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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Feedback Linearization Synchronization of Unified Chaotic Systems

Journal of Applied Nonlinear Dynamics 3(2) (2014) 173--186 | DOI:10.5890/JAND.2014.06.007

Chang-Zhong Chen$^{1}$,$^{2}$, Tao Fan$^{1}$,$^{2}$, Bang-Rong Wang$^{3}$, Hassan Saberi Nik$^{4}$, Ping He$^{5}$,$^{1}$,$^{2}$

$^{1}$ School of Automation and Electronic Information, Sichuan University of Science & Engineering, Zigong, Sichuan, 643000, China

$^{2}$ Artificial Intelligence Key Laboratory of Sichuan Province, Sichuan University of Science & Engineering, Zigong, Sichuan, 643000, China

$^{3}$ School of Science, Sichuan University of Science & Engineering, Zigong, Sichuan, 643000, China

$^{4}$ Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, 9177948974, Iran

$^{5}$ School of Information Science & Engineering, Northeastern University, Shenyang, Liaoning, 110819, China

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Abstract

The goal of this paper is to present a method that can be used to synchronize unified chaotic systems. The method is mainly based on the technology of feedback Linearization of nonlinear control systems. Numerical simulations are then provided to show the effectiveness and feasibility of the proposed chaos control and synchronization schemes.

Acknowledgments

This work was jointly supported by the Open Foundation of Artificial Intelligence Key Laboratory of Sichuan Province (Grant Nos. 2012RYJ01, 2013RYJ01 and 2014RYY02), the Research Foundation of Department of Education of Sichuan Province (Grant Nos. 14ZA0203 and 14ZB0210), the Open Foundation of Enterprise Informatization and Internet of Things Key Laboratory of of Sichuan Province (Grant No. 2013WYY06), and the Science Foundation of Sichuan University of Science & Engineering (Grant No. 2012KY19).

