A Novel Memristor Regulation Method for Chaos Enhancement in Unidirectional Ring Neural Networks

Evidences have manifested that unidirectional ring neural networks lack the ability to generate desired chaos. This paper formulates a novel memristor regulation (MR) approach to constructing a no-equilibrium bi-memristor unidirectional ring neural network (BMURNN), in which two distinct memristors are incorporated into a unidirectional ring neural network derived from the Hopfield neural network, with enhanced chaotic complexity, whereas one serving as a memristive synapse and the other as an emitter of electromagnetic radiation. Numerical simulations reveal that any desired number of multi-scroll hidden chaotic attractors can be generated from the BMURNN via the non-ideal multi-piecewise nonlinear memristor, while the time-controlled multi-scroll attractor growth is output from the periodic function memristor, demonstrating that the memristors can enhance the chaos complexity of the original unidirectional ring neural network. Additionally, diverse coexisting hidden attractors, that is, hidden heterogeneous/homogeneous multistability evoked by the memory attributes of memristors, can be dynamically regulated by varying the initial conditions. Finally, a digital circuit is designed and implemented based on CH32 to validate the numerical simulations and theoretical analyses, and a new pseudorandom number generator is devised to explore the BMURNN for practical applications. Performance analyses demonstrate its superiority and high randomness, providing further proof for the effectiveness of the proposed MR method.