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2014 Stability Analysis of Competing Insect Species for a Single Resource
Sizah Mwalusepo, Henri E. Z. Tonnang, Estomih S. Massawe, Tino Johansson, Bruno Pierre Le Ru
J. Appl. Math. 2014: 1-14 (2014). DOI: 10.1155/2014/285350


The models explore the effects of resource and temperature on competition between insect species. A system of differential equations is proposed and analysed qualitatively using stability theory. A local study of the models is performed around axial, planar, and interior equilibrium points to successively estimate the effect of (i) one species interacting with a resource, (ii) two competing species for a single resource, and (iii) three competing species for a single resource. The local stability analysis of the equilibrium is discussed using Routh-Hurwitz criteria. Numerical simulation of the models is performed to investigate the sensitivity of certain key parameters. The models are used to predict population dynamics in the selected cases studied. The results show that when a single species interacts with a resource, the species will be able to establish and sustain a stable population. However, in competing situation, it is observed that the combinations of three parameters (half-saturation, growth rate, and mortality rate) determine which species wins for any given resource. Moreover, our results indicate that each species is the superior competitor for the resource for the range of temperature for which it has the lowest equilibrium resource.


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Sizah Mwalusepo. Henri E. Z. Tonnang. Estomih S. Massawe. Tino Johansson. Bruno Pierre Le Ru. "Stability Analysis of Competing Insect Species for a Single Resource." J. Appl. Math. 2014 1 - 14, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131485
MathSciNet: MR3232908
Digital Object Identifier: 10.1155/2014/285350

Rights: Copyright © 2014 Hindawi


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