Influence of Memristive Activated Gradient on Chaotic Dynamics in Discrete Neural Networks

The memory characteristics and high nonlinearity of memristors make them ideal devices for simulating artificial synapses. The hyperbolic tangent function is a commonly used activation function in Hopfield neurons, where its activation gradient serves as a gain scaling parameter reflecting the response speed of neuronal electrical activity. This paper employs an exponential-type memristor as the activation gradient on the second neuron and proposes a novel method for integrating memristors with discrete coupled neural networks. Furthermore, the effect of the memristor’s gain on the hyperbolic tangent activation function is analyzed. Furthermore, a Discrete Hopfield Neural Network (DHNN) model with infinitely many equilibrium points is constructed by integrating a discrete magnetically controlled memristive model with sine and square functions as subsynapses of the first neuron. The results indicate that this DHNN can exhibit complex and diverse dynamical behaviors related to multiple system parameters, including rare hyperchaotic behavior characterized by four positive Lyapunov exponents, discharge mode transitions, and coexisting attractors phenomena. Based on these, an efficient and secure color image encryption scheme is designed, and extensive security analysis shows that the proposed scheme has strong security performance.