Couette-Taylor流三模系统的混沌行为及其仿真  

The Chaos Behavior and Simulation of Three Model Systems of Couette-Taylor Flow

作　　者：王贺元[1] 

机构地区：[1]辽宁工业大学理学院,辽宁锦州121001

出　　处：《数学物理学报（A辑）》2015年第4期769-779,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(41174090);锦州市科技专项基金(13A1D32)资助

摘　　要：研究了旋流式Couette-Taylor流三模态类Lorenz系统的动力学行为及其数值仿真问题.给出了此系统平衡点存在的条件,证明了其吸引子的存在性,给出了吸引子的Hausdorff维数上界的估计,数值模拟了系统分歧和混沌等的动力学行为发生的全过程,基于分岔图与最大Lyapunov指数谱和庞加莱截面以及功率谱和返回映射等仿真结果揭示了此系统混沌行为的普适特征.The dynamical behavior of a three-mode system of Couette-Taylor problem are studied,which is similar to the Lorenz equation.Condition of the stationary solutions,the existence of its attractor and the estimation of Hausdorff dimension are presented.The whole process,which shows bifurcation and chaos behavior with the changing of Reynolds number,is simulated numerically.Based on numerical simulation results of bifurcation diagram,Lyapunov exponent spectrum,Poincare section,power spectrum and return map of the system,chaos behavior of the system are revealed.

关 键 词：Couette-Taylor流 吸引子 HAUSDORFF维数 

分 类 号：O175.14[理学—数学]