In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fractional derivative. To realize asymptotical synchronization, two types of adaptive coupling weights are considered, namely: 1) coupling weights only related to time and 2) coupling weights dependent on both time and space. For each type of coupling weights, based on local information of the node's dynamics, an edge-based fractional-order adaptive law and an edge-based fractional-order pinning adaptive scheme are proposed. Furthermore, some new analytical tools, including the method of contradiction, L'Hopital rule, and Barbalat lemma are developed to establish adaptive synchronization criteria of the addressed networks. Finally, an example with numerical simulations is provided to illustrate the validity and effectiveness of the theoretical results.

中文翻译：

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基于边缘的分数阶自适应策略，用于分数阶耦合网络与Reaction__iffusion项的同步


本文将空间扩散引入分数阶耦合网络，并研究了具有反应扩散项的分数阶耦合神经网络的同步问题。首先，基于Caputo偏分数阶导数建立了新的分数阶不等式。为了实现渐近同步，考虑两种类型的自适应耦合权重，即：1）仅与时间相关的耦合权重；2）与时间和空间同时相关的耦合权重。对于每种类型的耦合权重，基于节点动态的局部信息，提出了基于边缘的分数阶自适应律和基于边缘的分数阶钉扎自适应方案。此外，还开发了一些新的分析工具，包括矛盾法、L'Hopital规则和Barbalat引理，以建立所解决网络的自适应同步标准。最后通过数值模拟算例说明了理论结果的有效性和有效性。