摘要:
通过在Hartley电路模型中引入周期变化的电流源, 选取适当的参数, 使得周期激励的频率与系统的固有频率之间存在量级上的差距, 从而建立了具有快慢效应的非线性电路. 引入广义自治系统的概念, 分析了其相应的平衡点及各种分岔行为, 给出了不同参数下广义自治系统存在fold分岔以及同时存在fold分岔与Hopf分岔下的两种不同的簇发现象, 即fold/fold簇发现象和fold/subHopf/supHopf簇发现象. 利用广义自治系统的分岔分析方法和转换相图, 揭示了不同簇发现象的产生机制.
Abstract:
By introducing periodically alternated current source aswell as suitable values for the parameters to ensure that there exists ordergap between the natural frequency and the exited frequency, nonlinearelectric circuit with fast-slow effect has been established. Based on theconception of generalized autonomous system and the analysis of theproperties of equilibrium points, all possible bifurcation forms have beendiscussed. Different types of bursting phenomena, such as fold/fold burster,fold/subHopf/supHopf burster, in which the fold or Hopf bifurcations mayconnect the quiescent states and the spiking states, have been presented.The mechanism of the bursters is explored via bifurcation analysis, whichhas been illustrated by transformed phase portraits of the generalizedautonomous system.
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