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Mathematical analysis of population growth subject to environmental change

Mohd Safuan, Hamizah (2015) Mathematical analysis of population growth subject to environmental change. Bulletin of the Australian Mathematical Society, 92 (2). pp. 351-352. ISSN 0004-9727

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Abstract

Many ecosystems are pressured when the environment is perturbed, such as when resources are scarce, or even when they are over-abundant. Changes in the environment impact on its ability to support a population of a given species. However, most current models do not take the changing environment into consideration. The standard approach in modelling a population in its environment is to assume that the carrying capacity, which is a proxy for the state of the environment, is unchanging. In effect, this assumption also posits that the population is negligible compared to the environment and cannot alter the carrying capacity in any way. Modelling the interplay of the population with its environments is important when describing the varying factors that exist in the system. This objective can be achieved by treating the carrying capacity as time- and space-dependent variables in the governing equations of the model. Thereby, any changes to the environment can be naturally reflected in the survival, movement and competition of the species within the ecosystem. In this thesis, detailed investigations of several mathematical models for population growth are presented. Formulating the carrying capacity as being time-dependent was the fundamental approach used to describe a varying environment, which resulted in the investigation of a nonautonomous equation [l,4]. This approach led to models that directly couple the dynamics of one or two species with their environments. To obtain this result, the carrying capacity was modelled as a state-variable 151. In these models, the ultimate state for the ecosystem depends on the resource enrichment ' parameter that was found to have significant impact on the growth of a population. leading to either coexistence or extinction of a particular species 12, 31. Other dynamical behaviours, including oscillations in population, have also been found to exist [2].

Item Type: Article
Subjects: Q Science > QH Natural history
Divisions: Faculty of Applied Science and Technology > Department of Mathematics and Statistic
Depositing User: Normajihan Abd. Rahman
Date Deposited: 29 Feb 2016 08:41
Last Modified: 29 Feb 2016 08:41
URI: http://eprints.uthm.edu.my/id/eprint/7686
Statistic Details: View Download Statistic

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