Dynamic analysis of FN–HR neural network coupled of bistable memristor and encryption application based on Fibonacci Q-Matrix

In this paper, a cosine hyperbolic memristor model is proposed with bistable asymmetric hysteresis loops. A neural network of coupled hyperbolic memristor is constructed by using the Fitzhugh–Nagumo model and the Hindmarsh–Rose model. The coupled neural network with a large number of equilibrium points is obtained by numerical analysis. In addition, the coexisting discharge behavior of the coupled neural network is revealed using local attractor basins. The complex dynamic properties of the memristor-coupled neural network are verified by analyzing the two-parameter Lyapunov exponential map and spectral entropy map, and the equivalent circuit of the coupled neural network is designed to prove the accuracy of the numerical analysis. Finally, an image encryption algorithm is proposed, which combines coupled neural network and Fibonacci Q-Matrix. The numerical analysis demonstrates that the algorithm exhibits strong security and resistance against cracking attempts.