Discrete Memristive Delay Feedback Rulkov Neuron Model: Chaotic Dynamics, Hardware Implementation, and Application in Secure Communication

Nowadays, while enjoying the convenience brought by the Internet of Things (IoT), people are also facing significant challenges in information security. A stable and reliable random source is an indispensable component of IoT secure communication system. This paper explores the dynamics in a discrete neuron map influenced by the memristive delay feedback. The investigation considers feedback strength, delay length, and initial conditions as key parameters, and employs numerical analyses including phase diagrams, Lyapunov exponents, bifurcation diagrams, and Kaplan-Yorke dimensions, to explore the diverse dynamical behaviors of the discrete memristive delay feedback neuron model. The study uncovers an inherent connection between the complexity of the dynamic behavior and the control parameters, as well as the delay length. Further exploration into initial condition-dependent dynamics reveals the intricate coexistence of homogeneous and heterogeneous attractors. Furthermore, the proposed model is successfully implemented on an FPGA platform, with experimental results validating its feasibility and effectiveness, contributing to a deeper understanding of delay effects in discrete memristive neural systems. Moreover, the secure communication system is designed based on the memristive delay feedback neuron model. The performance against noise is evaluated through numerical simulations demonstrating its effectiveness in secure communication.