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The dynamics of four-order modified Chua's circuit with slow-fast effect has been investigated in this letter. Different types of bursting phenomena can be observed in numerical simulations. By introducing slow-fast analysis, the bifurcation mechanism for the periodic bursting solutions, especially for Fold/Fold bursting and Fold/Hopf bursting, is presented, which is different from the usual case. With the variation of the parameter, the periodic bursting can evolve to chaotic bursting.
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Keywords:
- modified Chua's circuit /
- bursting /
- bifurcation mechanism /
- eigenvalues
[1] Maganti G B, Singh S N 2006 Chaos Solitons. Fract. 28 724
[2] Fu S H, Pei L J 2010 Acta Phys. Sin. 59 5985 (in Chinese) [付士慧, 裴利军 2010 59 5985]
[3] Liu C X 2002 Acta Phys.Sin. 51 1198 (in Chinese) [刘崇新 2002 51 1198]
[4] Yu H J, Liu Y Z 2005 Acta Phys. Sin. 54 3029 (in Chinese) [于洪洁,刘延柱 2005 54 3029]
[5] Zhong G Q 1994 Int. J. Bifur. Chaos 41 934
[6] Zhang Z X, Yu S M 2010 Acta Phys. Sin. 59 3017 (in Chinese) [张朝霞,禹思敏 2010 59 3017]
[7] Liu X, Wang J Z, Hang L 2006 Proceedings of the 25th Chinese Control Conference Harbin, China, August 7–11 2006 p227
[8] Lee I, Kim S, Jun S 2004 Comput. Methods Appl. Mech. Eng. 193 1633
[9] Ji Y, Bi Q S 2010 Chin. Phys. B 19 080510
[10] Hug G, Wang Y, Schoneich C, Jiang P, Fessenden R 1999 Radiat. Phys. Chem. 54 559
[11] Staddon J, Chelaru I, Higa J J 2002 Behavioural Processed 57 71
[12] Mease K D 2005 Appl. Math. Comput. 164 627
[13] Han X J, Jiang Bo, Bi Q S 2009 Acta Phys. Sin. 58 4408 (in Chinese) [韩修静,江波,毕勤胜 2009 58 4408]
[14] Ji Y, Bi Q S 2010 Phys. Lett. A 374 1434
[15] Izhikevich E M 2000 Int. J. Bifur. Chaos 10 1171
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[1] Maganti G B, Singh S N 2006 Chaos Solitons. Fract. 28 724
[2] Fu S H, Pei L J 2010 Acta Phys. Sin. 59 5985 (in Chinese) [付士慧, 裴利军 2010 59 5985]
[3] Liu C X 2002 Acta Phys.Sin. 51 1198 (in Chinese) [刘崇新 2002 51 1198]
[4] Yu H J, Liu Y Z 2005 Acta Phys. Sin. 54 3029 (in Chinese) [于洪洁,刘延柱 2005 54 3029]
[5] Zhong G Q 1994 Int. J. Bifur. Chaos 41 934
[6] Zhang Z X, Yu S M 2010 Acta Phys. Sin. 59 3017 (in Chinese) [张朝霞,禹思敏 2010 59 3017]
[7] Liu X, Wang J Z, Hang L 2006 Proceedings of the 25th Chinese Control Conference Harbin, China, August 7–11 2006 p227
[8] Lee I, Kim S, Jun S 2004 Comput. Methods Appl. Mech. Eng. 193 1633
[9] Ji Y, Bi Q S 2010 Chin. Phys. B 19 080510
[10] Hug G, Wang Y, Schoneich C, Jiang P, Fessenden R 1999 Radiat. Phys. Chem. 54 559
[11] Staddon J, Chelaru I, Higa J J 2002 Behavioural Processed 57 71
[12] Mease K D 2005 Appl. Math. Comput. 164 627
[13] Han X J, Jiang Bo, Bi Q S 2009 Acta Phys. Sin. 58 4408 (in Chinese) [韩修静,江波,毕勤胜 2009 58 4408]
[14] Ji Y, Bi Q S 2010 Phys. Lett. A 374 1434
[15] Izhikevich E M 2000 Int. J. Bifur. Chaos 10 1171
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