一个统一混沌系统及其研究(英文)

A Unified Chaotic System and Its Research

发现了一个新的混沌系统,它是介于著名的Lorenz系统和Chen系统之间的临界系统。同时,提出了一个单参数的统一混沌系统———Lorenz系统族,它包含Lorenz系统和Chen系统作为参数区间的两个极端系统,临界系统作为一个过渡系统。基于线性耦合多振子互同步问题的研究,提出了研究这一类问题的新方法———模式分解法,并首次从理论上给出了上述 3个典型系统混沌同步的几个严格的充分条件。还提出了一类新的简单的切换分段线性反控制器,它能够使一个简单的线性系统在三维空间中同时产生n个。

Produces a new chaotic system, which is a critical system betweem the Lorenz and Chen systems. At the same time, we introduce a unified chaotic system with single parameter, called Lorenz system families, which contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum, and acritical system as a transition system. Based on the study of the chaos synchronization between linearly coupled multi systems, presents a new method——mode decomposition for analyzing the stability of synchronization solution, some sufficient conditions for synchronization are gained from rigorously mathematical analysis for the first time. Finally, Introduces several new chaos generators,switching piecewise linear controllers, which can create simultaneously n , or one with multiple merged basins of attraction chaotic attractors from a 3 D linear system within a wide range of parameter values.