Chen系统的动力学行为及其吸引子结构的研究

利用受控Chen系统,并基于镜像操作方法,发现Chen吸引子是由左、右两个吸引子所组成的复合结构,且左、右吸引子均可由极限环生成.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Chen系统从规则运动转化到混沌运动所具有的普适特征:Chen系统可通过Pomeau-Manneville途径走向混沌,且其间歇性与Hopf分岔和倍周期分岔有关,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Chen吸引子、Chen系统和Lorenz系统之间的过渡吸引子和类Lorenz吸引子.

Research on Dynamic Activities of Chen System and Structure of Its Attractor

Utilizing the controlled Chen system,and according to the method of the mirror operation,the author find Chen attractor is a compound structure obtained by merging together two simple attractor,i.e.the left-attractor and the right-attractor,and each simple attractor is derived from some simple limit cycle.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 Chen system transforming from regularity to chaos: Chaotic patterns of Chen system may emerge out of Pomeau-Manneville route and its intermittence have something to do with Hopf bifurcation and period-doubling bifurcation.On these routes,we can observe not only phase locking and quasiperiodic motion,but also the similar Chen attractor,the transitional attractor which lies between the Chen system and Lorenz system,and the Lorenz similar attractor.