One of the main problems connected with neural networks is synchronization. We examine a model of a neural network with time-varying delay and also the case when the connection weights (the influential strength of the j j th neuron to the i i th neuron) are variable in time and unbounded. The rate of change of the dynamics of all neurons is described by the Caputo fractional derivative. We apply Lyapunov functions and the Razumikhin method to obtain some sufficient conditions to ensure synchronization in the model. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. We illustrate our theory with a particular nonlinear neural network.

中文翻译：

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具有有界时变延迟的 Caputo 分数阶神经网络的同步

与神经网络相关的主要问题之一是同步。我们研究了具有时变延迟的神经网络模型，以及连接权重（第 jj 个神经元对第 ii 个神经元的影响强度）随时间变化且无界的情况。所有神经元动力学的变化率由 Caputo 分数导数描述。我们应用 Lyapunov 函数和 Razumikhin 方法来获得一些充分条件以确保模型中的同步。这些充分条件用系统参数明确表示，因此很容易验证。我们用一个特定的非线性神经网络来说明我们的理论。