[01] B. Hari Prasad, Department of Mathematics, Chaitanya Degree College (Autonomous), Hanamkonda, Telangana State, India.

In this paper, we study on a three species discrete model syn ecology with limited resources. The system comprises of a commensal (S1), two hosts S2 and S3ie., S2 and S3 both benefit S1, without getting themselves effected either positively or adversely. Further S2 is a commensal of S3 and S3 is a host of both S1, S2. 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 and criteria for their stability are discussed. The model would be stable if absolute value of each of the eigen values of the characteristic equation is less than one.

Commensal, Eigen Value, Equilibrium Point, Host, Stable, Unstable

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