Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model

doi:10.1088/1674-1056/27/11/110501

Abstract

Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.

Keywords: multiple time scales grazing bifurcation across-sliding bifurcation non-smooth homoclinic bifurcation

Received: 15 May 2018
Revised: 06 July 2018
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	82.40.Bj	(Oscillations, chaos, and bifurcations)

Fund:

Project supported by the National Natural Science Foundation of China (Grant No. 11472116), the Key Program of the National Natural Science Foundation of China (Grant No. 11632008), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX17_1784).

Corresponding Authors: Zhengdi Zhang
E-mail: 747524263@qq.com

Cite this article:

Ran Zhang(张冉), Miao Peng(彭淼), Zhengdi Zhang(张正娣), Qinsheng Bi(毕勤胜) Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model 2018 Chin. Phys. B 27 110501

[1]	Lei Q and Jiang D 2014 J. Chin. Univ. Pet. 9 1415
[2]	Liao X, Li C and Zhou S 2005 Chaos Soliton. Fract. 1 91
[3]	Cai G and Huang J 2007 Int. J. Nonlinear Sci. 3 213
[4]	El-Sayed A M A, Nour H M and Elsaid A 2016 Appl. Math. Model. 5 3516
[5]	Elsonbaty A R and El-Sayed A M A 2017 Nonlinear Dynam. 2 1169
[6]	Agiza H N, Elabbasy E M and El-Metwally H 2009 Nonlinear Anal. -Real 1 116
[7]	Wang Q Y and Lu Q S 2008 International Journal of Bifurcation & Chaos 4 1189
[8]	Elsadany A A, Agiza H N and Elabbasy E M 2013 Appl. Math. Comput. 24 11110
[9]	Gissinger C 2012 Eur. Phys. J. B 4 137
[10]	Hughes D W and Proctor M R E 1990 Nonlinearity 1 127
[11]	Elsonbaty A and Elsadany A A 2017 Chaos Soliton. Fract. 103 325
[12]	Peng M, Zhang Z and Wang X 2017 Adv. Differ. Equ. 1 387
[13]	Wang B and Jian J 2010 Commun. Nonlinear Sci. 15 189
[14]	Yu W Q and Chen F Q 2010 Commun. Nonlinear Sci. 15 4007
[15]	Sokoloff D D 2017 Izv. Phys. Solid Earth 6 855
[16]	Li X H and Bi Q S 2012 Chin. Phys. B 21 060505
[17]	Bi Q S and Zhang Z D 2011 Phys. Lett. A 8 1183
[18]	Morel C, Morel J Y and Danca M F 2017 Math. Comput. Simulat. 10 1
[19]	Li S and Liu C 2015 J. Math. Anal. Appl. 2 1354
[20]	Han Q S, Chen D Y and Zhang H 2017 Chin. Phys. B 26 128202
[21]	Naschie M S E 2006 Chaos Soliton. Fract. 4 816
[22]	Marciniak-Czochra A and Mikelic A 2016 Vietnam Journal of Mathematics 1 1
[23]	Tian R L, Yang X J, Cao Q J and Wu Q L 2012 Chin. Phys. B 21 020503

[1]	Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic Liu Shuang (刘爽), Wang Zhao-Long (王兆龙), Zhao Shuang-Shuang (赵双双), Li Hai-Bin (李海滨), Li Jian-Xiong (李建雄). Chin. Phys. B, 2015, 24(7): 074501.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model

Cite this article:

Online attention