Fixed-time synchronization of coupled neural networks under Hölder continuous nonlinear activation function

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This paper investigates the fixed-time stability of dynamical systems and its application on the fixed-time synchronization (FTSYN) of the coupled neural networks (NNs). Firstly, a new theorem on fixed-time stability is established, along with an estimation of the settling time. Based on the new theorem and Lyapunov direct method, two different sufficient criteria are derived to ensure that the NNs in presence of Hölder continuity can achieve synchronization within fixed-time based on 1-norm and 2-norm, separately. Finally, two numerical simulations are conducted to demonstrate the validity and accuracy of the main findings.