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In this paper a nine-modes truncation of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained.The stationary solutions,the existence of attractor and the global stability of the equations are firmly proved.What is more,that the force f acts on the mode k3 and k7 respectively produces two systems,which lead to a much richer and varied phenomenon.Numerical simulation is given at last,which shows a.stochastic behavior approached through an involved sequence of bifurcations.