Kybernetika 50 no. 4, 632-642, 2014

Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification

Xiaobing Zhou, Murong Jiang and Yaqun HuangDOI: 10.14736/kyb-2014-4-0632

Abstract:

This paper investigates adaptive switched modified function projective synchronization between two complex nonlinear hyperchaotic systems with unknown parameters. Based on adaptive control and parameter identification, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve switched modified function projective synchronization between two different complex nonlinear hyperchaotic systems and to estimate the unknown system parameters. A numerical simulation is presented to demonstrate the validity and feasibility of the proposed controllers and update laws.

Keywords:

adaptive control, modified function projective synchronization, switched state, hyperchaotic system, complex variable

Classification:

34C28, 34D06, 34H10

paper.pdf

References:

  1. S. K. Bhowmick, P. Pal, P. K. Roy and S. K. Dana: Lag synchronization and scaling of chaotic attractor in coupled system. Chaos 22 (2012), 023151.   CrossRef
  2. Y. Chen and X. Li: Function projective synchronization between two identical chaotic systems. Int. J. Mod. Phys. C 18 (2007), 883-888.   CrossRef
  3. Y. Chen, J. Lü, X. Yu and Z. Lin: Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices. SIAM J. Control Optim. 51 (2013), 3274-3301.   CrossRef
  4. Y. Chen, J. Lü and Z. Lin: Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica 49 (2013), 1768-1775.   CrossRef
  5. Y. Chen, J. Lü, X. Yu and D. Hill: Multi-agent systems with dynamical topologies: Consensus and applications. IEEE Circuits Syst. Magazine 13 (2013), 21-34.   CrossRef
  6. H. Y. Du, Q. S. Zeng and C. H. Wang: Modified function projective synchronization of chaotic system. Chaos Solitons Fractals 42 (2009), 2399-2404.   CrossRef
  7. E. M. Elabbasy and M. M. El-Dessoky: Adaptive feedback control for the projective synchronization of the Lü dynamical system and its application to secure communication. Chin. J. Phys. 48 (2010), 863-872.   CrossRef
  8. C. F. Feng, Y. Zhang, J. T. Sun, W. Qi and Y. H. Wang: Generalized projective synchronization in time-delayed chaotic systems. Chaos, Solitons Fractals 38 (2008), 743-747.   CrossRef
  9. A. C. Fowler, J. D. Gibbon and M. J. McGuinness: The complex Lorenz equations. Physica D 4 (1982), 139-163.   CrossRef
  10. G. Grassi: Generalized synchronization between different chaotic maps via dead-beat control. Chin. Phys. B 21 (2012), 050505.   CrossRef
  11. J. D. Lambert: Numerical Methods for Ordinary Differential Systems: The Initial Value Problem. Wiley, New York 1991.   CrossRef
  12. G. H. Li: Modified projective synchronization of chaotic system. Chaos Solitons Fractals 32 (2007), 1786-1790.   CrossRef
  13. P. Liu, S. T. Liu and X. Li: Adaptive modified function projective synchronization of general uncertain chaotic complex systems. Phys. Scr. 85 (2012), 035005.   CrossRef
  14. V. Lynnyk and S. Čelikovský: On the anti-synchronization detection for the generalized lorenz system and its applications to secure encryption. Kybernetika 46 (2010) 1-18.   CrossRef
  15. J. Ma, F. Li, L. Huang and W. Y. Jin: Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system. Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 3770-3785.   CrossRef
  16. M. H. Ma, H. Zhang, J. P. Cai and et al.: Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch. Kybernetika 49 (2013), 539-553.   CrossRef
  17. G. M. Mahmoud and E. E. Mahmoud: Complete synchronization of chaotic complex nonlinear systems with uncertain parameters. Nonlinear Dyn. 62 (2010), 875-882.   CrossRef
  18. G. M. Mahmoud and A. A. M. Farghaly: Chaos control of chaotic limit cycles of real and complex van der Pol oscillators. Chaos Solitons Fractals 21 (2004), 915-924.   CrossRef
  19. G.M. Mahmoud, T. Bountis and E. E. Mahmoud: Active control and global synchronization of the complex Chen and Lü systems. Int. J. Bifur. Chaos 17 (2007), 4295-4308.   CrossRef
  20. G. M. Mahmoud, E. E. Mahmoud and M. E. Ahmed: A hyperchaotic complex Chen system and its dynamics. Int. J. Appl. Math. Stat. 12 (2007), 90-100.   CrossRef
  21. G. M. Mahmoud, M. E. Ahmed and E. E. Mahmoud: Analysis of hyperchaotic complex Lorenz systems. Int. J. Mod. Phys. C 19 (2008), 1477-1494.   CrossRef
  22. G. M. Mahmoud, E. E. Mahmoud and M. E. Ahmed: On the hyperchaotic complex Lü system. Nonlinear Dyn. 58 (2009), 725-738.   CrossRef
  23. G. M. Mahmoud, M. A. Al-Kashif and A. A. Farghaly: Chaotic and hyperchaotic attractors of a complex nonlinear system. J. Phys. A: Math. Theor. 41 (2008), 055104.   CrossRef
  24. G. M. Mahmoud, M. E. Ahmed and N. Sabor: On autonomous and nonautonomous modified hyperchaotic complex Lü systems. Int. J. Bifur. Chaos 21 (2011), 1913-1926.   CrossRef
  25. G. M. Mahmoud and M. E. Ahmed: A hyperchaotic complex system generating two-, three-, and four-scroll attractors. J. Vib. Control 18 (2012), 841-849.   CrossRef
  26. R. Mainieri and J. Rehacek: Projective synchronization in three-dimensioned chaotic systems. Phys. Rev. Lett. 82 (1999), 3042-3045.   CrossRef
  27. L. M. Pecora and T. L. Carroll: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821-824.   CrossRef
  28. C. Shen, S. Yu, J. Lu and G. Chen: A systematic methodology for constructing hyperchaotic systems with multiple positive Lyapunov exponents and circuit implementation. IEEE Trans. Circuits Syst. I 61 (2014), 854-864.   CrossRef
  29. K. S. Sudheer and M. Sabir: Switched modified function projective synchronization of hyperchaotic Qi system with uncertain parameters. Commun. Nonlinear Sci. Numer. Simul. 15 (2010), 4058-4064.   CrossRef
  30. J. W. Wang and A. M. Chen: Partial synchronization in coupled chemical chaotic oscillators. J. Comp. Appl. Math. 233 (2010), 1897-1904.   CrossRef
  31. X. J. Wu, H. Wang and H. T. Lu: Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication. Nonlinear Anal.: Real World Appl. 13 (2012), 1441-1450.   CrossRef
  32. F. Yu, C. H. Wang, Q. Z. Wan and Y. Hu: Complete switched modified function projective synchronization of a five-term chaotic system with uncertain parameters and disturbances. Pramana 80 (2013), 223-235.   CrossRef
  33. P. Zhou and W. Zhu: Function projective synchronization for fractional-order chaotic systems. Nonlinear Anal.: Real World Appl. 12 (2011), 811-816.   CrossRef