Stability Analysis of A Typical Three Species Syn-Eco-System With Unlimited Resources

B. Hari Prasad1 and N. Ch. Pattabhi Ramacharyulu2
1Department of Mathematics, Chaitanya Degree and PG College (Autonomous), Hanamkonda, Telangana, India-506 001, E-Mail:

2Professor (Retd) of Mathematics, NIT, Warangal, India. E-mail:


The present investigation is an analytical study of three species (S1, S2, S3) syn-eco system with unlimited resources. 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. The model equations constitute a set of three first order non-linear simultaneous coupled differential equations. All possible equilibrium points of the model are identified. The system would be stable, if all the characteristic roots are negative, in case they are real and have negative real parts, in case they are complex. Trajectories of the perturbations over the equilibrium states are illustrated and the numerical solutions for the growth rate equations are computed using Runge-Kutta fourth order scheme.

Keywords: Commensal, Equilibrium state, Host, Trajectories, Unstable.

AMS Classification: 92D25, 92D40






International eJournal of Mathematical Sciences, Technology and Humanities

Volume 4, Issue 3, Pages:  1309 - 1316