Persistence And Extinction In Prey Predator Models
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Date
2013-11
Authors
Al-Ebraheem, Jawdat Akeel Mohammad
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
One of the important aspects of any ecosystem is the interactions between entities
that make up the system. Interactions between prey and predator species form an
intensively researched area in theoretical ecology. A question that is frequently posed
is whether the interaction leads to coexistence between the species or whether it leads
to extinction of one or both species. This question forms the basis of this thesis.
The interaction can be captured by the functional response. In this thesis, a plausible
mathematical model with prey dependent functional response is proposed to investigate
the question. The model is formed by considering logistic growth for both prey
and predator, and the prey abundance is used to determine the carrying capacity of
predators. We present two approaches. In the first approach, it is assumed that the
prey predator interactions are time independent. The second approach involves the
temporal variation of the prey predator population interactions. In the case of linear
time independent interactions, the system is shown to be stable without conditions.
When there are two predators, the extinction of one or the other predator will depend
on the search, capture and competitive relationships. By considering nonlinear time
independent interactions, richer dynamics were obtained. In the case of temporal
interactions, bounds on the persistency and extinction of the species are found.
Description
Keywords
Persistence And Extinction , Prey Predator