POINCARE-LIKE CELL MAPPING METHOD AND ITS APPLICATION
Poincare型胞映射分析方法及其应用

A Poincare-like Cell Mapping method fit for both autonomous and periodic nonautonomous nonlinear dynamic systems is presented in this paper. Compared with the traditional Cell Mapping method, the new one has apparent advantages in practice due to introduction of Poincare section, and can be widely used in high dimension nonlinear dynamic systems. Using this new method, the global characteristic of balanced and unbalanced bearing rotor nonlinear dynamic systems are analyzed in this paper. The periodic solutions of these systems and their domains of attraction are given at the same time, so some new phenomenon and rules are got here. Comparing the global characteristic of balanced bearing rotor systems with that of unbalanced bearing rotor systems, some reference are given to establish the new stability rule for nonlinear balanced and unbalanced bearing rotor systems. At last, this paper also gives the theoretical explanation for great dispersion of logarithmic decrement of bearing rotor system.