Complicated behavior and mechanism of Chen system with slowly variable control

Zhang Xiao-Fang; Han Qing-Zhen; Chen Xiao-Ke; Bi Qin-Sheng

doi:10.7498/aps.63.180503

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:

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).

References

[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]

Cited By

[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]

[1]	Zhao Wu, Zhang Hong-Bin, Sun Chao-Fan, Huang Dan, Fan Jun-Kai. Subharmonic resonance bifurcation and chaos of simple pendulum system with vertical excitation and horizontal constraint. Acta Physica Sinica, 2021, 70(24): 240202. doi: 10.7498/aps.70.20210953
[2]	Jiang Yi-Lan, Lu Bo, Zhang Wan-Qin, Gu Hua-Guang. Fast autaptic feedback induced-paradoxical changes of mixed-mode bursting and bifurcation mechanism. Acta Physica Sinica, 2021, 70(17): 170501. doi: 10.7498/aps.70.20210208
[3]	Yang Yong-Xia, Li Yu-Ye, Gu Hua-Guang. Synchronization transition from bursting to spiking and bifurcation mechanism of the pre-Bötzinger complex. Acta Physica Sinica, 2020, 69(4): 040501. doi: 10.7498/aps.69.20191509
[4]	Zheng Lai-Yun, Zhao Bing-Xin, Yang Jian-Qing. Bifurcation and nonlinear evolution of convection in binary fluid mixtures with weak Soret effect. Acta Physica Sinica, 2020, 69(7): 074701. doi: 10.7498/aps.69.20191836
[5]	Cao Ben, Guan Li-Nan, Gu Hua-Guang. Bifurcation mechanism of not increase but decrease of spike number within a neural burst induced by excitatory effect. Acta Physica Sinica, 2018, 67(24): 240502. doi: 10.7498/aps.67.20181675
[6]	Yu Yue, Zhang Chun, Han Xiu-Jing, Jiang Hai-Bo, Bi Qin-Sheng. Oscillations and non-smooth bifurcation analysis of Chen system with periodic switches. Acta Physica Sinica, 2013, 62(2): 020508. doi: 10.7498/aps.62.020508
[7]	Li Hai-Bin, Wang Bo-Hua, Zhang Zhi-Qiang, Liu Shuang, Li Yan-Shu. Combination resonance bifurcations and chaos of some nonlinear relative rotation system. Acta Physica Sinica, 2012, 61(9): 094501. doi: 10.7498/aps.61.094501
[8]	Li Qun-Hong, Yan Yu-Long, Yang Dan. Bifurcations in coupled electrical circuit systems. Acta Physica Sinica, 2012, 61(20): 200505. doi: 10.7498/aps.61.200505
[9]	Jiang Hai-Bo, Zhang Li-Ping, Chen Zhang-Yao, Bi Qin-Sheng. Non-smooth bifurcation analysis of Chen system via impulsive force. Acta Physica Sinica, 2012, 61(8): 080505. doi: 10.7498/aps.61.080505
[10]	Li Xiang-Hong, Bi Qin-Sheng. Bursting oscillations and the bifurcation mechanism in oxidation on platinum group metals. Acta Physica Sinica, 2012, 61(2): 020504. doi: 10.7498/aps.61.020504
[11]	Ji Ying, Bi Qin-Sheng. Bifurcation analysis of slow-fast behavior in modified Chua's circuit. Acta Physica Sinica, 2012, 61(1): 010202. doi: 10.7498/aps.61.010202
[12]	Wu Shu-Hua, Sun Yi, Hao Jian-Hong, Xu Hai-Bo. Bifurcation and dual-parameter characteristic of the coupled dynamos system. Acta Physica Sinica, 2011, 60(1): 010507. doi: 10.7498/aps.60.010507
[13]	Zhang Yin, Bi Qin-Sheng. Non-smooth bifurcation in nonlinear electrical circuits with multiple switching boundaries. Acta Physica Sinica, 2011, 60(7): 070507. doi: 10.7498/aps.60.070507
[14]	Zhang Bo, Xie Fan, Yang Ru. Study on border collision and bifurcation of two-dimensional piecewise smooth systems in current mode controlled Buck converter. Acta Physica Sinica, 2010, 59(12): 8393-8406. doi: 10.7498/aps.59.8393
[15]	He Xue-Jun, Zhang Liang-Xin, Ren Ai-Di. The study of stability and bifurcation of highline cable of alongside replenishment system. Acta Physica Sinica, 2010, 59(5): 3088-3092. doi: 10.7498/aps.59.3088
[16]	Chen Zhang-Yao, Bi Qin-Sheng. Bifurcations and chaos of coupled Jerk systems. Acta Physica Sinica, 2010, 59(11): 7669-7678. doi: 10.7498/aps.59.7669
[17]	Chen Zhang-Yao, Zhang Xiao-Fang, Bi Qin-Sheng. Bursting phenomenon and the bifurcation mechanism in generalized Chua’s circuit. Acta Physica Sinica, 2010, 59(4): 2326-2333. doi: 10.7498/aps.59.2326
[18]	Ma Xi-Kui, Yang Mei, Zou Jian-Long, Wang Ling-Tao. Study of complex behavior in a time-delayed van der Pol’s electromagnetic system (Ⅰ)——The phenomena of bifurcations and chaos. Acta Physica Sinica, 2006, 55(11): 5648-5656. doi: 10.7498/aps.55.5648
[19]	Li Ming, Ma Xi-Kui, Dai Dong, Zhang Hao. Analysis of bifurcation and chaos in a class of piecewise smooth systems based on symbolic sequence. Acta Physica Sinica, 2005, 54(3): 1084-1091. doi: 10.7498/aps.54.1084
[20]	Song Xiao-Hong, Lin Sheng-Lu. A study of the bifurcation effect of closed orbits on the recurrence spectra of Li Rydberg atoms in an external electric field. Acta Physica Sinica, 2003, 52(7): 1611-1616. doi: 10.7498/aps.52.1611

Catalog

Vol. 63, Issue 18 - 2014-09-20

Metrics

Abstract views: 5751
PDF Downloads: 537
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板