Dynamics in a Memristive Neural Network With Three Discrete Heterogeneous Neurons and Its Application

Abstract

Real brains exist with neural networks consisting of heterogeneous neuronal connections. However, there have been many studies on memristive homogeneous neural networks and few studies on memristive heterogeneous neural networks. In this article, we propose a discrete memristor such that it acts as one of the synapses of a neural network model with three heterogeneous neurons to obtain a discrete heterogeneously coupled network (DHN), which consists of a 2D FitzHugh-Nagumo (FHN) neuron, a Rulkov neuron, and a 2D Hindmarsh-Rose (HR) neuron. Using methods such as Lyapunov exponent analysis and bifurcation diagrams, we carry out dynamical analysis of the DHN and find that it has rich dynamical behaviour, including hyperchaos with three positive exponents, hidden attractors, transient chaos, and attractor coexistence. In addition, we implement the DHN model on a hardware platform based on field programmable gate array (FPGA). This not only verifies the correctness of the model, but also provides a reference for designing hardware brain-like systems based on FPGA implementation. Last but not least, we apply the DHN to generative adversarial networks (GAN) and show that it can effectively improve the performance of GAN.