School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China.
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China.
Chaos. 2022 Aug;32(8):083133. doi: 10.1063/5.0099466.
As the shortest feedback loop of the nervous system, autapse plays an important role in the mode conversion of neurodynamics. In particular, memristive autapses can not only facilitate the adjustment of the dynamical behavior but also enhance the complexity of the nervous system, in view of the fact that the dynamics of the Hopfield neural network has not been investigated and studied in detail from the perspective of memristive autapse. Based on the traditional Hopfield neural network, this paper uses a locally active memristor to replace the ordinary resistive autapse so as to construct a 2 n-dimensional memristive autaptic Hopfield neural network model. The boundedness of the model is proved by introducing the Lyapunov function and the stability of the equilibrium point is analyzed by deriving the Jacobian matrix. In addition, four scenarios are established on a small Hopfield neural network with three neurons, and the influence of the distribution of memristive autapses on the dynamics of this small Hopfield neural network is described by numerical simulation tools. Finally, the Hopfield neural network model in these four situations is designed and implemented on field-programmable gate array by using the fourth-order Runge-Kutta method, which effectively verifies the numerical simulation results.
作为神经系统中最短的反馈回路，自突触在神经动力学的模式转换中起着重要作用。特别是，忆阻自突触不仅可以促进动力学行为的调整，还可以增强神经系统的复杂性，因为从忆阻自突触的角度来看，尚未对 Hopfield 神经网络的动力学进行详细的研究和探讨。本文基于传统的 Hopfield 神经网络，使用局部激活忆阻器代替普通的电阻自突触，从而构建了一个 2n 维忆阻自突触 Hopfield 神经网络模型。通过引入李雅普诺夫函数证明了模型的有界性，并通过推导雅可比矩阵分析了平衡点的稳定性。此外，在一个具有三个神经元的小 Hopfield 神经网络上建立了四个场景，并通过数值模拟工具描述了忆阻自突触的分布对这个小 Hopfield 神经网络动力学的影响。最后，通过使用四阶龙格-库塔法，在现场可编程门阵列上对这四种情况下的 Hopfield 神经网络模型进行了设计和实现，有效地验证了数值模拟结果。
