耦合电路中的复杂振荡行为分析

讨论了两个非线性电路适当连接后的耦合系统随耦合强度变化的演化过程.给出了两子系统各自的分岔行为及通向混沌的过程，指出原子系统均为周期运动时，耦合系统依然会由倍周期分岔进入混沌，同时在混沌区域中存在有周期急剧增加及周期增加分岔等现象.而当周期运动和混沌振荡相互作用时，在弱耦合条件下，受混沌子系统的影响，原周期子系统会在其原先的轨道邻域内作微幅振荡，其振荡幅值随耦合强度的增加而增大，混沌的特征越加明显，相反，周期子系统不仅可以导致混沌子系统的失稳，也会引起混沌吸引子结构的变化.关键词：非线性电路耦合强度分岔混沌

Complicated oscillations in coupled electrical circuits

The dynamical evolution process of the coupled system connecting two nonlinear electrical circuits with suitable circuit is investigated. The bifurcation behavior as well as the ways to chaos of the two subsystems is presented. It is pointed out when both of the two subsystems behave as periodic, the coupled system may also be led to chaos via cascading of period-doubling bifurcations. Meanwhile, in the chaotic region, critical increase of period as well as period-adding bifurcation can be observed. As to the interaction between periodic movement and the chaotic oscillation, the original periodic subsystem may chaotically oscillate around the original orbit. The amplitude associated with the oscillation increases rapidly, resulting in the obvious chaotic characteristics. On the contrary, the periodic subsystem may not only cause the instability of the chaotic subsystem, but also lead to change of the chaotic structures.