一种时延范德波尔电磁系统中的复杂行为(Ⅰ)——分岔与混沌现象

建立了一种可积的无穷维系统——时延范德波尔电磁系统，采用Poincaré映射分析了系统随参数E和λ变化发生的分岔与混沌现象，发现这种时延系统具有复杂的非线性动力学特性，例如吸引子共存、间歇性混沌、类似边界碰撞分岔通向混沌以及周期增加的现象.在研究系统时间混沌行为的同时，还对空间混沌行为进行了初步分析，通过描绘空间分布图发现时延范德波尔电磁系统随参数E和λ变化时，在空间中会呈现出周期和混沌等不同的图案. 关键词： 分岔 混沌 无穷维系统 时延范德波尔电磁系统

Study of complex behavior in a time-delayed van der Pol's electromagnetic system ( Ⅰ )——The phenomena of bifurcations and chaos

In this paper, a simple infinite dimensional system (time-delayed van der Pol’s electromagnetic system) with rigorous solution is developed. Based on Poincaré mapping of the right-traveling voltage wave at the left end of the transmission line (x=0), the phenomena of bifurcations and chaos are investigated with the variation of system parameters E and λ. Numerical results show that there are very complex nonlinear dynamical behaviors in this time-delayed system, such as attractor co-existing, intermittent chaos, quasi border collision bifurcation to chaos and period-adding phenomena. In the meantime of studying the temporal chaotic behaviors, the spatial chaotic behaviors are preliminarily analyzed. Through depicting spatial distribution profile of the voltages, the different spatial patterns are observed in the time-delayed van der Pol’s electromagnetic system with the variation of system parameters E and λ, such as chaos, period and so on.