Dynamics of a population in two patches with dispersal

Yunshyong Chow, Sophia R.J. Jang, Nai Sher Yeh

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A two-dimensional discrete system of a species in two patches proposed by Newman et al. is studied. It is shown that the unique interior steady state is globally asymptotically stable if the active population has a Beverton–Holt type growth rate. If the population is also subject to Allee effects, then the system has two interior steady states whenever the density-independent growth rate is large. In addition, the model has period-two solutions if the symmetric dispersal exceeds a critical threshold. For small dispersal, populations may either go extinct or eventually stabilize. However, populations are oscillating over time if dispersal is beyond the critical value and the initial populations are large.

Original languageEnglish
Pages (from-to)543-563
Number of pages21
JournalJournal of Difference Equations and Applications
Issue number4
StatePublished - Apr 3 2018


  • Dispersal
  • period-doubling bifurcation
  • saddle point
  • supercritical


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