Dynamics of population communities with prey migrations and Allee effects: A bifurcation approach

Faina Berezovskaya, S. Wirkus, Baojun Song, C. Castillo-Chavez

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The population dynamics of predator-prey systems in the presence of patch-specific predators are explored in a setting where the prey population has access to both habitats. The emphasis is in situations where patch-prey abundance drives prey dispersal between patches, with the fragile prey populations, i.e. populations subject to the Allee effect. The resulting 3D and 4D non-linear systems depending on some parameters, which reflect 'measures' of factors under consideration, support rich dynamics and in particular a diverse number of predator-prey life history outcomes. The model's mathematical analysis is carried out via submodels that focus in lower-dimensional settings. The outcomes depend on and, in fact, are quite sensitive to the structure of the system, the range of parameter values and initial conditions. We show that the system can support multistability and a diverse set of predator-prey life-history dynamics that include rather complex dynamical system outcomes. It is argued that, in general, evolution should favour heterogeneous settings including Allee effects, prey refuges and patch-specific predators.

Original languageEnglish
Pages (from-to)129-152
Number of pages24
JournalMathematical Medicine and Biology
Volume28
Issue number2
DOIs
StatePublished - 20 Jun 2011

Fingerprint

Allee Effect
Allee effect
Population Dynamics
Prey
bifurcation
Migration
Bifurcation
Patch
predator
Predator prey systems
Population dynamics
Predator-prey
Population
Nonlinear systems
Predator
Dynamical systems
Mathematical models
life history
Ecosystem
Complex Dynamical Systems

Keywords

  • Allee effect
  • Bifurcations
  • Dispersal
  • Population community dynamics

Cite this

Berezovskaya, Faina ; Wirkus, S. ; Song, Baojun ; Castillo-Chavez, C. / Dynamics of population communities with prey migrations and Allee effects : A bifurcation approach. In: Mathematical Medicine and Biology. 2011 ; Vol. 28, No. 2. pp. 129-152.
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Dynamics of population communities with prey migrations and Allee effects : A bifurcation approach. / Berezovskaya, Faina; Wirkus, S.; Song, Baojun; Castillo-Chavez, C.

In: Mathematical Medicine and Biology, Vol. 28, No. 2, 20.06.2011, p. 129-152.

Research output: Contribution to journalArticle

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