Synchronization of the Complex Dynamical Networks with a Gui Chaotic Strange Attractor

Zhanji Gui, Lan Kang

Abstract

In this paper, impulsive neural networks with a Gui chaotic strange attractor is studied. By employing the Lyapunov-like stability theory of impulsive functional differential equations, some criteria for synchronization of impulsive neural networks are derived. An illustrative example is provided to show the effectiveness and feasibility of the proposed method and results.

References

  1. Amritkar, R. and Gupte, N. (1993). Synchronization of chaotic orbits: the effect of a finite time steps. In Physical Review E. 47: 3889C3895.
  2. Anzo, A. Barajas-Ramlrez J.G. (2014). Synchronization in complex networks under structural evolution. In Journal of the Franklin Institute. 351: 358-372.
  3. Cao, J. (1999). Global stability analysis in delayed cellular neural networks. In Phys Rev E. 59: 5940-5944.
  4. Dörfler, F. and Bullo, F. (2014). Synchronization in complex networks of phase oscillators: A survey. In Automatica. 50: 1539-1564.
  5. Gopalsamy, K. and He, H. (1994). Stability in asymmetric hopfield nets with transmission delay. In Physics D. 76: 344C358.
  6. Gui, Z. and Ge, W. (2006). Existence and uniqueness of periodic solutions of nonautonomous cellular neural networks with impulses. In Physics Letters A. 354: 84C94.
  7. Hopfield, J. (1982). Neural networks and physical systems with emergent collective computational abilities. In Proc Nat Acad Sci USA. 79: 2554-2558.
  8. Luo, R. (2008). Impulsive control and synchronization of a new chaotic system. In Physics Letters A. 372: 648C653.
  9. Subashini, M. M. and Sahoo, S. K. (2014). Pulse coupled neural networks and its applications. In Expert Systems with Applications. 41: 3965-3974.
  10. Song, Q. and Zhang, J. (2008). Global exponential stability of impulsive cohencgrossberg neural network with time-varying delays. In Nonlinear Anal Real World Appl. 9:500C510.
  11. Wan, D. and Huang, L. (2014). Periodicity and global exponential stability of generalized CohenCGrossberg neural networks with discontinuous activations and mixed delays. In Neural Networks. 51:80-95.
  12. Wan, Y. and Cao, J. (2015). Periodicity and synchronization of coupled memristive neural networks with supremums. In Neurocomputing. 159:137-143.
  13. Xie, C. and Xu, Y. (2014). ynchronization of time varying delayed complex networks via impulsive control. In Optik - International Journal for Light and Electron Optics. 125:3781-3787.
  14. Yang, T. and Chua, L. (1997). Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. In IEEE Transactions on Circuits and Systems-I. 44:976C988.
  15. Yang, T. and Chua, L. (1999a). Generalized synchronization of chaos via linear transformations. In International Journal of Bifurcation and Chaos. 9:215C219.
  16. Yang, T. and Chua, L. (1999b). Impulsive control and synchronization of non-linear dynamical systems and application to secure communication. In International Journal of Bifurcation and Chaos. 7:645C664.
  17. Yang, Y. and Cao, J. (2007). Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects. In Physica A. 386:492-502.
  18. Yang, Y. and Cao, J. (2010). Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects. In Nonlinear Analysis: Real World Applications. 11: 1650-1659.
  19. Zhang, C. (2009). Complete synchronization for impulsive cohencgrossberg neural networks with delay under noise perturbation. In Chaos, Solitons and Fractals. 42: 1664C1669.
  20. Zhang, J. and Gui, Z. (2009a). Existence and stability of periodic solutions of high-order hopfield neural networks with impulses and delays. In Journal of Computational and Applied Mathematics. 224: 602-613.
  21. Zhang, J. and Gui, Z. (2009b). Periodic solutions of nonautonomous cellular neural networks with impulses and delays. In Nonlinear Analysis: Real World Applications. 10: 1891-1903.
Download


Paper Citation


in Harvard Style

Gui Z. and Kang L. (2015). Synchronization of the Complex Dynamical Networks with a Gui Chaotic Strange Attractor . In Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-120-5, pages 257-262. DOI: 10.5220/0005504902570262


in Bibtex Style

@conference{simultech15,
author={Zhanji Gui and Lan Kang},
title={Synchronization of the Complex Dynamical Networks with a Gui Chaotic Strange Attractor},
booktitle={Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2015},
pages={257-262},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005504902570262},
isbn={978-989-758-120-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Synchronization of the Complex Dynamical Networks with a Gui Chaotic Strange Attractor
SN - 978-989-758-120-5
AU - Gui Z.
AU - Kang L.
PY - 2015
SP - 257
EP - 262
DO - 10.5220/0005504902570262