IEEE Trans Neural Netw Learn Syst. 2018 Apr;29(4):807-818. doi: 10.1109/TNNLS.2017.2647811. Epub 2017 Jan 24.
In this paper, an antisynchronization problem is considered for an array of linearly coupled reaction-diffusion neural networks with cooperative-competitive interactions and time-varying coupling delays. The interaction topology among the neural nodes is modeled by a multilayer signed graph. The state evolution of a neuron in each layer of the coupled neural network is described by a reaction-diffusion equation (RDE) with Dirichlet boundary conditions. Then, the collective dynamics of the multilayer neural network are modeled by coupled RDEs with both spatial diffusion coupling and state coupling. An edge-based adaptive antisynchronization strategy is proposed for each neural node to achieve antisynchronization by using only local information of neighboring nodes. Furthermore, when the activation functions of the neural nodes are unknown, a linearly parameterized adaptive antisynchronization strategy is also proposed. The convergence of the antisynchronization errors of the nodes is analyzed by using a Lyapunov-Krasovskii functional method and a structural balance condition. Finally, some numerical simulations are presented to demonstrate the effectiveness of the proposed antisynchronization strategies.
本文研究了一类具有合作竞争相互作用和时变耦合时滞的线性耦合反应扩散神经网络的反同步问题。通过多层有向符号图来建模神经网络节点之间的相互作用拓扑。耦合神经网络中每层的神经元的状态演化由具有狄利克雷边界条件的反应扩散方程（RDE）来描述。然后，通过具有空间扩散耦合和状态耦合的耦合 RDE 来对多层神经网络的集体动力学进行建模。针对每个神经元提出了基于边的自适应反同步策略，通过仅使用相邻节点的局部信息来实现反同步。此外，当神经元的激活函数未知时，还提出了一种线性参数化自适应反同步策略。通过使用李雅普诺夫-克拉索夫斯基泛函方法和结构平衡条件分析了节点反同步误差的收敛性。最后，给出了一些数值模拟结果，以验证所提出的反同步策略的有效性。
