Please wait a minute...
Chin. Phys. B, 2016, Vol. 25(7): 070501    DOI: 10.1088/1674-1056/25/7/070501
GENERAL Prev   Next  

Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation

Xiaofang Zhang(张晓芳), Lei Wu(吴磊), Qinsheng Bi(毕勤胜)
Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
Abstract  We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system. By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency. Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples, in which different types of bursting oscillations such as subHopf/subHopf burster, subHopf/fold-cycle burster, and double-fold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states (QSs) and the repetitive spiking states (SPs) may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically.
Keywords:  coupled BVP oscillator      two timescales      bursting oscillations      bifurcation mechanism  
Received:  02 June 2015      Accepted manuscript online: 
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 21276115).
Corresponding Authors:  Xiaofang Zhang     E-mail:  xfzhang@ujs.edu.cn

Cite this article: 

Xiaofang Zhang(张晓芳), Lei Wu(吴磊), Qinsheng Bi(毕勤胜) Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation 2016 Chin. Phys. B 25 070501

[1] Yang Z Q, Lu Q S and Li L 2006 Chaos Soliton. Fract. 27 689
[2] Bravo de la Parra R, Arino O, Sánchez E and Auger P 2000 Math. Comput. Model. 31 17
[3] Wang H X, Lu Q S and Wang Q Y 2008 Commun. Nonlinear Sci. Numer. Simulat. 13 1668
[4] Both R, Finger W and Chaplain R A 1976 Biol. Cybernet. 23 1
[5] Han X J, Jiang B and Bi Q S 2010 Nonlinear Dyn. 61 667
[6] Bi Q S and Zhang Z D 2011 Phys. Lett. A 375 1183
[7] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[8] Chen Z Y, Zhang X F and Bi Q S 2009 Acta Phys. Sin. 59 2326 (in Chinese)
[9] Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500
[10] Lewis T J and Rinzel J 2003 J. Comput. Neurosci. 14 283
[11] Li Q S and Zhu R 2004 Chaos Soliton. Fract. 19 195
[12] Valorani M and Goussis D A 2001 J. Comput. Phys. 169 44
[13] Zhang X F, Han Q Z, Cheng X K and Bi Q S 2014 Acta Phys. Sin. 18 180503 (in Chinese)
[14] Wang H X, Wang Q Y and Lu Q S 2011 Chaos Soliton. Fract. 44 667
[15] Zhang X F, Chen Z Y and Bi Q S 2010 Acta Phys. Sin. 59 3802 (in Chinese)
[16] Wu X Q P and Wang L C 2013 Appl. Math. Comput. 219 5303
[17] Han X J, Bi Q S, Zhang C and Yu Y 2014 Nonlinear Dyn. 77 1285
[1] Bursting oscillations in a hydro-turbine governing system with two time scales
Qing-Shuang Han(韩青爽), Di-Yi Chen(陈帝伊), Hao Zhang(张浩). Chin. Phys. B, 2017, 26(12): 128202.
[2] Bifurcation analysis of the logistic map via two periodic impulsive forces
Jiang Hai-Bo (姜海波), Li Tao (李涛), Zeng Xiao-Liang (曾小亮), Zhang Li-Ping (张丽萍). Chin. Phys. B, 2014, 23(1): 010501.
[3] Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode
Zhang Wei-Ya (张玮亚), Li Yong-Li (李永丽), Chang Xiao-Yong (常晓勇), Wang Nan (王楠). Chin. Phys. B, 2013, 22(9): 098401.
[4] Forced bursting and transition mechanism in CO oxidation with three time scales
Li Xiang-Hong (李向红), Bi Qin-Sheng (毕勤胜). Chin. Phys. B, 2013, 22(4): 040504.
[5] Bursting oscillation in CO oxidation with small excitation and the enveloping slow-fast analysis method
Li Xiang-Hong(李向红) and Bi Qin-Sheng(毕勤胜) . Chin. Phys. B, 2012, 21(6): 060505.
[6] Dynamical behaviors of a system with switches between the Rössler oscillator and Chua circuits
Zhang Chun (张春), Yu Yue (余跃), Han Xiu-Jing (韩修静), Bi Qin-Sheng (毕勤胜). Chin. Phys. B, 2012, 21(10): 100501.
[7] Symmetric bursting behaviour in non-smooth Chua's circuit
Ji Ying(季颖) and Bi Qin-Sheng(毕勤胜). Chin. Phys. B, 2010, 19(8): 080510.
No Suggested Reading articles found!