Symmetric bursting behaviour in non-smooth Chua's circuit

doi:10.1088/1674-1056/19/8/080510

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 80510-080510.doi: 10.1088/1674-1056/19/8/080510

Symmetric bursting behaviour in non-smooth Chua's circuit

季颖, 毕勤胜

Faculty of Science, Jiangsu University, Zhenjiang 212013, China

收稿日期:2009-09-22 修回日期:2010-01-27 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10972091, 20976075 and 10872080).

Symmetric bursting behaviour in non-smooth Chua's circuit

Ji Ying(季颖) and Bi Qin-Sheng(毕勤胜)^†

Faculty of Science, Jiangsu University, Zhenjiang 212013, China

Received:2009-09-22 Revised:2010-01-27 Online:2010-08-15 Published:2010-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10972091, 20976075 and 10872080).

摘要/Abstract

摘要： The dynamics of a non-smooth electric circuit with an order gap between its parameters is investigated in this paper. Different types of symmetric bursting phenomena can be observed in numerical simulations. Their dynamical behaviours are discussed by means of slow-fast analysis. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the bifurcation mechanism for the bursting solutions, which can also be used to account for the evolution of the complicated structures of the phase portraits. With the variation of the parameter, the periodic symmetric bursting can evolve into chaotic symmetric bursting via period-doubling bifurcation.

Abstract: The dynamics of a non-smooth electric circuit with an order gap between its parameters is investigated in this paper. Different types of symmetric bursting phenomena can be observed in numerical simulations. Their dynamical behaviours are discussed by means of slow-fast analysis. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the bifurcation mechanism for the bursting solutions, which can also be used to account for the evolution of the complicated structures of the phase portraits. With the variation of the parameter, the periodic symmetric bursting can evolve into chaotic symmetric bursting via period-doubling bifurcation.

Key words: non-smooth electric circuit, symmetric bursting, bifurcation mechanism

中图分类号: (Circuit theory)

84.30.Bv

02.10.Yn (Matrix theory) 02.30.Oz (Bifurcation theory) 02.60.Cb (Numerical simulation; solution of equations)

季颖, 毕勤胜. Symmetric bursting behaviour in non-smooth Chua's circuit[J]. 中国物理B, 2010, 19(8): 80510-080510.

Ji Ying(季颖) and Bi Qin-Sheng(毕勤胜). Symmetric bursting behaviour in non-smooth Chua's circuit[J]. Chin. Phys. B, 2010, 19(8): 80510-080510.

参考文献 13

[1]	Lee I, Kim S and Jun S 2004 Comput. Methods Appl. Mech. Enger. 193 1633
[2]	Hu G, Wang Y, Schoneich C, Jiang P and Fessenden R 1999 Radiation Phys. Chem. 54 559
[3]	Rajesh S and Ananthakrishna G 2000 Phys. Rev. E 61 3664
[4]	Yang Z Q and Lu Q S 2006 Chin. Phys. 15 518
[5]	Dai X G, Li H Q and Luo X H 2008 Acta Phys. Sin. 57 7511 (in Chinese)
[6]	Han X J, Jiang B and Bi Q S 2009 Acta Phys. Sin. 58 4408 (in Chinese)
[7]	Cui B T, Ji Y and Qiu F 2009 Chin. Phys. B 18 5203
[8]	Izhikevich E 2000 Int. J. Bifur. Chaos 6 1171
[9]	Maeda Y and Makino H 2000 BioSystems 58 93
[10]	Savino G V and Formigli C M 2009 BioSystems 97 9
[11]	Liu X, Wang J Z and Huang L Proceedings of the 25th Chinese Control Conference Harbin p. 227
[12]	Leine R I and Nijmeijer H 2004 Dynamics and Bifurcations of Non-smooth Mechanical Systems (Berlin: Springer-Verlag)
[13]	Leine R I and van Campen D H 2006 European Journal of Mechanics A: Solids 25 595

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Symmetric bursting behaviour in non-smooth Chua's circuit

Symmetric bursting behaviour in non-smooth Chua's circuit

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