References

  1. [1]  Muthusamy Lakshmanan and Krishna Murali (1996), Chaos in Nonlinear Oscillators: Controlling and Synchronization, 13, World Scientific, Singapore.
  2. [2]  Seung Kee Han, Christian Kurrer, and Yoshiki Kuramoto (1995), Dephasing and bursting in coupled neural oscillators. Physical Review Letters, 75(17), 3190-3193.
  3. [3]  Bernd Blasius, Amit Huppert, and Lewi Stone (1999), Complex dynamics and phase synchronization in spatially extended ecological systems, Nature, 399(6734), 354-359.
  4. [4]  S. Roy Choudhury and Robert A. Van Gorder (2012), Competitive modes as reliable predictors of chaos versus hyperchaos and as geometric mappings accurately delimiting attractors. Nonlinear Dynamics, 69(4), 2255-2267.
  5. [5]  Robert A. Van Gorder (2013), Shil'nikov chaos in the 4D lorenz-stenflo system modeling the time evolution of nonlinear acoustic-gravity waves in a rotating atmosphere. Nonlinear Dynamics, 72(4), 837-851.
  6. [6]  Edward N. Lorenz (1963), Deterministic nonperiodic flow, Journal of the atmospheric sciences, 20(2), 130-141.
  7. [7]  Louis M. Pecora and Thomas L. Carroll (1990), Synchronization in chaotic systems, Physical review letters, 64(8), 821-824.
  8. [8]  Xin Ping Guan, Zheng Ping Fan, Cai Lian Chen, and Chang Chun Hua (2002), Chaotic Control and Its Application on Secure Communication, National Defence Industry Press, Beijing.
  9. [9]  Xing-Yan Wang (2003), Chaos in the Complex Nonlinearity System, Electronics Industry Press, Beijing.
  10. [10]  Chuandong Li, Xiaofeng Liao, and Kwok-Wo Wong (2005), Lag synchronization of hyperchaos with application to secure communications, Chaos, Solitons & Fractals, 23(1), 183-193.
  11. [11]  Ming-Chung Ho, Yao-Chen Hung, and Chien-Ho Chou (2002), Phase and anti-phase synchronization of two chaotic systems by using active control, Physics letters A, 296(1), 43-48.
  12. [12]  Nastaran Vasegh and F.Khellat (2009), Projective synchronization of chaotic time-delayed systems via sliding mode controller, Chaos, Solitons & Fractals, 42(2), 1054-1061.
  13. [13]  Guo-Hui Li (2007), Modified projective synchronization of chaotic system, Chaos, Solitons & Fractals, 32(5), 1786-1790.
  14. [14]  Cun-Fang Feng, Yan Zhang, Jin-Tu Sun, Wei Qi, and Ying-Hai Wang (2008), Generalized projective synchronization in time-delayed chaotic systems, Chaos, Solitons & Fractals, 38(3), 743-747.
  15. [15]  Guilin Wen and Daolin Xu (2005), Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems, Chaos, Solitons & Fractals, 26(1), 71-77.
  16. [16]  Yun Chen, Minyong Li, and Zhifeng Cheng (2010), Global anti-synchronization of master-slave chaotic modified chua's circuits coupled by linear feedback control, Mathematical and Computer Modelling, 52(3), 567-573.
  17. [17]  Jun Ma, Fan Li, Long Huang, and Wu-Yin Jin (2011), Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system, Communications in Nonlinear Science and Numerical Simulation, 16(9), 3770-3785.
  18. [18]  Juan Chen, Hui Liu, Jun-an Lu, and Qunjiao Zhang (2011), Projective and lag synchronization of a novel hyperchaotic system via impulsive control, Communications in Nonlinear Science and Numerical Simulation, 16(4), 2033-2040.
  19. [19]  Hanlin He, Jianjun Tu, and Ping Xiong (2011), lr-synchronization and adaptive synchronization of a class of chaotic lurie systems under perturbations, Journal of the Franklin Institute, 348(9), 2257-2269.
  20. [20]  Xinsong Yang, Quanxin Zhu, and Chuangxia Huang (2011), Generalized lag-synchronization of chaotic mixdelayed systems with uncertain parameters and unknown perturbations, Nonlinear Analysis: Real World Applications, 12(1), 93-105.
  21. [21]  Chao-Jung Cheng (2012), Robust synchronization of uncertain unified chaotic systems subject to noise and its application to secure communication, Applied Mathematics and Computation, 219(5), 2698-2712.
  22. [22]  Xing-Yuan Wang and Bing Fan (2012), Generalized projective synchronization of a class of hyperchaotic systems based on state observer, Communications in Nonlinear Science and Numerical Simulation, 17(2), 953-963.
  23. [23]  M. Mossa Al-sawalha and M.S.M. Noorani (2012), Chaos reduced-order anti-synchronization of chaotic systems with fully unknown parameters, Communications in Nonlinear Science and Numerical Simulation, 17(4), 1908-1920.
  24. [24]  Thongchai Botmart, Piyapong Niamsup, and Xinzhi Liu (2012), Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control, Communications in Nonlinear Science and Numerical Simulation, 17(4), 1894-1907.
  25. [25]  Sourav K. Bhowmick, Chittaranjan Hens, Dibakar Ghosh, and SyamalK. Dana (2012), Mixed synchronization in chaotic oscillators using scalar coupling, Physics Letters A, 376(36), 2490-2495.
  26. [26]  Tae H. Lee, Ju H. Park, and Sang-Choel Lee (2010), Functional projective lag synchronization of chaotic systems with disturbances, Scientific Research and Essays, 5(10), 1189-1193.
  27. [27]  Hassan K. Khalil (2002), Nonlinear systems, volume 3, Prentice hall Upper Saddle River.
  28. [28]  Jinhu Lü, Guanrong Chen, Daizhan Cheng, and Sergej Celikovsky (2002), Bridge the gap between the lorenz system and the chen system, International Journal of Bifurcation and Chaos, 12(12), 2917-2926.
  29. [29]  Ping He, Shu-Hua Ma, and Tao Fan (2012), Finite-time mixed outer synchronization of complex networks with coupling time-varying delay, Chaos, 22(4), 043151.
  30. [30]  Ping He, Chun-Guo Jing, Tao Fan, and Chang-Zhong Chen (2013), Outer synchronization of complex networks with multiple coupling time-varying delays, International Journal of Control and Automation, 6(4), 197-216.
  31. [31]  Ping He, Chun-Guo Jing, Tao Fan, and Chang-Zhong Chen (2014) Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties, Complexity,19(10), 10-26

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