| The dynamical behaviors, chaos simulation and control of three chaotic systems are investigated in this paper. Couette-Taylor flow system which between coaxial cylinder rotational flow, Lorenz-84 system and the four-dimensional system are analyzed. This text researched the simulation of those three systems. And aimed at the Couette-Taylor flow system, I discussed the control and synchronization of that.Firstly, this article described the chaos with basic knowledge and research status, generalized the development research of three chaotic systems.Aimed at the Couette-Taylor flow system, this paper analyzed its dynamical behavior and simulation. We presented the evolutionary history of bifurcation and chaos of this model. Moreover, using these results we explained successive transitions of Couette-Taylor flow from laminar flow to turbulence in the experiment, and the chaotic behavior of the Couette-Taylor flow is simulated and analyzed from one side. Based on Lyapunov function the globally exponentially attractive set and positive invariant set of the chaotic system are studied. Drive-Response methods is used to achieve the globally exponentially synchronization. The effectiveness of these methods has been showed by numerical simulation results.Secondly, the dynamical behavior and numerical simulation of the Lorenz-84 system and the four-dimensional system are analyzed. We present the evolutionary history of bifurcation and chaos of two models respectively. Based on Lyapunov function the globally exponentially attractive set and positive invariant set of the two chaotic systems are studied. We described the dynamic behavior of the two systems by Lyapunov index map, bifurcation diagrams, attractor diagrams and Poincare sectional view. These showed that on some parameters interval, two systems exist chaos. Results of simulation and analysis for future climate projections provide research data and theoretical basis. |
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