王贺元1,2 陈相霆2
1广东科技学院通识教育学院;
摘要: 为揭示混沌的生成机理，探讨了强迫Lorenz模型混沌行为的力学机制。将强迫Lorenz模型转化成柯尔莫哥洛夫系统，把系统的力矩分解成惯性力矩，耗散力矩和外力矩。分析各种力矩耦合模式对系统动力学行为的影响，从中揭示系统生成混沌的力学机理。研究表明只有耗散因素，驱动因素和内能都存在的全力矩模式下，并且驱动因素和耗散因素相匹配时强迫Lorenz系统才能产生混沌。构造卡西米尔（Casimir）函数进行全局稳定性分析，估计强迫Lorenz模型吸引子的边界。
基金资助: 国家自然科学科研基金(11572146)
Mechanical Mechanism Analysis of Forced Lorenz Model
Heyuan Wang1,2, Xiangting Chen2
1.College of General Education, Guangdong University of Science and Technology;
2.College of Mathematics and Systematics Sciences, Shenyang Normal University Abstract：In order to reveal the generation mechanism of chaos, the mechanical mechanism of forced Lorenz model are discussed in this paper. The forced Lorenz model is transformed into Kolmogorov system, and the torques of the system are decomposed into inertial torques, dissipative torques and external torques. The effects of various torque coupling modes on the System dynamics behavior are analyzed to reveal the mechanism of chaos generation. It is shown that only when the dissipation factor, the driving factor and the internal energy exist in the full moment mode, and the driving factor and the dissipation factor match, the forced Lorenz system can produce chaos. The global stability of the forced Lorenz model is analyzed by constructing the Casimir function, and the boundary of the attractor of the forced Lorenz model is estimated.
Keywords: chaos; Kolmogorov system; mechanical mechanism；Casimir function
第一作者：王贺元(1963-），男，辽宁黑山人，博士，教授，毕业于西安交通大学，主要研究方向为非线性系统方面的研究。
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