Journal of Applied Mathematics

Stability Analysis of Competing Insect Species for a Single Resource

Sizah Mwalusepo, Henri E. Z. Tonnang, Estomih S. Massawe, Tino Johansson, and Bruno Pierre Le Ru

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Abstract

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.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 285350, 14 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305874

Digital Object Identifier
doi:10.1155/2014/285350

Mathematical Reviews number (MathSciNet)
MR3232908

Citation

Mwalusepo, Sizah; Tonnang, Henri E. Z.; Massawe, Estomih S.; Johansson, Tino; Le Ru, Bruno Pierre. Stability Analysis of Competing Insect Species for a Single Resource. J. Appl. Math. 2014 (2014), Article ID 285350, 14 pages. doi:10.1155/2014/285350. https://projecteuclid.org/euclid.jam/1425305874


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