A Study on Host Mortality Rate of a Three Species Multi Ecology with Unlimited Resources for the First Species

B. Hari Prasad
2017 Journal of Asian Scientific Research  
Article History Keywords Commensal Equilibrium state Host Trajectories Neutrally stable Stable Unstable. The purpose of this paper is to examine the stability analysis of a three species ecology with mortality rate for the host. The system comprises of a commensal (S1), two hosts S2 and S3 ie, S2 and S3 both benefit S1, without getting themselves affected either positively or adversely. Further the first species has unlimited resources. The model equations constitute a set of three first order
more » ... on-linear coupled ordinary differential equations. Criteria for the asymptotic stability of all the four equilibrium states are established. Trajectories of the perturbations over the equilibrium states are illustrated and the global stability of the system is established with the aid of suitably constructed Liapunov's function and finally fourth order Runge-Kutta method is applied to obtain numerical solutions of the growth rate equations. Contribution/ Originality: The paper contributes the first logical analysis in biological investigations with an iterative procedure of information collection. If such models are properly developed and used, they can provide insight into the relations between the physical variables and process influencing the system being studied. The resulting interplay between the experimental investigation and the theoretical model can be an essential factor in designing experiments and in the interpretation of data. Mathematical modeling has been playing an important role for the last half a century in explaining several phenomena concerned with individuals and groups of populations in nature. The general concept of modeling has been presented in the monographs of Meyer [3]; Kushing [4]; Paul [5]; Kapur [6]. Srinivas [7] studied competitive ecosystem of two species and three species with limited and unlimited resources. Lakshmi [8]; Lakshmi and Pattabhiramacharyulu [9] studied prey-predator ecological models with partial cover for the prey and alternate food for the predator. Stability analysis of competitive species was carried out by Archana, et al. [10] and by Bhaskara and Pattabhiramacharyulu [11] while Ravindra [12] investigated mutualism between two species.
doi:10.18488/journal.2.2017.74.134.144 fatcat:bgkm2qrqkjb5naiz6wl4vdr4km