Lorenz-like系统族的不稳定性和混沌机制研究

不稳定性是混沌运动的主要特征之一。对Lorenz-like系统族中那些只有稳定平衡点和无平衡点的混沌系统，经典Lyapunov不稳定性已不足以描述这些系统不稳定现象的本质。本项目主要研究：1）讨论Zhukovskij稳定性和Jacobi稳定性对连续系统极限集结构和混沌吸引子几何结构的影响；2）分析Zhukovskij不稳定和Jacobi不稳定对Lorenz-like系统族混沌复杂性的影响。通过比较不同不稳定性态对Lorenz-like系统生成混沌吸引子的影响，探讨系统混沌的数学机理，希冀在连续微分系统的混沌机制方面，有新的突破。

Instability is one of the main features of chaotic motion. For chaotic systems with stable equilibrium points and no equilibrium points in the Lorenz-like system family, classical Lyapunov instability is not sufficient to describe the nature of instability phenomena in these systems. The main research of this project is as follows: 1) discuss the influence of Zhukovskij stability and Jacobi stability on the limit set structure and chaotic attractor geometry of continuous systems; 2) analyze the instability of Zhukovskij and Jacobi instability on the chaotic complexity of Lorenz-like system family influences. By comparing the influence of different instabilities on the generation of chaotic attractors in Lorenz-like system, we are to explore the mathematical mechanism of chaos. There is a new breakthrough in the chaotic mechanism of continuous differential systems.