Abstract and Applied Analysis

Adaptive Synchronization for a Class of Cellular Neural Networks with Pantograph Delays

Xuehui Mei, Jiuju Xing, Haijun Jiang, Cheng Hu, and Liwei Zhang

Full-text: Open access

Abstract

This paper deals with the synchronization problem for a class of cellular neural networks with pantograph delays. By using Lyapunov functional theory and inequality technique, some new and useful results are obtained for asymptotical synchronization under adaptive feedback controller.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 198780, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512202

Digital Object Identifier
doi:10.1155/2013/198780

Mathematical Reviews number (MathSciNet)
MR3139476

Zentralblatt MATH identifier
1298.34141

Citation

Mei, Xuehui; Xing, Jiuju; Jiang, Haijun; Hu, Cheng; Zhang, Liwei. Adaptive Synchronization for a Class of Cellular Neural Networks with Pantograph Delays. Abstr. Appl. Anal. 2013 (2013), Article ID 198780, 7 pages. doi:10.1155/2013/198780. https://projecteuclid.org/euclid.aaa/1393512202


Export citation

References

  • L. O. Chua and L. Yang, “Cellular neural networks: theory,” IEEE Transactions on Circuits and Systems, vol. 35, no. 10, pp. 1257–1272, 1988.
  • L. O. Chua and L. Yang, “Cellular neural networks: applications,” IEEE Transactions on Circuits and Systems, vol. 35, no. 10, pp. 1273–1290, 1988.
  • Z. J. Gui and X. S. Yang, “Stability and existence of periodic solutions of periodic cellular neural networks with time-varying delays,” Computers & Mathematics with Applications, vol. 52, no. 12, pp. 1657–1670, 2006.
  • H. Jiang, Z. Li, and Z. Teng, “Boundedness and stability for nonautonomous cellular neural networks with delay,” Physics Letters A, vol. 306, no. 5-6, pp. 313–325, 2003.
  • Z. J. Gui and W. G. Ge, “Existence and uniqueness of periodic solutions of nonautonomous cellural neural networks with impulses,” Physics Letters A, vol. 354, pp. 84–94, 2006.
  • H. J. Jiang and Z. D. Teng, “A new criterion on the global exponential stability for cellural neural networks with multiple time-varying delays,” Physics Letters A, vol. 338, pp. 461–471, 2005.
  • Q. Song and J. Cao, “Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses,” Journal of the Franklin Institute, vol. 345, no. 1, pp. 39–59, 2008.
  • W. Ding, “Synchronization of delayed fuzzy cellular neural networks with impulsive effects,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 11, pp. 3945–3952, 2009.
  • W. Ding, M. Han, and M. Li, “Exponential lag synchronization of delayed fuzzy cellular neural networks with impulses,” Physics Letters A, vol. 373, no. 8-9, pp. 832–837, 2009.
  • X. Gao, S. Zhong, and F. Gao, “Exponential synchronization of neural networks with time-varying delays,” Nonlinear Analysis, vol. 71, no. 5-6, pp. 2003–2011, 2009.
  • J. Yu, C. Hu, H. Jiang, and Z. Teng, “Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control,” Mathematics and Computers in Simulation, vol. 82, no. 5, pp. 895–908, 2012.
  • M. Hu and Z. Xu, “Adaptive feedback controller for projective synchronization,” Nonlinear Analysis: Real World Applications, vol. 9, no. 3, pp. 1253–1260, 2008.
  • W. Ding and M. Han, “Synchronization of delayed fuzzy cellular neural networks based on adaptive control,” Physics Letters A, vol. 372, no. 26, pp. 4674–4681, 2008.
  • X. Yang and J. Cao, “Stochastic synchronization of coupled neural networks with intermittent control,” Physics Letters A, vol. 373, no. 36, pp. 3259–3272, 2009.
  • Y. Yang and J. Cao, “Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects,” Physica A, vol. 386, no. 1, pp. 492–502, 2007.
  • X. Yang, J. Cao, Y. Long, and R. Wei, “Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations,” IEEE Transactions on Neural Networks, vol. 21, no. 10, pp. 1656–1667, 2010.
  • X. Yang, C. Huang, and J. Cao, “An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays,” Neural Computing and Applications, vol. 21, no. 8, pp. 2033–2047, 2012.
  • J. Cao and J. Lu, “Adaptive synchronization of neural networks with or without time-varying delay,” Chaos, vol. 16, no. 1, Article ID 013133, 2006.
  • X. Huang and J. Cao, “Generalized synchronization for delayed chaotic neural networks: a novel coupling scheme,” Nonlinearity, vol. 19, no. 12, pp. 2797–2811, 2006.
  • P. Li, J. Cao, and Z. Wang, “Robust impulsive synchronization of coupled delayed neural networks with uncertainties,” Physica A, vol. 373, pp. 261–272, 2007.
  • Y. Sun, J. Cao, and Z. Wang, “Exponential synchronization of stochastic perturbed chaotic delayed neural networks,” Neurocomputing, vol. 70, no. 13–15, pp. 2477–2485, 2007.
  • Y. Sun and J. Cao, “Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation,” Physics Letters A, vol. 364, no. 3-4, pp. 277–285, 2007.
  • Q. Gan, R. Hu, and Y. Liang, “Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 9, pp. 3708–3718, 2012.
  • Y. Tang, R. Qiu, J. Fang, Q. Miao, and M. Xia, “Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays,” Physics Letters A, vol. 372, no. 24, pp. 4425–4433, 2008.
  • C. Hu, H. Jiang, and Z. Teng, “Fuzzy impulsive control and synchronization of general chaotic system,” Acta Applicandae Mathematicae, vol. 109, no. 2, pp. 463–485, 2010.
  • K. Tanaka and H. O. Wang, “Fuzzy control of chaotic systems using LMIs: regulation, synchronization and chaos model following,” in Proceedings of the IEEE International Conference on Fuzzy Systems, vol. 1, pp. 434–439, May 1998.
  • H. Zhang, Z.-H. Guan, and D. W. C. Ho, “On synchronization of hybrid switching and impulsive networks,” in Proceedings of the 45th IEEE Conference on Decision and Control (CDC '06), vol. 1, pp. 2765–2770, San Diego, Calif, USA, December 2006.
  • W. Xia and J. Cao, “Pinning synchronization of delayed dynamical networks via periodically intermittent control,” Chaos, vol. 19, no. 1, Article ID 013120, 2009.
  • B. Liu, X. Liu, G. Chen, and H. Wang, “Robust impulsive syn-chronization of uncertain dynamical networks,” IEEE Transactions on Circuits and Systems I, vol. 52, no. 7, pp. 1431–1441, 2005.
  • W. Yu and J. Cao, “Synchronization control of stochastic delayed neural networks,” Physica A, vol. 373, pp. 252–260, 2007.
  • X. Liao, K. W. Wong, and Z. Wu, “Bifurcation analysis on a two-neuron system with distributed delays,” Physica D, vol. 149, no. 1-2, pp. 123–141, 2001.
  • J. Cao and D. W. C. Ho, “A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach,” Chaos, Solitons & Fractals, vol. 24, no. 5, pp. 1317–1329, 2005.