A Stability Analysis on Models of Cooperative and Competitive Species (original) (raw)
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The present paper is devoted to an analytic investigation of a three species syn-eco system comprising two mutually helping species, both amensol on a third species. All possible equilibrium points are identified and their stability criteria is discussed by using Routh-Hurwitz criteria. Further, the analytical results are supported by numerical simulation using Mat Lab. 1. Introduction. Every since research in the discipline of theoretical ecology was initiated by Lotka [8] and by Volterra [15], several mathematicians and ecologists contributed in the growth of this area of knowledge, which has been extensively reported in the treatises of Meyer [9],Cushing [2], Paul Conlinvaux [10], Freedman [3], Kanpur [5,6]. The ecological interactions can be broadly classified as prey-predation, competitions, neutralism, and mutualism and so on. N. C Srinivas [14] studied the competitive ecosystem of two species and three species with regard to limited and unlimited resources. Later, Lakshmi Narayan [7] has investigated the two species prey-predator models. Recently stability analysis of competitive species was investigated by Archana Reddy [1]. Local stability analysis for two-species ecological mutualism model has been presented by B. Ravindra Reddy et al [11]. Recently, stability analysis of prey, two predators which are neutral to each other [12], prey, predator and super-predator [13] were carried out by Shiva Reddy and N. Ch. Pattabhi Ramacharyulu. The present investigation is an analytical study of three species system comprising two mutualistic spices, which are amonsolon third species. The model is represented by a system of three ordinary differential equations. All possible equilibrium points are identified and their stability was discussed using Routh-Hurwitz criteria. Further solutions of quasi-linearized equations are identified and the results are simulated by Numerical examples using Mat Lab.