A Study on Discrete Model of Three Species Syn-Eco-System with Unlimited Resources for the First Species

1B. Hari Prasad,   2 K.Sandhya Rani and   3P. S. Rama Chandra Rao

1Department of Mathematics, Chaitanya Degree College (Autonomous),  Hanamkonda, Warangal, Telangana-506 001, India. e-mail:

2Department of Mathematics, S.V.S.Group of Institutions,Bheemaram, Hanamkonda, Telangana State, India.

3Department of Mathematics. Kakatiya Institute of Technology & Science, Warangal, Telangana-506015, India.  e-mail:



In this paper, the three species syn eco-system comprises of a commensal (S1), two hosts S2 and S3 ie., S2 and S3 both benefit S1, without getting themselves effected either positively or adversely. Further S2 is a commensal of S3, S3 is a host of both S1, S2 and the first species has unlimited resources. The basic equations for this model constitute as three first order non-linear coupled ordinary difference equations. All possible equilibrium points are identified based on the model equations at two stages and criteria for their stability are discussed.  Further the numerical solutions are computed for specific values of the various parameters and the initial conditions.

Keywords:  Commensal, equilibrium state, host, stable, oscillatory.

2010 Mathematics Subject Classification:  92D25, 92D40


InternationaleJournal of Mathematical Sciences, Technology and Humanities

Volume 6, Issue 1, Pages:  1 - 21