DYNAMICAL BEHAVIORS ANALYSIS AND NUMERICAL SIMULATION OF THE LORENZ-TYPE SYSTEM FOR COUETTE-TAYLOR FLOW

In this paper, we investigate the problem of dynamical behaviors and numerical simulation of the Lorenz-type systems for the incompressible flow between two concentric rotating cylinders. The estimation of Hausdorff dimension of its attractor is discussed, and the globally exponentially attractive set and positive invariant set of the chaotic system are studied via Lyapunov function. We present a detailed numerical result of the whole process from bifurcation to chaos, and analyze the evolutionary mechanism of the dynamical behavior of the system. Moreover, by using numerical simulation results of attractors, bifurcation diagram, Lyapunov exponent spectrum and Poincare map, return map of the system we show abundant and complex dynamical behaviors of the system, and explain successive transitions of Couette-Taylor flow from Laminar flow to turbulence in the experiment.