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合电路系统的分岔研究串
Bifurcations in coupled electrical circuit systems
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摘要: 研究了由两个非线性电路系统耦合所构成的系统，给出高维系统平衡点的存在性条件和具体解析形式，分析了平衡点的余维1和余维2分岔，并对极限环进行了延拓，得到比较复杂的分岔形式．两个周期运动的子系统在不同的耦合参数下相互作用时，可能导致周期运动、混沌等丰富的动力学行为，通过对耦合前后平衡点的定性分析，得到了在弱耦合情况下平衡点变为中立型鞍点与分岔图出现的不连续现象之间的联系．Abstract: A coupled system composed of two nonlinear circuit systems is investigated. In this paper, the existence condition and the analytical expressions of equilibrium in higher-dimensional system are derived, and the co-dimension 1 and co-dimension 2 bifurcations of equilibrium are also studied. Furthermore, the complicated bifurcations are obtained through the continuation of limit cycles. It may lead to various dynamical behaviors such as periodic motion, chaos, etc., for the interaction of two subsystems with periodic motions under different coupling parameters. Using the qualitative analysis of equilibrium before and after coupling, the relation between the discontinuity of bifurcation diagram and occurrence of neutral saddle in the case of weak coupling is presented.
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