快慢耦合振子的张驰簇发及其非光滑分岔机制

张晓芳; 陈小可; 毕勤胜

doi:10.6052/0459-1879-2012-3-20120314

快慢耦合振子的张驰簇发及其非光滑分岔机制

doi: 10.6052/0459-1879-2012-3-20120314

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(10872080)和江苏大学高级人才基金(10JDG144)资助项目.

详细信息

中图分类号: O322
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出版历程
- 收稿日期: 2011-09-23
- 修回日期: 2011-12-06
- 刊出日期: 2012-05-18

RELAXATION BURSTING OF A FAST-SLOW COUPLED OSCILLATOR AS WELL AS THE MECHANISM OF NON-SMOOTH BIFURCATION

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

Funds: The project was supported by the National Natural Science Foundation of China (10872080) and the Senior Qualified PersonalFoundation of Jiangsu University, China (10JDG144)

摘要

摘要: 通过引入适当的参数值, 得到了两时间尺度下的快慢耦合振子, 分析了耦合系统及子系统的平衡点及其性质, 进而利用微分包含理论, 探讨了非光滑分界面上的奇异性, 指出在适当的参数条件下, 系统轨迹在穿越分界面时会产生由Hopf分岔和Fold分岔组合的非常规分岔. 给出了不同参数条件下的周期簇发行为, 分析了簇发过程的振荡特性, 指出激发态的频率取决于快子系统在非光滑分界面上的Hopf分岔频率, 而慢子系统的固有频率影响了簇发行为的振荡周期, 并进一步揭示了由非光滑分岔引起的不同周期簇发的分岔机制.
- 非光滑 /
- 簇发 /
- 分岔 /
- 耦合 /
- 快慢系统
Abstract: By introducing suitable values of the parameters, a fast-slow coupled oscillator has been obtained. Under the analysis of the equilibrium points as well as the characteristics of the coupled system and the subsystems, combining the theory of Clarke differential inclusions, the singularities on the non-smooth boundaries are explored, which reveals that the non-conventional bifurcation composed of Hopf bifurcation and Fold bifurcation may occur when the trajectory passes across the boundary for suitable parameters. Different types of bursting phenomena associated with the corresponding parameters conditions have been obtained, the oscillating characteristics of which is discussed in details. It is pointed out that the frequency of the spiking in bursters may depend on the frequency related to Hopf bifurcation of the fast subsystem on the non-smooth boundary, while the natural frequency of the slow subsystem may influence the oscillating period of the bursters. The bifurcation mechanism of the different periodic bursters caused by the non-smooth bifurcation are presented in the end.
- non-smooth /
- bursting /
- bifurcation /
- coupling /
- fast-slow system

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参考文献(15)

Chiba H. Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points. J Differential Equations, 2011, 250: 112-160

Mease KD. Multiple time-scales in nonlinear flight mechanics: diagnosis and modeling. Appl Math Comput, 2005, 164: 627-648

Wang HX, Wang QY, Lu QS. Bursting oscillations, bifurcation and synchronization in neuronal systems. Chaos Solitons Fract, 2011, 44: 667-675

Rinzel J. Bursting oscillation in an excitable membrance model. In: Sleeman B D, Jarvis R J, eds. Ordinary and Partial Differential Equations. Berlin: Springer-Verlag, 1985. 304-316

Lashina EA, Chumakova NA, Chumakov GA, et al. Chaotic dynamics in the three-variable kinetic model of CO oxidation on platinum group metals. Chem Eng J, 2009, 154: 82-87

Jia Z, Leimkuhler B. A parallel multiple time-scale reversible integrator for dynamics simulation. Future Generation Comp Syst, 2003, 19: 415-424

刘永强, 雷文, 吴捷等. 多时间尺度电力系统的模型降阶及稳定性分析(二)电力系统的降阶与中长期失稳. 电力系统自动化, 2003, 27:45-51 (Liu Yongqiang, Lei Wen, Wu Jie, et al. Order reduction and stability analysis for multi-time scale power systems (Part Two) Order reduction and loss of mid-term and long-term stability. Autom Elec Power Syst, 2003, 27:45-51 (in Chinese))

Harvey E, Kirk V, Wechselberger M, et al. Multiple timescales, mixed mode oscillations and canards in models of intracellular calcium dynamics. J Nonli Sci, 2011, 21: 639-683

Both R, Finger W, Chaplain RA. Model predictions of the ionic mechanisms underlying the beating and bursting pacemaker characteristics of molluscan neurons. Biol Cybernetics, 1976, 23: 1-11

Lu QS, Yang ZQ, Duan LX, et al. Dynamics and transitions of firing patterns in deterministic and stochastic neuronal systems. Chaos Solitons Fract, 2009, 40: 577-597

Perc M, Marhl M. Different types of bursting calcium oscillations in non-excitable cells. Chaos Solitons Fract, 2003, 18: 759-773

Izhikevich EM. Neural excitability, spiking and bursting. Int J Bifur Chaos, 2000, 10: 1171-1266

Shil'nikov LP. Chua's circuit: rigorous results and future problems. IEEE Trans Circuits Sys, 1993, 40: 784-786

Koliopanos CL, Kyprianidis IM, Stouboulos IN, et al. Chaotic behaviour of a fourth-order autonomous electric circuit. Chaos Solitons Fract, 2003, 16: 173-182

禹思敏, 禹之鼎. 一个新的五阶超混沌电路及其研究. 物理学报, 2008, 57: 6859-6867 (Yu Simin, Yu Zhiding. A novel fifth-order hyperchaotic circuit and its research. Acta Phys Sin,2008, 57:6859-6867 (in Chinese))

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