This paper investigates the behavior and synchronization of a network of reaction–diffusion neural dynamics models using a highly efficient numerical method. In fact, the dynamical modeling, behavior analysis and controlled synchronization of a network of FitzHugh–Nagumo (FHN) neurons which promising the understanding of cognitive processing are studied by considering the unidirectional gap junctions in the medium between two distant neurons. In this study, radial basis function generated finite differences (RBF-FD) technique is employed in conjunction with a suitable operator splitting technique, which allows us to decouple the nonlinear partial differential equations of neural network models into independent linear algebraic equations of very small dimensions. The most important advantages of the proposed method can be high accuracy and high speed, very low computational complexity, and the sparsity property of the matrix of the coefficients derived from its linear systems, which distinguish the proposed method from other methods. The analyses and numerical results presented totally confirm these claims.

本文使用高效的数值方法研究了反应扩散神经动力学模型网络的行为和同步性。实际上，通过考虑两个遥远神经元之间的介质中的单向间隙连接，研究了有望认识认知加工的FitzHug–Nagumo（FHN）神经元网络的动力学建模，行为分析和受控同步。在这项研究中，径向基函数生成有限差分（RBF-FD）技术与合适的算子拆分技术结合使用，这使我们能够将神经网络模型的非线性偏微分方程解耦为尺寸非常小的独立线性代数方程。所提出的方法的最重要的优点可以是高精度和高速度，非常低的计算复杂度以及从其线性系统导出的系数矩阵的稀疏性，这使所提出的方法与其他方法区别开来。提出的分析和数值结果完全证实了这些主张。