规则连接神经网络的同步分析与模拟
Synchronization Analysis and Simulation on Regular Coupled Neural Networks
DOI: 10.12677/DSC.2019.82009, PDF,    国家自然科学基金支持
作者: 温 娜, 刘深泉：华南理工大学数学学院，广东 广州
关键词: Hindmarsh-Rose模型；李雅普诺夫函数；全局渐近稳定；Hindmarsh-Rose Model； Lyapunov Function； Global Asymptotic Stability
摘要: 我们以Hindmarsh-Rose (HR)模型作为例子，研究了规则连接神经网络的同步特性。通过引入适当的偏差变量，将同步流形的稳定性转化为偏差方程零解的稳定性。为偏差方程构造合适的李雅普诺夫函数，得到了HR神经网络实现全局渐近同步的相关准则。理论结果显示了神经元数目和连接方式对神经网络同步的影响。数值模拟验证了文中结果的可靠性。
Abstract: We take Hindmarsh-Rose (HR) model as an example to study the synchronization property of reg-ular coupled neural networks. Through introducing appropriate error variable, we transform the stability of synchronization manifold into that of null solution of error equations. By constructing a proper Lyapunov function for error equations, the relative criterion is theoretically provided for global asymptotic synchronization of HR neural networks. Further, the theoretical result shows the influence of neuron numbers and connection types in neural network on synchronization. Numerical simulations test the reliability of the results in this paper.
文章引用：温娜, 刘深泉. 规则连接神经网络的同步分析与模拟[J]. 动力系统与控制, 2019, 8(2): 71-80. https://doi.org/10.12677/DSC.2019.82009

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