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Population Dynamics Model for Coexistence of Three Interacting Species
Applied and Computational Mathematics
Volume 4, Issue 4, August 2015, Pages: 258-263
Received: May 31, 2015; Accepted: Jun. 11, 2015; Published: Jun. 29, 2015
Authors
M. Rafique, Department of Mathematics, Faculty of Science, HITEC University, Taxila, Pakistan
M. Abdul Qader, Department of Mathematics, Faculty of Science, HITEC University, Taxila, Pakistan
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Abstract
Over the years applications of mathematics in the form of mathematical modeling in a whole range of different fields including physical, social, management, biological, and medical sciences have broken all bounds. In particular, the mathematical models to study population dynamics of various interacting species in an isolated environment have attracted the attention of mathematical biologists. In nature, there may be two, three, or more species interacting within themselves giving rise to the corresponding predator-prey models. In each case, both predator and prey evolve their own strategies to deal with the situation. The parameters which influence both the predator and the pry to evoke strategies for their survival include environmental conditions, predator’s appetite, aggressiveness, liking for some particular prey, its physical fitness versus that of the prey, prey’s agility, active prudence to run away or hide, etc. In the literature interactions between, two, three or more species, sharing the same habitat have been discussed in detail. In this paper we present a model pertaining to the interaction between three species. It is a realistic model in which three species, x, y and z, interact within themselves in such a way that species y (predator) preys on species x (prey), while the species z preys on both the species x and y. Accordingly, the resulting situation has been analyzed. The objective of this paper is to analyze the possibility for three interacting species to live in an isolated environment harmoniously. The model presented here has three equilibrium points, however, only one of them has been ascertained to be locally stable. The existence of this equilibrium point signifies amicable coexistence of the three species, if no outside intervention accrues any destabilization to the existing environment.
Keywords
Malthusian Growth Model, Carrying Capacity of Environment, Logistic Equation, Malthus-Verhulst Equation, Lotka-Volterra Equations, Equilibrium Point, Jacobian Matrix
M. Rafique, M. Abdul Qader, Population Dynamics Model for Coexistence of Three Interacting Species, Applied and Computational Mathematics. Vol. 4, No. 4, 2015, pp. 258-263. doi: 10.11648/j.acm.20150404.14
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