Global stability analysis of a two mutualistic species ammnesal on third species with cover for third species

The present work is devoted to an analytical study of a three species syn-ecological model which the first species (X) and second species (Y) are ammensal on the third species (Z). Here first and second species are mutually helping to each other. A Cover is incorporated in the interaction of third species and second species (α31) and the interaction of third species and second species (α32). Equilibrium point (Normal steady state) is identified and local and global stability for Normal steady state is discussed discussed by constructing suitable Lyapunov function. Further, exact solutions of perturbed equations have been derived. The stability analysis is supported by numerical simulation using Mat Lab.