基于分数阶忆阻器的4D-Hopfield神经网络动力学分析

Dynamical Analysis on 4D-Hopfield Neural Network Based on a Fractional-order Memristor

忆阻Hopfield神经网络是研究人脑行为的一种重要模型。研究人员运用Caputo分数阶微分定义,将整数阶双曲型忆阻器推导至分数阶双曲型忆阻器,同时验证了它的忆阻特性,并且提出了分数阶忆阻Hopfield神经网络。对该模型的平衡点与稳定性的理论分析,表明了系统具有多个平衡点的特点。此外,运用Adams–Bashforth–Moulton算法对所提出的分数阶忆阻Hopfield神经网络系统进行的相图及时域图的数值仿真,揭示了在不同耦合强度、不同分数阶阶次下系统展现出复杂的动力学行为。

The memristive Hopfield neural network is an important model for studying human brain behavior. Researchers pushed the theory of hyperbolic-type memristor from integer-order to fractional-order by use of the Caputo fractional-order differential definition, and verified its memristive characteristics. On this basis, the fractional-order memristive Hopfield neural network is proposed. The theoretical analysis on the equilibrium point and stability of this network presented that the network has multiple equilibrium points. Meanwhile, the numerical simulation of the phase diagrams and time domain figures of the fractional-order memristive Hopfield neural network by means of Adams–Bashforth–Moulton method reveals that the complex dynamic behavior of the system in different coupling strength and fractional orders.