慢变控制下Chen系统的复杂行为及其机理

张晓芳; 韩清振; 陈小可; 毕勤胜

doi:10.7498/aps.63.180503

摘要

由于Chen系统的控制分析大都是基于同一时间尺度，而两时间尺度耦合问题的相关研究基本上局限于单维慢变量情形. 本文探讨了基于慢时间尺度上的Duffing振子，即含有两维慢子系统控制下Chen系统的动力学演化过程. 给出了诸如对称式fold/fold、对称式fold/Hopf、对称式homoclinic/homoclinic等不同形式的簇发振荡行为，并揭示了其相应的产生机制，指出慢子系统中两维慢变量的相互影响导致系统产生了类似于周期激励下的簇发行为.

关键词:

Chen系统 /
簇发 /
分岔 /
快慢效应

Abstract

Since most of the work relevant to the control of Chen system is based on the same time scale, and the results associated with the coupled systems with two time scales are mainly for the cases with only one slow variable, in this paper we investigate the dynamical evolution of the Chen system with the controller described by Duffing oscillator on a slow time scale, which implies two slow variables may be involved in the coupled vector field. Different types of bursting oscillations such as the symmetric fold/fold bursting, symmetric fold/Hopf bursting, symmetric homoclinic/homoclinic bursting, and mechanism are presented, revealing that the mutual influence between the two slow variables may cause the bursting behaviors similar to those in the periodic excited systems.

Keywords:

作者及机构信息

1.
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（批准号：21276115）资助的课题.

Authors and contacts

1.
Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 21276115).

参考文献

[1]	Hadef S, Boukabou A 2014 J. Franklin Inst. 351 2728
[2]	Smaoui N, Karouma A, Zribi M 2011 Commun. Nonlinear Sci. Numer. Simul. 16 3279
[3]	Alhajaj A, Dowell N M, Shah N 2013 Energy Procedia 37 2552
[4]	Powathil G G, Gordon K E, Hill L A, Chaplain M A 2012 J. Theor. Biol. 308 1
[5]	Bridge J, Mendelowitz L, Rand R, Sah S, Verdugo A 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1598
[6]	Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[7]	Gyorgui L 1992 Field R J. Nature 355 808
[8]	Shen J H, Zhou Z Y 2013 Commun. Nonlinear Sci. Numer. Simul. 18 2213
[9]	Shinizu K, Sekikawa M, Inaba N 2011 Phys. Lett. A 375 1566
[10]	Han X J, Jiang B, Bi Q S 2009 Phys. Lett. A 373 3643
[11]	Shi M, Wang Z H 2014 Commun. Nonlinear Sci. Numer. Simul. 19 1956
[12]	Wang Q Y, Aleksandra M, MAtjaz P, Lu Q S 2011 Chin. Phys. B 20 040504
[13]	L Y B, Shi X, Zheng Y H 2013 Chin. Phys. B 22 040505
[14]	Wang M J, Zeng Y C, Chen G H, He J 2011 Acta Phys. Sin. 60 010509(in Chinese)[王梦蛟, 曾以成, 陈光辉, 贺娟 2011 物理学报 60 010509]
[15]	Zhang X F, Chen Z Y, Bi Q S 2010 Acta Phys. Sin. 59 3802(in Chinese)[张晓芳, 陈章耀, 毕勤胜 2010 物理学报 59 3802]

施引文献

[1]	Hadef S, Boukabou A 2014 J. Franklin Inst. 351 2728
[2]	Smaoui N, Karouma A, Zribi M 2011 Commun. Nonlinear Sci. Numer. Simul. 16 3279
[3]	Alhajaj A, Dowell N M, Shah N 2013 Energy Procedia 37 2552
[4]	Powathil G G, Gordon K E, Hill L A, Chaplain M A 2012 J. Theor. Biol. 308 1
[5]	Bridge J, Mendelowitz L, Rand R, Sah S, Verdugo A 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1598
[6]	Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[7]	Gyorgui L 1992 Field R J. Nature 355 808
[8]	Shen J H, Zhou Z Y 2013 Commun. Nonlinear Sci. Numer. Simul. 18 2213
[9]	Shinizu K, Sekikawa M, Inaba N 2011 Phys. Lett. A 375 1566
[10]	Han X J, Jiang B, Bi Q S 2009 Phys. Lett. A 373 3643
[11]	Shi M, Wang Z H 2014 Commun. Nonlinear Sci. Numer. Simul. 19 1956
[12]	Wang Q Y, Aleksandra M, MAtjaz P, Lu Q S 2011 Chin. Phys. B 20 040504
[13]	L Y B, Shi X, Zheng Y H 2013 Chin. Phys. B 22 040505
[14]	Wang M J, Zeng Y C, Chen G H, He J 2011 Acta Phys. Sin. 60 010509(in Chinese)[王梦蛟, 曾以成, 陈光辉, 贺娟 2011 物理学报 60 010509]
[15]	Zhang X F, Chen Z Y, Bi Q S 2010 Acta Phys. Sin. 59 3802(in Chinese)[张晓芳, 陈章耀, 毕勤胜 2010 物理学报 59 3802]

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