旋转的Rayleigh-Bénard问题Lorenz模型的动力学行为及数值仿真

Dynamic behavior and numerical simulation of Lorenz model for rotating rayleigh-bénard problem

基于旋转的Rayleigh-Bénard问题的四维Lorenz方程,探讨了该系统的动力学行为及其数值仿真问题。在文献中线性稳定性分析和局部稳定性分析的基础上,讨论了该系统的全局稳定性。首先借助Young和Gronwall不等式对系统的全局吸引子存在性进行证明,再构造李雅普诺夫函数进行全局稳定性的证明。通过最大李雅普诺夫指数和分岔图观察系统的动力学行为,借助7种混沌指标对系统的动力学行为进行分析。通过对系统的全局稳定性分析可知系统的全局吸引子存在,系统是全局稳定的。通过数值仿真可知,系统的分岔过程和最大李雅普诺夫指数图像相一致;而且随着参量r值的增大,系统是趋于稳定的。

Based on the four-dimensional Lorenz equation of rotating rayleigh-bénard,the dynamic behavior and numerical simulation of the system are discussed.Based on the linear stability analysis and local stability analysis in the literature,the global stability of the system is discussed.For the global stability analysis of the system,firstly,the existence of the global attractor of the system is proved by means of Young inequality and Gronwall inequality,and then the Lyapunov function is constructed to prove the global stability.The dynamic behavior of the system is observed through the maximum Lyapunov exponent and bifurcation diagram,and the dynamic behavior of the system is analyzed with the help of seven chaotic indexes.Through the analysis of the global stability of the system,it is known that the global attractor of the system exists and the system is globally stable.The numerical simulation shows that the bifurcation process of the system is consistent with the maximum Lyapunov exponent image.Moreover,with the increase of parameter value,the system tends to be stable.