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**Novel criteria for global exponential periodicity and stability of recurrent neural networks with time-varying delays.**
*(English)*
Zbl 1141.93393

Summary: The global exponential periodicity and stability of recurrent neural networks with time-varying delays are investigated by applying the idea of vector Lyapunov function, \(M\)-matrix theory and inequality technique. We assume neither the global Lipschitz conditions on these activation functions nor the differentiability on these time-varying delays, which were needed in other papers. Several novel criteria are found to ascertain the existence, uniqueness and global exponential stability of periodic solution for recurrent neural network with time-varying delays. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. Some previous results are improved and generalized, and an example is given to show the effectiveness of our method.

### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

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

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\textit{Q. Song}, Chaos Solitons Fractals 36, No. 3, 720--728 (2008; Zbl 1141.93393)

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### References:

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