Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2018, Article ID 6581493, 15 pages
https://doi.org/10.1155/2018/6581493
Research Article

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

Department of Electrical Engineering, Capital University of Science and Technology, Islamabad, Pakistan

Correspondence should be addressed to Nazam Siddique; moc.liamg@qiddis.mizan

Received 10 August 2017; Revised 11 October 2017; Accepted 28 November 2017; Published 30 January 2018

Academic Editor: Ton D. Do

Copyright © 2018 Nazam Siddique and Fazal ur Rehman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. H. Serrano-Guerrero, C. Cruz-Hernandez, R. M. Lopez-Gutierrez, L. Cardoza-Avendano, and R. A. Chávez-Párez, “Chaotic synchronization in nearest-neighbor coupled Networks of 3D CNNs,” Journal of Applied Research and Technology, vol. 11, no. 1, pp. 26–41, 2013. View at Publisher · View at Google Scholar · View at Scopus
  3. L. Jin, Y. Zhang, and L. Li, “One-to-many chaotic synchronization with application in wireless sensor network,” IEEE Communications Letters, vol. 17, no. 9, pp. 1782–1785, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. V. Dronov, Application of Chaotic Synchronization and Controlling Chaos to Communications, Diss, 2005.
  5. S. Das, U. Halder, and D. Maity, “Chaotic dynamics in social foraging swarms-an analysis,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 42, no. 4, pp. 1288–1293, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. Yu and H.-X. Li, “Adaptive generalized function projective synchronization of uncertain chaotic systems,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 2456–2464, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. G. M. Mahmoud, E. E. Mahmoud, and A. A. Arafa, “On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications,” Physica Scripta, vol. 87, no. 5, Article ID 055002, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Zhou, J.-a. Lu, and J. Lu, “Adaptive synchronization of an uncertain complex dynamical network,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 51, no. 4, pp. 652–656, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Sun, Q. Yin, and Y. Shen, “Compound synchronization for four chaotic systems of integer order and fractional order,” EPL (Europhysics Letters), vol. 106, no. 4, Article ID 40005, 2014. View at Publisher · View at Google Scholar
  10. J. Sun, Y. Shen, X. Wang, and J. Chen, “Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control,” Nonlinear Dynamics, vol. 76, no. 1, pp. 383–397, 2014. View at Publisher · View at Google Scholar · View at Scopus
  11. C. Jiang and S. Liu, “Synchronization and antisynchronization of N-coupled complex permanent magnet synchronous motor systems with ring connection,” Complexity, vol. 2017, Article ID 6743184, 15 pages, 2017. View at Publisher · View at Google Scholar · View at Scopus
  12. Q. Wei, X.-Y. Wang, and X.-P. Hu, “Hybrid function projective synchronization in complex dynamical networks,” AIP Advances, vol. 4, no. 2, Article ID 027128, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. C. Li, Q. Chen, and T. Huang, “Coexistence of anti-phase and complete synchronization in coupled chen system via a single variable,” Chaos, Solitons & Fractals, vol. 38, no. 2, pp. 461–464, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. F. Nian and W. Liu, “Hybrid synchronization of heterogeneous chaotic systems on dynamic network,” Chaos, Solitons & Fractals, vol. 91, pp. 554–561, 2016. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Wang, Y. Yu, and G. Wen, “Hybrid projective synchronization of time-delayed fractional order chaotic systems,” Nonlinear Analysis: Hybrid Systems, vol. 11, pp. 129–138, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. C.-H. Chen, L.-J. Sheu, H.-K. Chen et al., “A new hyper-chaotic system and its synchronization,” Nonlinear Analysis: Real World Applications, vol. 10, no. 4, pp. 2088–2096, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Hu, Z. Xu, R. Zhang, and A. Hu, “Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems,” Physics Letters A, vol. 361, no. 3, pp. 231–237, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. X. Wu and H. Lu, “Hybrid synchronization of the general delayed and non-delayed complex dynamical networks via pinning control,” Neurocomputing, vol. 89, pp. 168–177, 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. Q. Song, J. Cao, and F. Liu, “Pinning-controlled synchronization of hybrid-coupled complex dynamical networks with mixed time-delays,” International Journal of Robust and Nonlinear Control, vol. 22, no. 6, pp. 690–706, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. Y. Xu, W. Zhou, J. Fang, W. Sun, and L. Pan, “Adaptive synchronization of stochastic time-varying delay dynamical networks with complex-variable systems,” Nonlinear Dynamics, vol. 81, no. 4, pp. 1717–1726, 2015. View at Publisher · View at Google Scholar · View at Scopus
  21. W. Yu, J. Cao, and J. Lü, “Global synchronization of linearly hybrid coupled networks with time-varying delay,” SIAM Journal on Applied Dynamical Systems, vol. 7, no. 1, pp. 108–133, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  22. C. Jiang and S. Liu, “Generalized combination complex synchronization of new hyperchaotic complex Lü-like systems,” Advances in Difference Equations, vol. 2015, no. 1, article no. 214, 2015. View at Publisher · View at Google Scholar · View at Scopus
  23. N. Cai, Y. Jing, and S. Zhang, “Generalized projective synchronization of different chaotic systems based on antisymmetric structure,” Chaos, Solitons & Fractals, vol. 42, no. 2, pp. 1190–1196, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. I. M. Kyprianidis and I. N. Stouboulos, “Chaotic synchronization of three coupled oscillators with ring connection,” Chaos, Solitons & Fractals, vol. 17, no. 2-3, pp. 327–336, 2003. View at Publisher · View at Google Scholar · View at Scopus
  25. Q. Song and J. Cao, “Synchronization and anti-synchronization for chaotic systems,” Chaos, Solitons & Fractals, vol. 33, no. 3, pp. 929–939, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. G. M. Mahmoud and E. E. Mahmoud, “Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems,” Nonlinear Dynamics, vol. 61, no. 1-2, pp. 141–152, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. S. B. Wang, X. Y. Wang, X. Y. Wang, and Y. F. Zhou, “Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems,” AIP Advances, vol. 6, no. 4, Article ID 045011, 2016. View at Publisher · View at Google Scholar
  28. T. Dahms, J. Lehnert, and E. Schöll, “Cluster and group synchronization in delay-coupled networks,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 86, no. 1, part 2, Article ID 016202, 2012. View at Publisher · View at Google Scholar
  29. M. Jiménez-Martín, J. Rodríguez-Laguna, O. D'Huys, J. de la Rubia, and E. Korutcheva, “Synchronization of fluctuating delay-coupled chaotic networks,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 95, no. 5, article 052210, 2017. View at Publisher · View at Google Scholar
  30. Y. Sun, W. Li, and J. Ruan, “Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 4, pp. 989–998, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. J. Lu, D. W. Ho, and J. Cao, “Synchronization in an array of nonlinearly coupled chaotic neural networks with delay coupling,” International Journal of Bifurcation and Chaos, vol. 18, no. 10, pp. 3101–3111, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. X. Chen, J. Qiu, J. Cao, and H. He, “Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection,” Neurocomputing, vol. 173, pp. 1299–1309, 2016. View at Publisher · View at Google Scholar
  33. V. Utkin and J. Shi, “Integral sliding mode in systems operating under uncertainty conditions,” in Proceedings of the 35th IEEE Conference on Decision and Control, vol. 4, pp. 4591–4596, 1996.