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The complex dynamics of Chen system via impulsive force is investigated in this paper. The non-smooth bifurcation of Chen system via impulsive force is analyzed. The system can evolve to chaos by the cascading of period-doubling bifurcations. Besides, the system can evolve to chaos immediately by saddle-node bifurcations from period solutions. Finally, the Floquet theory is used to explore the non-smooth bifurcation mechanism for the periodic solutions.
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Keywords:
- Chen system /
- impulse /
- non-smooth bifurcation /
- chaos
[1] Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[2] Chen G R, Lü J H 2003 Dynamical Analyses, Control and Synchronization of the Lorenz System Family (Beijing: Science Press) Chap 2 (in Chinese) [陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京: 科学出版社) 第2章]
[3] Lorenz E N 1963 J. Atmos. Sci. 20 130
[4] Wang X Y, Wu X J 2006 Acta Phys. Sin. 55 605 (in Chinese) [王兴元, 武相军 2006 55 605]
[5] Zhang X F, Chen Z Y, Bi Q S 2010 Acta Phys. Sin. 59 3802 (in Chinese) [张晓芳, 陈章耀, 毕勤胜 2010 59 3802]
[6] Jiang H B, Yu J J, Zhou C G 2008 IET Control Theory Appl. 2 654
[7] Zhang L P, Jiang H B, Bi Q S 2010 Chin. Phys. B 19 010507
[8] Qian L N, Lu Q S, Meng Q G, Feng Z S 2010 J. Math. Anal. Appl. 363 345
[9] Wang L, Zhao R, Xu W, Zhang Y 2011 Chin. Phys. B 20 020506
[10] Wang X Y, Zhang Y L, Lin D, Zhang N 2011 Chin. Phys. B 20 030506
[11] Kawakami H 1984 IEEE Trans. Circuits Syst. 31 248
[12] Kitajima H, Kawakami H 2001 International Symposium on Circuits and Systems (Vol. 2) (Sydney: IEEE) p285
[13] Jin L, Lu Q S, Wang Q 2004 Chin. J. Appl. Mech. 21 21 (in Chinese) [金俐, 陆启韶, 王琪 2004 应用力学学报 21 21]
[14] Lu Q S, Jin L 2005 Acta Mech. Sol. Sin. 26 132 (in Chinese) [陆启韶, 金俐 2005 固体力学学报 26 132]
[15] Zhang S W, Chen L S 2005 Chaos Solitons Fract. 24 73
[16] Georgescu P, Zhang H, Chen L S 2008 Appl. Math. Comput. 202 675
[17] Jiang G R, Yang Q G 2008 Chin. Phys. B 17 4114
[18] Jiang G R, Xu B G, Yang Q G 2009 Chin. Phys. B 18 5235
[19] Ji Y, Bi Q S 2010 Acta Phys. Sin. 59 7612 (in Chinese) [季颖, 毕勤胜 2010 59 7612]
[20] Zhang Y, Bi Q S 2011 Acta Phys. Sin. 60 070507 (in Chinese) [张银, 毕勤胜 2011 60 070507]
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[1] Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[2] Chen G R, Lü J H 2003 Dynamical Analyses, Control and Synchronization of the Lorenz System Family (Beijing: Science Press) Chap 2 (in Chinese) [陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京: 科学出版社) 第2章]
[3] Lorenz E N 1963 J. Atmos. Sci. 20 130
[4] Wang X Y, Wu X J 2006 Acta Phys. Sin. 55 605 (in Chinese) [王兴元, 武相军 2006 55 605]
[5] Zhang X F, Chen Z Y, Bi Q S 2010 Acta Phys. Sin. 59 3802 (in Chinese) [张晓芳, 陈章耀, 毕勤胜 2010 59 3802]
[6] Jiang H B, Yu J J, Zhou C G 2008 IET Control Theory Appl. 2 654
[7] Zhang L P, Jiang H B, Bi Q S 2010 Chin. Phys. B 19 010507
[8] Qian L N, Lu Q S, Meng Q G, Feng Z S 2010 J. Math. Anal. Appl. 363 345
[9] Wang L, Zhao R, Xu W, Zhang Y 2011 Chin. Phys. B 20 020506
[10] Wang X Y, Zhang Y L, Lin D, Zhang N 2011 Chin. Phys. B 20 030506
[11] Kawakami H 1984 IEEE Trans. Circuits Syst. 31 248
[12] Kitajima H, Kawakami H 2001 International Symposium on Circuits and Systems (Vol. 2) (Sydney: IEEE) p285
[13] Jin L, Lu Q S, Wang Q 2004 Chin. J. Appl. Mech. 21 21 (in Chinese) [金俐, 陆启韶, 王琪 2004 应用力学学报 21 21]
[14] Lu Q S, Jin L 2005 Acta Mech. Sol. Sin. 26 132 (in Chinese) [陆启韶, 金俐 2005 固体力学学报 26 132]
[15] Zhang S W, Chen L S 2005 Chaos Solitons Fract. 24 73
[16] Georgescu P, Zhang H, Chen L S 2008 Appl. Math. Comput. 202 675
[17] Jiang G R, Yang Q G 2008 Chin. Phys. B 17 4114
[18] Jiang G R, Xu B G, Yang Q G 2009 Chin. Phys. B 18 5235
[19] Ji Y, Bi Q S 2010 Acta Phys. Sin. 59 7612 (in Chinese) [季颖, 毕勤胜 2010 59 7612]
[20] Zhang Y, Bi Q S 2011 Acta Phys. Sin. 60 070507 (in Chinese) [张银, 毕勤胜 2011 60 070507]
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