##
**Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control.**
*(English)*
Zbl 1197.93135

Summary: A new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

### MSC:

93D15 | Stabilization of systems by feedback |

PDF
BibTeX
XML
Cite

\textit{B. Cui} and \textit{X. Lou}, Chaos Solitons Fractals 39, No. 1, 288--294 (2009; Zbl 1197.93135)

Full Text:
DOI

### References:

[1] | Arik, S., Stability analysis of delayed neural networks, IEEE trans circuits syst I, fundam theory appl, 47, 10, 1089-1092, (2000) · Zbl 0992.93080 |

[2] | Forti, M.; Nistri, P.; Papini, D., Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain, IEEE trans neural networ, 16, 6, 1449-1463, (2005) |

[3] | Gopalsamy, K.; He, X., Stability in asymmetric Hopfield nets with transmission delays, Phys D, 76, 344-358, (1994) · Zbl 0815.92001 |

[4] | Cao, J.; Wang, L., Periodic oscillatory solution of bidirectional associative memory networks with delays, Phys rev E, 61, 2, 1825-1828, (2000) |

[5] | Lou, X.Y.; Cui, B.T., Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays, J math anal appl, 330, 144-158, (2007) · Zbl 1111.68104 |

[6] | Cao, J.; Huang, D.S.; Qu, Y., Global robust stability of delayed recurrent neural networks, Chaos, solitons & fractals, 23, 1, 221-229, (2005) · Zbl 1075.68070 |

[7] | Lou, X.Y.; Cui, B.T., Passivity analysis of integro-differential neural networks with time variable delays, Neurocomputing, 70, 1071-1078, (2007) |

[8] | Lou, X.Y.; Cui, B.T., Absolute exponential stability analysis of delayed bi-directional associative memory neural networks, Chaos, solitons & fractals, 31, 3, 695-701, (2006) · Zbl 1147.34358 |

[9] | Lou, X.Y.; Cui, B.T., New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks, Neurocomputing, 69, 16-18, 2374-2378, (2006) |

[10] | Lou, X.Y.; Cui, B.T., Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays, IEEE trans syst, man cy part B, 37, 7, 713-719, (2007) |

[11] | Zou, F.; Nossek, J.A., Bifurcation and chaos in cellular neural networks, IEEE trans circuit syst I, 40, 3, 166-173, (1993) · Zbl 0782.92003 |

[12] | Gilli, M., Strange attractors in delayed cellular neural networks, IEEE trans circuit syst I, 40, 11, 849-853, (1993) · Zbl 0844.58056 |

[13] | Lu, H.T., Chaotic attractors in delayed neural networks, Phys lett A, 298, 109-116, (2002) · Zbl 0995.92004 |

[14] | Chen, G.; Zhou, J.; Liu, Z., Global synchronization of coupled delayed neural networks with application to chaotic CNN models, Int J bifurcat chaos, 14, 2229-2240, (2004) · Zbl 1077.37506 |

[15] | Lu, W.; Chen, T., Synchronization of coupled connected neural networks with delays, IEEE trans circuit syst I, 51, 2491-2503, (2004) · Zbl 1371.34118 |

[16] | Cao, J.; Lu, J., Adaptive synchronization of neural networks with or without time-varying delays, Chaos, 16, 1, 013133-1-013133-6, (2006) · Zbl 1144.37331 |

[17] | Lu, H.T.; van Leeuwen, C., Synchronization of chaotic neural networks via output or state coupling, Chaos, solitons & fractals, 30, 166-176, (2006) · Zbl 1144.37377 |

[18] | Lou, X.Y.; Cui, B.T., Asymptotic synchronization of a class of neural networks with reaction-diffusion terms and time-varying delays, Comput math appl, 52, 6-7, 897-904, (2006) · Zbl 1126.35083 |

[19] | Boyd, S., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia |

[20] | Xu, S.; Chen, T.; Lam, J., Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays, IEEE trans automat contr, 48, 900-907, (2003) · Zbl 1364.93816 |

[21] | Dawson, D.; Qu, Z.; Carroll, J.C., On the state observation and output feedback problems for nonlinear uncertain dynamic systems, Syst cont lett, 18, 217-222, (1992) · Zbl 0752.93021 |

[22] | Lou XY, Cui BT. Synchronization of competitive neural networks with different time scales. Physica A, in press. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.