Globally exponential synchronization criterion of chaot-ic oscillators using active control

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    This research paper focuses the globally exponential synchronization between two identical and two nonidentical chaotic oscillators. With the help of Lyapunov direct method and using the active control technique, suitable algebraic conditions are obtained analytically that establish the globally exponential synchronization. The proposed globally exponential synchronization criterion is more general and much less conservative than the previously published works. A comparison, based upon the synchronization speed, cost and quality have been performed with our study of the previously published results. The effect of unknown external disturbances has also been discussed. Numerical simulation results are presented to illustrate the performance and efficiency of this study.

  • Keywords

    Chaos Synchronization; Active Control; Lyapunov Stability Theory; Extended Bonhoeffer-Van Der Pol Oscillator; Chen Oscillator.

  • References

      [1] Pecora L, Carroll T (1991), Synchronization in chaotic systems. Physics Review Letters 64, 821–823.

      [2] Boccalettia S, Kurths J, Osipov G, Valladares DL, Zhou CS (2002), The synchronization of chaotic systems. Physics Reports 366, 201–101.

      [3] Xu Y, He Z (2013), Synchronization of variable-order fractional financial system via active control. Central European Journal of Physics 11, 6, 824-835.

      [4] Ahmad I, Saaban A, Ibrahim A, Shahzad M, Naveed N (2016),The Synchronization of chaotic systems with different dimensions by a robust generalized active control. Optik-International Journal for Light and Electron Optics 127, 11, 4859–4871.

      [5] Li X (2009), Generalized projective synchronization using nonlinear control method. International Journal of Nonlinear Science 8, 1, 79-85.

      [6] Ahmad I, Saaban A, Ibrahim A, Shahzad M (2016), Global chaos synchronization of new chaotic system using linear active control. Complexity 21, 1, 379-386.

      [7] Ahmad I, Saaban A, Ibrahim A, Shahzad M, Alsawalha M (2016), Robust reduced-order synchronization of times-delay chaotic systems with known and unknown parameters, Optik-International Journal for Light and Electron Optics 127, 13, 5506-5514.

      [8] Yan, ZY (2005), a new scheme to generalize (lag, anticipated, and complete) synchronization in chaotic and hyperchaotic systems. Chaos 15:013101-013110.

      [9] Zhang B, Li H (2014), Universal function projective synchronization of two different hyperchaotic systems with unknown parameters. Journal of Applied Mathematics, Article ID 549201, 10 pages.

      [10] Chen Y, Li M, Cheng Z (2010), Global anti-synchronization of master–slave chaotic modified Chua’s circuits coupled by linear feedback control. Mathematical and Computer Modeling 52, 3-4, 567-573.

      [11] Ho M, Hung Y (2001), Synchronization of two different systems by using generalized active control. Physics Letters A 301, 424–428.

      [12] Chen H (2002), Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping. Journal of Sound and Vibration 255, 719–740.

      [13] Ucar A, Lonngren KE, Bai EW (2007), Chaos synchronization in RCL-shunted Josephson junction via active control. Chaos, Solitons and Fractals 31, 105–111.

      [14] Vincent UE, Ucar A (2007), Synchronization and anti-synchronization of chaos in permanent magnet reluctance machine. Far East Journal of Dynamical Systems 9, 211–221.

      [15] Njah AN, Vincent UE (2009), Synchronization and anti-synchronization of chaos in an extended Bonhoffer-van der Pol oscillator using active control. Journal of Sound and Vibration 319, 493-504.

      [16] Khalil HK (2002), Nonlinear Systems, 3rded. Prentice Hall, New Jersey.

      [17] Anderson P, Fouad A (1984), Power System Control and Stability, Iowa State University Press, Ames, Iowa.

      [18] Liao X, Yu P (2006), Study of globally exponential synchronization for the family of Rossler systems. International Journal of Bifurcation and Chaos 16, 8, 2395-2406.

      [19] Zhou T, Chen G (2006), Classification of chaos in 3-D autonomous quadratic system-1. Basic framework and method. International Journal of Bifurcation and Chaos 16(9) 2456-2479, 2006.

      [20] Wang Q, You Y, Wang H (2014), robust synchronization of hyperchaotic systems with uncertainties and external disturbances. Journal of Applied Mathematics. Article ID 523572, 8 pages.

      [21] Boyd S (2004). Convex optimization, Cambridge University Press, NY, USA.

      [22] Wirkus S, Rand R (2002), the dynamics of two coupled Van der Pol oscillators with delay coupling. Nonlinear Dynamics 30, 205-221.

      [23] Sekikawa M, Inaba N, Yoshinaga T, Hikihara T (2010), Period-doubling cascades of canards from the extended Bonhoeffer‒van der Pol oscillator. Physics Letters A 374, 36, 3745-3751.

      [24] Sekikawa M, Shimizu K, Inaba N, Kita H, Endo T, Fujimoto K, Yoshinaga T, Aihara K (2011), Sudden change from chaos to oscillation death in the Bonhoeffer–van der Pol oscillator under weak periodic perturbation. Physics Review E 84, 056209.

      [25] Ramesh M, Narayanan S (2001), Chaos control of Bonho¨ ffer–van der Pol oscillator using neural networks. Chaos, Solitons and Fractals 12, 2395–2405.




Article ID: 7770
DOI: 10.14419/ijams.v5i2.7770

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.