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Impacts of biotic resource enrichment on a predator-prey population

Mohd Safuan, Hamizah and Sidhu, H. S. and Jovanoski, Z. and Towers, I. N. (2013) Impacts of biotic resource enrichment on a predator-prey population. Bulletin of Mathematical Biology, 75 (10). pp. 1798-1812. ISSN 1522-9602

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Abstract

The environmental carrying capacity is usually assumed to be fixed quantity in the classical predator-prey population growth models. However, this assumption is not realistic as the environment generally varies with time. In a bid for greater realism, functional forms of carrying capacities have been widely applied to describe varying environments. Modelling carrying capacity as a state variable serves as another approach to capture the dynamical behavior between population and its environment. The proposed modified predator-prey model is based on the ratio-dependent models that have been utilized in the study of food chains. Using a simple non-linear system, the proposed model can be linked to an intra-guild predation model in which predator and prey share the same resource. Distinct from other models, we formulate the carrying capacity proportional to a biotic resource and both predator and prey species can directly alter the amount of resource available by interacting with it. Bifurcation and numerical analyses are presented to illustrate the system's dynamical behavior. Taking the enrichment parameter of the resource as the bifurcation parameter, a Hopf bifurcation is found for some parameter ranges, which generate solutions that posses limit cycle behavior.

Item Type: Article
Uncontrolled Keywords: carrying capacity; food chain; predator-prey; intra-guild; hopf bifurcation
Subjects: Q Science > QH Natural history
Divisions: Faculty of Applied Science and Technology > Department of Science and Mathematics
Depositing User: Normajihan Abd. Rahman
Date Deposited: 22 Oct 2013 02:56
Last Modified: 22 Oct 2013 02:56
URI: http://eprints.uthm.edu.my/id/eprint/4397
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