Discrete-time fractional-order local active memristor-based Hopfield neural network and its FPGA implementation

Abstract

In this paper, a fractional-order discrete-time Hopfield neural network (HNN) with three neurons is studied, and discrete-time fractional-order local active memristor is used as the mutual synapses and electromagnetic radiation of HNN neurons respectively. Chaotic dynamic characteristics of the entire four-dimensional fractional discrete-time system are analyzed, including Li’s index, phase diagram, bifurcation diagram analysis. The results show that the system has attractor coexistence, multi-stability phenomena and other, which proves its complex dynamic characteristics. In addition, the truncation method is applied to the caputo operator for the first time to realize the discrete fractional order system with FPGA, and the results are shown.