基于Vanecek和Celikovsky对三维自治系统的分类方法,本文给出了介于Lorenz系统和Chen系统之间的新系统。采用一维时间序列相空间重构技术和系统混沌的定量判据准则,揭示出新系统从规则运动转化到混沌运动所具有的普适特征:新系统可通过Pomeau-Manneville途径走向混沌,且其间歇性与Hopf分岔有关,在这些途径上既可观察到锁相和准周期运动,也可观察到类Lorenz吸引子、Lorenz系统和Chen系统之间的过渡吸引子、类Chen吸引子和与前三者具有不同结构特征的奇怪吸引子。
Based on Vanecek and Celikovsky's classification method to three-dimensional autonomous system, this paper puts forward a new system which connects the Lorenz system and Chen's system. By using phase space reconstruct technique from a time series and the quantitative criterion and rule of system chaos, the author reveal the general features of the new system transforming from regularity to chaos: chaotic patterns of the new system may emerge out of Pomeau-Manneville route and its intermittence have something to do with Hopf bifurcation. On these routes, we can observe not only phase locking and quasiperiodic motion, but also the similar Lorenz attractor, the transitional attractor which lies between the Lorenz system and Chen system, the similar Chen attractor, and the strange attractor which has different structure features from the former attractors.