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The dynamics of a nonlinear capacitor circuit is investigated in this paper. The symmetric periodic solution and the chaotic attractor can be observed in numerical simulations. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the non-smooth bifurcation mechanism for the periodic solutions. Discontinuous bifurcation in the combination of the Hopf bifurcation and the turning point bifurcation occurs at the non-smooth boundaries. Here, the Hopf bifurcation may result in a new frequency, which leads to periodic oscillation. With the variation of the parameter, the periodic symmetric solution oscillates more quickly, which can also be explained through non-smooth bifurcation, and the conclusion accord well with the numerical results.
[1] Bartissol P, Chua L O 1988 IEEE Trans. Circ. Syst. 35 1512
[2] Yu H J, Liu Y Z 2005 Acta Phys. Sin. 54 3029 (in chinese) [于洪洁、 刘延柱 2005物理学报 54 3029]
[3] Bai E W, Lonngren K E, J C 2002 Chaos, Solitons and Fractals 13 1515
[4] Liu C X 2002 Acta Phys. Sin. 51 1198 (in Chinese) [刘崇新 2002 物理学报 51 1198]
[5] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) [王发强、 刘崇新 2006 物理学报 55 5055]
[6] Matsumoto T 1984 IEEE Trans. Circ. Syst. CAS-31 1055
[7] Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. Circuits Syst. CAS-33 073
[8] Chua L O, Lin G N 1990 IEEE Trans. Circ. Syst. 37 885
[9] Stouboulos I N, Miliou A N, Valaristos A P, Kyprianidis I M, Anagnostopoulos A N 2007 Chaos, Solitons and Fractals 33 1256
[10] Nordmark A 1997 Physical Review E 55 62
[11] Lu Q S, Zhang S J, Jin L 2004 Dynamica of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms 11A 171
[12] Gao J F, Ma X K, Luo X J 2001 Transactions of China Electrotechnical Society 16 75 (in Chinese) [高金峰、马西奎、 罗先觉 2001电工技术学报 16 75]
[13] Xuemei Wang, Bo Zhang 2007 Proceedings of the IEEE International Conference on Automation and Logistics Jinan, China August 2462
[14] Leine R I, Campen D H 2006 European Journal of Mechanics A/Solids 25 595
[15] Chen Y S, Leung A Y T, Bifurcation and Chaos in Engineering Springer, London, 1998
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[1] Bartissol P, Chua L O 1988 IEEE Trans. Circ. Syst. 35 1512
[2] Yu H J, Liu Y Z 2005 Acta Phys. Sin. 54 3029 (in chinese) [于洪洁、 刘延柱 2005物理学报 54 3029]
[3] Bai E W, Lonngren K E, J C 2002 Chaos, Solitons and Fractals 13 1515
[4] Liu C X 2002 Acta Phys. Sin. 51 1198 (in Chinese) [刘崇新 2002 物理学报 51 1198]
[5] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) [王发强、 刘崇新 2006 物理学报 55 5055]
[6] Matsumoto T 1984 IEEE Trans. Circ. Syst. CAS-31 1055
[7] Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. Circuits Syst. CAS-33 073
[8] Chua L O, Lin G N 1990 IEEE Trans. Circ. Syst. 37 885
[9] Stouboulos I N, Miliou A N, Valaristos A P, Kyprianidis I M, Anagnostopoulos A N 2007 Chaos, Solitons and Fractals 33 1256
[10] Nordmark A 1997 Physical Review E 55 62
[11] Lu Q S, Zhang S J, Jin L 2004 Dynamica of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms 11A 171
[12] Gao J F, Ma X K, Luo X J 2001 Transactions of China Electrotechnical Society 16 75 (in Chinese) [高金峰、马西奎、 罗先觉 2001电工技术学报 16 75]
[13] Xuemei Wang, Bo Zhang 2007 Proceedings of the IEEE International Conference on Automation and Logistics Jinan, China August 2462
[14] Leine R I, Campen D H 2006 European Journal of Mechanics A/Solids 25 595
[15] Chen Y S, Leung A Y T, Bifurcation and Chaos in Engineering Springer, London, 1998
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