**InternationaleJournals**

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

**B.
Hari Prasad ^{1} and N. Ch. Pattabhi Ramacharyulu^{2}**

^{2}Professor
(Retd) of Mathematics, NIT, Warangal, India. E-mail: pattabhi1933@yahoo.com

**ABSTRACT:**

The present investigation is
an analytical study of three species (S_{1}, S_{2}, S_{3})
syn-eco system with unlimited resources. The system comprises of a commensal (S_{1}),
two hosts S_{2} and S_{3} ie, S_{2} and S_{3}
both benefit S_{1}, 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