Abstract

We mathematically modelled the process of asymptotic synchronization in all-to-all coupled structures using a formulated discrete protocol with time delays. We utilized the oscillatory nature of synchronization to transform the discrete protocol onto quantinuum dynamics of a known class of first order nonlinear neutral delay difference equations (NDDE) with variable coefficients. We applied some mathematical inequality techniques to obtain bounded solutions of the NDDE. We utilized the known oscillatory property of all neutral delay difference equations to classify the bound solutions as asymptotically synchronizing over a given time domain projected through the initial and boundary conditions. The solutions obtained are in the form of converging sequences. Some illustrative examples were provided to validate the main results.

Keywords: Asymptotic synchronization, Mathematical inequality, Variable coefficients