Periodic-noise-tolerant neurodynamic approach for kWTA operation applied to opinions evolution

For the k-winners-take-all (kWTA) operation, several anti-noise neurodynamic approaches have been investigated to counteract various types of disturbances and uncertainties. However, these approaches still fail to effectively address periodic noise originating from external environmental interference, sensor inaccuracies, or internal system oscillations. To address this issue, a periodic-noise-tolerant neurodynamic (PNTND) approach for kWTA operation is proposed, which exhibits the capability to learn and compensate for errors induced by periodic noise. Additionally, the PNTND approach effectively eliminates interference caused by the aperiodic noise originating from the superposition of periodic noises. Theoretical analyses and numerical simulations reveal the excellent convergence performance of the PNTND approach. Moreover, we construct a social opinion evolution model that incorporates periodic noise interference based on the proposed PNTND approach, thereby demonstrating its practical applicability.