In this article, the exponential stability problem for fractional-order complex multi-links networks with aperiodically intermittent control is considered. Using the graph theory and Lyapunov method, two theorems, including a Lyapunov-type theorem and a coefficient-type theorem, are given to ensure the exponential stability of the underlying networks. The theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative. To be specific, the larger control gain, the higher the exponential convergence rate. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control, a corollary is also provided to ensure the exponential stability of the underlying networks. Furthermore, to show the practicality of theoretical results, as an application, the exponential stability of fractional-order multi-links competitive neural networks with aperiodically intermittent control is investigated and a stability criterion is established. Finally, the effectiveness and feasibility of the theoretical results are demonstrated through a numerical example.

中文翻译：

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具有非周期性间歇控制的分数阶复杂多链路网络的指数稳定性

在本文中，考虑了具有非周期性间歇控制的分数阶复杂多链路网络的指数稳定性问题。利用图论和李雅普诺夫方法，给出了两个定理，包括李雅普诺夫型定理和系数型定理，以保证底层网络的指数稳定性。理论结果表明，指数收敛速度取决于控制增益和分数阶导数。具体来说，控制增益越大，指数收敛速度越高。同时，当非周期性间歇控制退化为周期性间歇控制时，还提供了一个推论来保证底层网络的指数稳定性。此外，为了展示理论结果的实用性，作为一个应用，研究了具有非周期性间歇控制的分数阶多链接竞争神经网络的指数稳定性，并建立了稳定性判据。最后，通过数值算例证明了理论结果的有效性和可行性。