Abstract: The stability of the fixed points of two-dimensional dynamical system is analyzed through Jacobian matrix and using its Eigen values. The species disappears for λ ∈ (0, 0.75) due to non stable co-existence. The species is synchronized to a stable non-vanishing fixed quantity when λ ∈(0.75, 0.866).Each one of the species oscillates out of phase between the same two fixed values when λ ∈(0.866, 0.957) and the species oscillate among infinitely many different states when λ ∈(0.957, 1.03) but symbiosis model moves towards the chaotic region when the value of the parameter λ crosses one.