Please wait a minute...
Chin. Phys. B, 2015, Vol. 24(2): 020502    DOI: 10.1088/1674-1056/24/2/020502
GENERAL Prev   Next  

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Jiang Hai-Boa, Zhang Li-Pinga, Yu Jian-Jiangb
a School of Mathematics, Yancheng Teachers University, Yancheng 224002, China;
b School of Information Science and Technology, Yancheng Teachers University, Yancheng 224002, China
Abstract  Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.
Keywords:  impulsively coupled oscillators      bifurcation      periodic solutions      Floquet theory  
Received:  18 June 2014      Revised:  10 September 2014      Published:  05 February 2015
PACS:  05.45.Ac (Low-dimensional chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11402224, 11202180, 61273106, and 11171290), the Qing Lan Project of the Jiangsu Higher Educational Institutions of China, and the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents.
Corresponding Authors:  Jiang Hai-Bo     E-mail:  yctcjhb@gmail.com

Cite this article: 

Jiang Hai-Bo, Zhang Li-Ping, Yu Jian-Jiang Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure 2015 Chin. Phys. B 24 020502

[1] Kuramoto Y 1984 Chemical Oscillations, Wave, and Turbulence (Berlin: Springer)
[2] Bi Q S 2007 Phys. Lett. A 369 418
[3] Pikovsky A, Rosenblum M and Kurths J 2001 Synchronization: A Universal Concept in Nonlinear Science (Cambridge: Cambridge University Press)
[4] Strogatz S H 2000 Physica D 143 1
[5] Fotsin H B and Woafo P 2005 Chaos, Solitons and Fractals 24 1363
[6] Zhou J, Cheng X H, Xiang L and Zhang Y C 2007 Chaos, Solitons and Fractals 33 607
[7] Wang Q Y and Lu Q S 2010 Int. J. Non-Linear Mech. 45 640
[8] Rene Y 2006 Physica A 366 187
[9] Barrón M A and Sen M 2009 Nonlinear Dyn. 56 357
[10] Barron M A, Sen M and Corona E 2008 Innovations and Advanced Techniques in Systems, Computing Sciences and Software Engineering (Berlin: Springer Netherlands) 346
[11] Perlikowski P, Yanchuk S, Wolfrum M, Stefanski A, Mosiolek P and Kapitaniak T 2010 Chaos 20 013111
[12] Mirollo R M and Strogatz S H 1990 SIAM J. Appl. Math. 50 1645
[13] Nakano H and Saito T 2004 IEEE Trans. Neural Networks 15 1018
[14] Han X P, Lu J A and Wu X Q 2008 Int. J. Bifur. Chaos 18 1539
[15] Yang M, Wang Y W, Xiao J W and Wang H O 2010 Nonlinear Anal. Real World Appl. 11 3008
[16] Jiang H B and Bi Q S 2012 Nonlinear Dyn. 67 781
[17] Jiang H B, Yu J J and Zhou C G 2011 Int. J. Systems Sci. 42 967
[18] Jiang H B and Bi Q S 2010 Phys. Lett. A 374 2723
[19] Jiang H B, Bi Q S and Zheng S 2012 Commun. Nonlinear Sci. Numer. Simul. 17 378
[20] Zhou J, Wu Q J and Xiang L 2012 Nonlinear Dyn. 69 1393
[21] Kitajima H and Kawakami H 2001 IEEE International Symposium on Circuit and Systems (ISCAS2001), May 6-9, 2001, Sydney, NSW, Vol. 2, p. 285
[22] Lenci S and Rega G 2000 Chaos, Solitona and Fractals 11 2453
[23] Zhang S W, Tan D J and Chen L S 2006 Chaos, Solitons and Fractals 29 474
[24] Georgescu P, Zhang H and Chen L S 2008 Appl. Math. Comput. 202 675
[25] Jiang G R and Yang Q G 2008 Chin. Phys. B 17 4114
[26] Jiang G R, Xu B G and Yang Q G 2009 Chin. Phys. B 18 5235
