Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control.

*(English)*Zbl 1197.93135Summary: 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 |

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

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[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. |

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