Zhang Hao, Zeng Zhigang, Han Qing-Long
IEEE Trans Cybern. 2019 Aug;49(8):2980-2991. doi: 10.1109/TCYB.2018.2837090. Epub 2018 Jun 13.
The synchronization problem of multiple/coupled reaction-diffusion neural networks with time-varying delays is investigated. Differing from the existing considerations, state delays among distinct neurons and coupling delays among different subnetworks are included in the proposed model, the assumptions posed on the arisen delays are very weak, time-varying, heterogeneous, even unbounded delays are permitted. To overcome the difficulties from this kind of delay as well as diffusion effects, a comparison-based approach is applied to this model and a series of algebraic criteria are successfully obtained to verify the global asymptotical synchronization. By specifying the existing delays, some M -matrix-based criteria are derived to justify the power-rate synchronization and exponential synchronization. In addition, new criterion on synchronization of general connected neural networks without diffusion effects is also given. Finally, two simulation examples are given to verify the effectiveness of the obtained theoretical results and provide a comparison with the existing criterion.
研究了具有时变延迟的多个/耦合反应扩散神经网络的同步问题。与现有研究不同，所提出的模型中包含了不同神经元之间的状态延迟以及不同子网络之间的耦合延迟，对所出现延迟的假设非常宽松，允许时变、异构甚至无界延迟。为了克服这种延迟以及扩散效应带来的困难，将一种基于比较的方法应用于该模型，并成功获得了一系列代数准则来验证全局渐近同步。通过指定现有的延迟，推导了一些基于M矩阵的准则来证明幂率同步和指数同步。此外，还给出了无扩散效应的一般连通神经网络同步的新准则。最后，给出了两个仿真例子来验证所获理论结果的有效性，并与现有准则进行比较。
