Unveiling Hyperchaos and Homogeneous Multistability in Discrete Memristive Hopfield Neural Networks with Dual Electromagnetic Radiation: From Transient Chaos to Hardware Implementation

Abstract External stimuli can influence the activities of neurons, leading to diverse and complex dynamical behaviors. Memristors can be employed to characterize the external electromagnetic radiation experienced by neurons, providing an effective approach for investigating the complex dynamics of neural networks under electromagnetic radiation. Accordingly, two discrete memristors are introduced into a discrete Hopfield neural network (HNN) with two neurons to model the external electromagnetic radiation acting on the two neurons, resulting in two four-dimensional discrete HNN models corresponding to scenarios involving electromagnetic radiation of the same and different types, respectively. The dynamical characteristics of the two models are systematically investigated using phase portraits, time series, bifurcation diagrams, Lyapunov exponents, and basins of attraction. The results demonstrate that both models exhibit rich dynamical behaviors, including periodic, chaotic, and hyperchaotic states, as well as homogeneous multistability. In addition, the scenario involving different types of electromagnetic radiation exhibits complex transient chaotic behavior. For hardware implementation, the two four-dimensional discrete HNN models are implemented on an FPGA, demonstrating their physical realizability. Furthermore, a color image encryption algorithm is designed using the hyperchaotic sequences generated by the model in Scenario 2, and its effectiveness is evaluated through multiple security performance metrics, demonstrating the models potential for image encryption applications.