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**Exponential stability of continuous-time and discrete-time cellular neural networks with delays.**
*(English)*
Zbl 1030.34072

Summary: Convergence characteristics of continuous-time cellular neural networks with discrete delays are studied. By using Lyapunov functionals, we obtain delay independent sufficient condition for the networks to converge exponentially toward the equilibria associated with the constant input sources. Halanay-type inequalities are employed to obtain sufficient conditions for the networks to be globally exponentially stable. It is shown that the estimates obtained from the Halanay-type inequalities improve the estimates obtained from the Lyapunov methods. Discrete-time analogues of the continuous-time cellular neural networks are formulated and studied. It is shown that the convergence characteristics of the continuous-time systems are preserved by the discrete-time analogues without any restriction imposed on the uniform discretization step size.

### MSC:

34K20 | Stability theory of functional-differential equations |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

39A99 | Difference equations |

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\textit{S. Mohamad} and \textit{K. Gopalsamy}, Appl. Math. Comput. 135, No. 1, 17--38 (2003; Zbl 1030.34072)

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