由多平衡态快子系统所诱发的簇发振荡及机理

陈章耀; 陈亚光; 毕勤胜

doi:10.6052/0459-1879-14-353

由多平衡态快子系统所诱发的簇发振荡及机理

江苏大学土木工程与力学学院, 镇江212013

基金项目: 国家自然科学基金项目(20976075, 11472115, 11302136, 11472116) 和镇江市工业支撑项目(GY2013032, GY2013052) 资助.

详细信息

通讯作者:
陈章耀, 副教授, 主要研究方向:非线性动力学. E-mail:zychen@ujs.edu.cn

中图分类号: O322
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出版历程
- 收稿日期: 2014-11-15
- 修回日期: 2015-04-19
- 刊出日期: 2015-07-17

BURSTING OSCILLATIONS AS WELL AS THE BIFURCATION MECHANISM INDUCED BY FAST SUBSYSTEM WITH MULTIPLE BALANCES

Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China

Funds: The project was supported by the National Natural Science Foundation of China (20976075, 11472115, 11302136, 11472116) and the Scientific and Technological Foundation of Zhenjiang, China (GY2013032, GY2013052).

摘要

摘要: 通过引入子电路模块, 并选取适当的参数及非线性电阻特性, 建立了多时间尺度下具有多平衡态的四维广义哈特利(Hartley) 电路模型. 基于快子系统的多平衡态及其稳定性, 给出了参数空间的分岔集, 得到了不同区域中的动力学特性及其相应的分岔模式和临界条件. 针对两种典型具有不同分岔特征的情形, 分别给出了多平衡态参与下的两种不同的周期簇发振荡行为, 结合快子系统的分岔分析, 揭示了沉寂态和激发态之间相互转化的产生机制, 指出多平衡态不仅会导致多种沉寂态和激发态同时参与同一周期簇发振荡, 也会导致簇发振荡模式的多样性.
- 多平衡态 /
- 多时间尺度 /
- 簇发振荡 /
- 分岔机理
Abstract: By introducing subcircuit module and taking suitable values for the parameters as well as the characteristics of the nonlinear resistance, a four-dimensional generalized Hartley model whose fast subsystem has multiple balances is established. Based on the multiple balances as well as stabilities of the fast subsystem, bifurcation sets are derived, which divide the parameter space into different regions. In each region, nonlinear dynamical behaviors as well as the bifurcation patterns corresponding to different critical conditions are obtained. Two typical cases with different bifurcations are investigated, in which two different bursting oscillations with multiple balances of the fast subsystem involved are presented. Combining with the bifurcation analysis of the fast subsystem, the mechanism of the alternation between quiescent state and the spiking state is explored, which reveals that multiple balances of the fast subsystem not only may cause multiple quiescent states and spiking states to involve a periodic burster simultaneously, but also may lead to the multiplicity of patterns of bursting oscillations.
- multiple balances /
- multiple time scales /
- bursting oscillation /
- bifurcation mechanism

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