Dynamic analysis of a memristor Hopfield neural network with adjustable neuron activation gradient and synaptic weight

To aid researchers in gaining a deeper understanding of the evolutionary laws within the dynamical system of neural networks, we propose a neural network with variable neuron activation gradient and synaptic weight. This paper investigates the stability and dynamics of a memristor Hopfield neural network (HNN) model. Numerical simulations, carried out in terms of two-parameter bifurcation diagrams, dynamical maps, local basins of attraction, and time sequence diagrams, are used to demonstrate the abundant and complex phenomena of the model. These nonlinear dynamical behaviors include the alternation of unbounded and stable regions, the existence of stable point boundaries in unbounded regions, the coexistence of multi-stability and hidden phenomena (e.g., transient period, intermittent chaos, coexistence transient chaos, and transient quasi-period). Moreover, the circuit simulation and implementation verify that the experimental results are in good agreement with the theoretical analysis.