 830046, P.R. China. e-mail: zhidong@xju.edu.cnCN
  2. 2.Department of Mathematics, Sichuan University, Chengdu 610064, P.R. ChinaCN

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