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.
By introducing periodically alternated current source as well as suitable values for the parameters to ensure that there exists order gap between the natural frequency and the exited frequency,nonlinear electric circuit with fast-slow effect has been established.Based on the conception of generalized autonomous system and the analysis of the properties of equilibrium points,all possible bifurcation forms have been discussed. Different types of bursting phenomena,such as fold/fold burster,fold/subHopf/supHopf burster,in which the fold or Hopf bifurcations may connect the quiescent states and the spiking states,have been presented.The mechanism of the bursters is explored via bifurcation analysis,which has been illustrated by transformed phase portraits of the generalized autonomous system.
出处
《力学学报》
EI
CSCD
北大核心
2010年第4期765-773,共9页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(10872080
20976075)
江苏大学高级人才启动基金(10JDG062)资助项目~~
关键词
周期激励Hartley模型
广义自治系统
转换相图
簇发现象
periodically excited Hartley model
generalized autonomous system
transformed phase portraits
bursting phenomenon
