Delayed discrete memristive ring neural network and application in pseudorandom number generator

Synaptic delay effects play a crucial role in biological neural networks, influencing the dynamical behaviors of neural networks. However, the dynamical characteristics of neural networks based on discrete memristors with synaptic delay effects have not yet been thoroughly investigated. This paper presents a novel discrete memristor model with delay effects and incorporates it as an autapse into a ring Hopfield neural network to simulate biological synapse delay properties, constructing a delayed discrete memristive ring neural network (DDMRNN). The system’s dynamical behavior becomes significantly more complex as the delay length increases. Through modulation of the synapse weight w11, the system exhibits rich dynamical evolution properties, including diversified attractors, transient chaos, and synapse weight-dependent offset-boosting. Additionally, coexisting behaviors of homogeneous and heterogeneous chaotic attractors are revealed under varying initial conditions. FPGA-based hardware experiments validate the implementability of the DDMRNN circuit. Furthermore, the application of DDMRNN to pseudorandom number generation demonstrates that the produced sequences successfully pass stringent statistical randomness tests, confirming the system’s potential applicability in information security domains.