Dynamics of heterogeneous Hopfield neural network with adaptive activation function based on memristor

Abstract

Memristor and activation function are two important nonlinear factors of the memristive Hopfield neural network. The effects of different memristors on the dynamics of Hopfield neural networks have been studied by many researchers. However, less attention has been paid to the activation function. In this paper, we present a heterogeneous memristive Hopfield neural network with neurons using different activation functions. The activation functions include fixed activation functions and an adaptive activation function, where the adaptive activation function is based on a memristor. The theoretical and experimental study of the neural network’s dynamics has been conducted using phase portraits, bifurcation diagrams, and Lyapunov exponents spectras. Numerical results show that complex dynamical behaviours such as multi-scroll chaos, transient chaos, state jumps and multi-type coexisting attractors can be observed in the heterogeneous memristive Hopfield neural networks. In addition, the hardware implementation of memristive Hopfield neural network with adaptive activation function is designed and verified. The experimental results are in good agreement with those obtained using numerical simulations.