Chaotic Behavior Analysis And Simulation Study Of Lorenz Models Such As The Rotating Rayleigh-Bénard Proble

The classical Lorenz model is one of the representative systems in the field of chaos.This paper mainly studies the dynamic behavior and simulation of the Lorenz model of the rotating Rayleigh-Bénard problem,the five-mode Lorenz-like model of the plane incompressible Navier-Stokes equation and the external-forced Lorenz model.There are formal differences between the Lorenz models of different problems,which leads to different research focuses on each Lorenz model.For the Lorenz model of the rotating Rayleigh-Bénard problem,the global stability of the Lorenz model of the rotating Rayleigh-Bénard problem is analyzed by using the Lyapunov second method,and the mathematical proof of the existence of the global attractor is given.The dynamic behavior of the system is analyzed by numerical simulation results.By using the truncated spectral method,the Navier-Stokes equation is expanded on the plane and truncated.After selecting a new model,a new five-mode Lorenz-like system for the plane incompressible Navier-Stokes equation is obtained.Combined with the numerical simulation results,the dynamic behavior of the new five-mode Lorenz-like system for the plane incompressible Navier-Stokes equation is discussed.The Lorenz model subjected to external force is transformed into a Kolmogorov system,and the influence of the coupling between various moments in the Kolmogorov system on the dynamic behavior of the system is analyzed.The Casimir function is constructed to judge the relationship among equilibrium point,trajectory and energy conversion.Combined with the numerical simulation results,it can be seen that the existence of all torques is a necessary condition for the system to generate chaos,and the matching of the dissipation term and the driving term is the key factor to generate chaos.The introduction of the Casimir function not only analyzes the cause of chaos from the perspective of energy,but also obtains a clear boundary of the attractor of the externally forced Lorenz model.