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Hybrid Projective Synchronization of a New Hyperchaotic System

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Book cover Proceedings of 2013 Chinese Intelligent Automation Conference

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 254))

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Abstract

The hybrid projective synchronization (HPS) of a new hyperchaotic system is studied using a nonlinear feedback control. The nonlinear controller is designed according to Lyapunov’s direct method to guarantee HPS, which includes synchronization, anti-synchronization and projective synchronization. Numerical examples are presented in order to verify the effectiveness of the proposed scheme.

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References

  1. Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824

    Google Scholar 

  2. Carroll TL, Pecora LM (1991) Synchronizing chaotic circuits. IEEE Trans Circuits Syst 38(4):453–456

    Google Scholar 

  3. Ma J, Li F, Huang L, Jin W-Y (2011) Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system. Commun Nonlin Sci Numer Simul 16(9):3770–3785

    Article  MATH  Google Scholar 

  4. Taghvafard H, Erjaee DH (2011) Phase and anti-phase synchronization of fractional order chaotic systems via active control. Commun Nonlin Sci Numer Simul 16(10):4079–4088

    Article  MathSciNet  MATH  Google Scholar 

  5. Li D, Li XL, Cui D, Li ZH (2011) Phase synchronization with harmonic wavelet transform with application to neuronal populations. Neurocomputing 74(17):3389–3403

    Article  Google Scholar 

  6. Chen Y, Li MY, Cheng ZF (2010) Global anti-synchronization of master–slave chaotic modified Chua’s circuits coupled by linear feedback control. Math Comput Model 52(3):567–573

    Article  MathSciNet  MATH  Google Scholar 

  7. Liu ST, Liu P (2011) Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters. Nonlin Anal Real World Appl 12(6):3046–3055

    Article  MATH  Google Scholar 

  8. Zhao HY, Zhang Q (2011) Global impulsive exponential anti-synchronization of delayed chaotic neural networks. Neurocomputing 74(4):563–567

    Article  Google Scholar 

  9. Zhang LP, Jiang HB (2011) Impulsive generalized synchronization for a class of nonlinear discrete chaotic systems. Commun Nonlin Sci Numer Simul 16(4):2027–2032

    Article  MathSciNet  MATH  Google Scholar 

  10. Wu YQ, Li CP, Wu YJ, Jürgen K (2012) Generalized synchronization between two different complex networks. Commun Nonlin Sci Numer Simul 17(1):349–355

    Article  MATH  Google Scholar 

  11. Mainieri R, Rehacek J (1999) Projective synchronization in three-dimensional chaotic systems. Phys Rev Lett 82:3042–3045

    Article  Google Scholar 

  12. Chen CY, Xu D (2005) Secure digital communication using controlled projective synchronization of chaos. Chaos Solitons Fractals 23:1063–1070

    Google Scholar 

  13. Wen GL, Xu D (2005) Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems. Chaos Solitons Fractals 26:71–77

    Article  MathSciNet  MATH  Google Scholar 

  14. Pang S, LiuY (2011) A new hyperchaotic system from the Lu system and its control. J Comput Appl Math 235:2775–2789

    Google Scholar 

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Acknowledgments

This research is supported by the Science Foundation of Shandong Jiaotong University (Nos: Z201030, Z201130, Z201203 and Z201204) and the Scientific Research Foundation of Shandong Education Office of China (No J12LI55).

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Correspondence to Jinchen Yu .

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Yu, J., Zhang, C. (2013). Hybrid Projective Synchronization of a New Hyperchaotic System. In: Sun, Z., Deng, Z. (eds) Proceedings of 2013 Chinese Intelligent Automation Conference. Lecture Notes in Electrical Engineering, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38524-7_42

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  • DOI: https://doi.org/10.1007/978-3-642-38524-7_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38523-0

  • Online ISBN: 978-3-642-38524-7

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