Exploring uncharted dynamics of a novel memristive Hopfield network with a dGaussian activation function

Memristors and activation functions represent two critical nonlinear elements that collectively govern the dynamics of memristive Hopfield neural networks. The influence of different memristors on the dynamics of Hopfield neural networks has been extensively studied by numerous researchers. However, most of these Hopfield neural networks employ the hyperbolic tangent function as their activation function, leaving the behavior of such networks under other types of activation functions relatively unexplored. This paper proposes a memristive Hopfield neural network that utilizes the Gaussian derivative function as its activation function. The network is structured as a three-neuron Hopfield neural network, implemented by replacing the autaptic connection of one neuron with a memristive synapse. Theoretical and experimental investigations of the neural network dynamics have been conducted using phase portraits, bifurcation diagrams, Lyapunov exponent spectra, two-parameter dynamic plots, and three-parameter plots. Numerical simulations reveal complex dynamical behaviors, including chaotic bursting, periodic bursting, transient chaos, and chaotic state jump. Furthermore, circuit simulations using LTspice were performed to validate the feasibility of the design, which was subsequently successfully deployed on an FPGA development board. The experimental results show good agreement with the numerical simulations.