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

doi:10.1088/1674-1056/25/7/070501

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

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

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