[27] Qian L N, Lu Q S, Meng Q G and Feng Z S 2010 J. Math. Anal. Appl. 363 345
[28] Jiang H B, Zhang L P, Chen Z Y and Bi Q S 2012 Acta Phys. Sin. 61 080505 (in Chinese)
[29] Jiang H B, Li T, Zeng X L and Zhang L P 2013 Acta Phys. Sin. 62 120508 (in Chinese)
[30] Jiang H B, Li T, Zeng X L and Zhang L P 2014 Chin. Phys. B 23 010501
[31] Liu F, Guan Z H and Wang H O 2010 Nonlinear Anal. Real World Appl. 11 1491
[32] Jin L, Lu Q S and Twizell E H 2006 J. Sound Vibration 298 1019
[33] Dankowicz H and Schilder F 2011 J. Comput. Nonlinear Dyn. 6 031003
[34] Zhang Y X and Luo G W 2013 J. Sound Vibration 332 5462
[1] Analysis and implementation of new fractional-order multi-scroll hidden attractors
Li Cui(崔力), Wen-Hui Luo(雒文辉), and Qing-Li Ou(欧青立). Chin. Phys. B, 2021, 30(2): 020501.
[2] Dynamics and coherence resonance in a thermosensitive neuron driven by photocurrent
Ying Xu(徐莹), Minghua Liu(刘明华), Zhigang Zhu(朱志刚), Jun Ma(马军). Chin. Phys. B, 2020, 29(9): 098704.
[3] Generating mechanism of pathological beta oscillations in STN-GPe circuit model: A bifurcation study
Jing-Jing Wang(王静静), Yang Yao(姚洋), Zhi-Wei Gao(高志伟), Xiao-Li Li(李小俚), Jun-Song Wang(王俊松). Chin. Phys. B, 2020, 29(5): 058701.
[4] The second Hopf bifurcation in lid-driven square cavity
Tao Wang(王涛), Tiegang Liu(刘铁钢), Zheng Wang(王正). Chin. Phys. B, 2020, 29(3): 030503.
[5] Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator
Hong-Bo Yan(闫洪波), Hong Gao(高鸿), Gao-Wei Yang(杨高炜), Hong-Bo Hao(郝宏波), Yu Niu(牛禹), Pei Liu(刘霈). Chin. Phys. B, 2020, 29(2): 020504.
[6] Nonlinear dynamics in non-volatile locally-active memristor for periodic and chaotic oscillations
Wen-Yu Gu(谷文玉), Guang-Yi Wang(王光义), Yu-Jiao Dong(董玉姣), and Jia-Jie Ying(应佳捷). Chin. Phys. B, 2020, 29(11): 110503.
[7] Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation
Ming Song(宋明)†, Beidan Wang(王贝丹), and Jun Cao(曹军). Chin. Phys. B, 2020, 29(10): 100206.
[8] Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation
Li-Juan Shi(师利娟), Zhen-Shu Wen(温振庶). Chin. Phys. B, 2019, 28(4): 040201.
[9] Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts
Deli Wang(王德莉), Wei Xu(徐伟), Xudong Gu(谷旭东). Chin. Phys. B, 2019, 28(1): 010203.
[10] Hopf bifurcation control of a Pan-like chaotic system
Liang Zhang(张良), JiaShi Tang(唐驾时), Qin Han(韩芩). Chin. Phys. B, 2018, 27(9): 094702.
[11] Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation
Zhen-Shu Wen(温振庶), Li-Juan Shi(师利娟). Chin. Phys. B, 2018, 27(9): 090201.
[12] Multi-stability involved mixed bursting within the coupled pre-Bötzinger complex neurons
Zijian Wang(王子剑), Lixia Duan(段利霞), Qinyu Cao(曹秦禹). Chin. Phys. B, 2018, 27(7): 070502.
[13] Dynamic characteristics in an external-cavity multi-quantum-well laser
Sen-Lin Yan(颜森林). Chin. Phys. B, 2018, 27(6): 060501.
[14] Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model
Ran Zhang(张冉), Miao Peng(彭淼), Zhengdi Zhang(张正娣), Qinsheng Bi(毕勤胜). Chin. Phys. B, 2018, 27(11): 110501.
[15] Magneto-elastic dynamics and bifurcation of rotating annular plate
Yu-Da Hu(胡宇达), Jiang-Min Piao(朴江民), Wen-Qiang Li(李文强). Chin. Phys. B, 2017, 26(9): 094302.
No Suggested Reading articles found!