Existence of heteroclinic orbits in a novel three-order dynamical system

doi:10.1088/1674-1056/22/11/110502

中国物理B ›› 2013, Vol. 22 ›› Issue (11): 110502-110502.doi: 10.1088/1674-1056/22/11/110502

Existence of heteroclinic orbits in a novel three-order dynamical system

胡瑀, 闵乐泉, 甄平

Beijing University of Science and Technology, Beijing 100083, China

收稿日期:2013-02-06 修回日期:2013-04-16 出版日期:2013-09-28 发布日期:2013-09-28
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61170037 and 61074192).

Existence of heteroclinic orbits in a novel three-order dynamical system

Hu Yu (胡瑀), Min Le-Quan (闵乐泉), Zhen Ping (甄平)

Beijing University of Science and Technology, Beijing 100083, China

Received:2013-02-06 Revised:2013-04-16 Online:2013-09-28 Published:2013-09-28
Contact: Min Le-Quan E-mail:0605m@sina.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61170037 and 61074192).

摘要/Abstract

摘要： In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit in the system. As a result, the Ši’lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.

关键词: novel chaotic system, heteroclinic orbit, Ši’lnikov criterion, undetermined coefficient method

Abstract: In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit in the system. As a result, the Ši’lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.

Key words: novel chaotic system, heteroclinic orbit, Ši’lnikov criterion, undetermined coefficient method

中图分类号: (High-dimensional chaos)

05.45.Jn

05.45.Pq (Numerical simulations of chaotic systems)

胡瑀, 闵乐泉, 甄平. Existence of heteroclinic orbits in a novel three-order dynamical system[J]. 中国物理B, 2013, 22(11): 110502-110502.

Hu Yu (胡瑀), Min Le-Quan (闵乐泉), Zhen Ping (甄平). Existence of heteroclinic orbits in a novel three-order dynamical system[J]. Chin. Phys. B, 2013, 22(11): 110502-110502.

参考文献 36

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Chen G and Ueta T 1999 Int. J. Bifurcat. Chaos 9 1465
[3]	Lü J and Chen G R 2002 Int. J. Bifurcat. Chaos 12 659
[4]	Lü J H, Chen G and Cheng D 2004 Int. J. Bifurcat. Chaos 14 1507
[5]	Liu C X, Liu T, Liu L and Liu K 2004 Chaos Soliton. Fract. 22 1031
[6]	Dong E Z, Chen Z P, Chen Z Q and Yuan Z Z 2009 Chin. Phys. B 18 2680
[7]	Si G Q, Cao H and Zhang Y B 2011 Chin. Phys. B 20 010509
[8]	Jia H Y, Chen Z Q and Yuan Z Z 2010 Chin. Phys. B 19 020507
[9]	Li C B, Chen S and Zhu H Q 2009 Acta Phys. Sin. 58 2255 (in Chinese)
[10]	Ma S H, Fang J P, Ren Q B and Yang Z 2012 Chin. Phys. B 21 050511
[11]	Liu Y and Tong X J 2012 Chin. Phys. B 21 090506
[12]	Hossein G, Amir H and Azita A 2013 Chin. Phys. B 22 010503
[13]	Han Q, Liu C X, Sun L and Zhu D R 2013 Chin. Phys. B 22 020502
[14]	Li G L and Chen X Y 2009 Commun. Nonlinear Sci. 14 194
[15]	Dong E Z, Chen Z Q, Chen Z P and Ni J Y 2012 Chin. Phys. B 21 030501
[16]	Dai H, Jia L X, Hui M and Si G Q 2011 Chin. Phys. B 20 040507
[17]	Yu F, Wang C H, Yin J W and Xu H 2011 Chin. Phys. B 20 110505
[18]	Sara D and Hamid R M 2010 Chin. Phys. B 19 060506
[19]	Chen Z Q, Wu W J and Chen P F 2010 Chin. Phys. B 19 040509
[20]	Chen Y and Yang Y Q 2010 Chin. Phys. B 19 120510
[21]	Silva C P 1993 IEEE Trans. Circ. Syst. I 40 675
[22]	Shil’nikov L P 1969 Sov. Math. B 10 1368
[23]	Zhou T, Tang Y and Chen G R 2004 Int. J. Bifurcat. Chaos 14 3167
[24]	Wang J W, Zhao M C, Zhang Y B and Xiong X H 2007 Physica A 375 438
[25]	Zhou T, Chen G R and Člikovsky S 2005 Nonlinear Dyn. 39 319
[26]	Zhou L and Chen F 2008 Chaos 18 013113
[27]	El-Dessoky M M, Yassen M T, Saleh E and Aly E S 2012 Appl. Math. Comput. 218 11859
[28]	Xu P C and Jing Z J 2000 Chaos Soliton. Fract. 11 853
[29]	Li Z, Chen G R and Halang W A 2004 Inform. Sci. 165 235
[30]	Elhadj Z 2008 Radio Eng. 17 9
[31]	Jiang L and Sun J 2007 Chaos Soliton. Fract. 32 150
[32]	Zhou L and Chen F 2009 Chaos Soliton. Fract. 40 1413
[33]	Xu P C and Jing Z J 2011 J. Math. Anal. Appl. 376 103
[34]	Antonio A, Fernando F S, Manuel M and Alejandro J R L 2012 Commun. Nonlinear Sci. 17 2708
[35]	Zheng Z H and Chen G R 2012 J. Math. Anal. Appl. 392 102
[36]	Tian R L, Yang X W, Cao Q J and Wu Q L 2012 Chin. Phys. B 21 020503

Existence of heteroclinic orbits in a novel three-order dynamical system

Existence of heteroclinic orbits in a novel three-order dynamical system

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 36

相关文章 3

Metrics

本文评价

推荐阅读 0

[1]	李震波, 唐驾时, 蔡萍. A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators[J]. , 2014, 23(12): 120501-120501.
[2]	冯晶晶, 张琪昌, 王炜. The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant[J]. 中国物理B, 2011, 20(9): 90202-090202.
[3]	刘娜, 关治洪. Chaotification for a class of nonlinear systems[J]. 中国物理B, 2009, 18(5): 1769-1773.