The dynamical behavior and numerical simulation of a new five-mode system of the plane incompressible Navier-Stokes equations

A new five-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is studied. And its stationary solutions, the existence of an attractor, and the global stability of the equations are firmly established. Several issues, such as basic dynamical behaviors and routes to chaos, are demonstrated numerically by varying the Reynolds number. The system exhibits chaotic behavior approached through an involved sequence of bifurcations. Based on numerical simulation results of the bifurcation diagram, Lyapunov exponent spectrum, Poincaré section, and power spectrum, some basic dynamical behaviors of the new chaos system are revealed.