Recently study on the rational systems having both a linear numerator and a linear denominator have started extensively by Gerry Ladas and colleagues. This substantial research makes a strong case for studying the behaviour of rational difference equations as well as providing a great deal of information about the behaviour of rational equations with linear terms. But there is no systematically study on the rational systems having quadratic terms about all of dynamics specifically chaotic dynamics. A We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important center manifolds, and study their bifurcation. Saddle-node and period-doubling bifurcation route to chaos are exhibited via numerical simulations.