Dynamics of a system of three interacting populations with Allee effects and stocking

Yunshyong Chow, Sophia R.J. Jang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A model of three interacting populations where two populations engage in competition and two populations are in predator–prey type interaction is proposed and analysed. One of the two competing populations is subject to Allee effects and is also a pest population. The other competing population is regarded as a control agent and is the host for the predator population. There is a constant level of the external control agents released into the interaction at each generation after parasitism. We provide asymptotic dynamics of the competition subsystem and prove that a Neimark–Sacker bifurcation occurs for the host–parasitoid subsystem when the unique interior steady state loses its stability. The three interacting populations are impossible to persist for all positive initial conditions. Sufficient conditions based on the initial population size of the population with Allee effects are derived for persistence of the three populations.

Original languageEnglish
Pages (from-to)336-359
Number of pages24
JournalJournal of Difference Equations and Applications
Issue number4
StatePublished - Apr 3 2015


  • Allee effects
  • Neimark–Sacker bifurcation
  • competitive exclusion
  • persistence


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