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A Stability Analysis on Models of Cooperative and Competitive Species

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Author Affiliations

  • 1Department of Mathematics, Kwame Nkrumah University of Science and Technology, GHANA
  • 2Department of Mathematics, Kwame Nkrumah University of Science and Technology, GHANA
  • 3Department of ICT and Mathematics, Presbyterian University College, GHANA

Res. J. Mathematical & Statistical Sci., Volume 2, Issue (7), Pages 17-22, July,12 (2014)

Abstract

This paper presents a stability analysis on generalised mathematical models for cooperative and competitive species. For each system, we determined all the relevant equilibrium points and analysed the behavior of solutions whose initial conditions satisfy either x1 = 0 or x2 = 0. The curves in the phase plane along which the vector field is either horizontal or vertical were determined. For each of the systems, we described all possible population scenarios using the phase potraits. The cooperative system was found to be stable at one of the two equilibrium points presents and unstable (Saddle) at the other. Four equilibrium points existed for the competitive species model for which the system is stable at one point and locally asymptotically stable at the other three points. The asymptotical stability is based on the inhibition and the coexistence factors between the two competing species.

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