Heterogeneous anti-synchronization of stochastic complex dynamical networks involving uncertain dynamics: an approach of the space-time discretizations

The modeling of discrete space-time stochastic heterogeneous complex networks with unknown factors was achieved through the utilization of differencing techniques with respect to the time and space variables of the nodes' states. Via the space-time discrete Lyapunov-Krasovskii functional and the approach of linear matrix inequality, this paper derived the mean-squared asymptotic anti-synchronization of the aforementioned discrete networks. This was achieved by defining an updated law for the hitherto unknown parameters and incorporating boundary values within the feedback controller. The theoretical and experimental findings indicated that the feedback controller at the boundary represented a more effective and cost-effective control technique for the networks. Furthermore, an adaptive rule has been designed to identify the uncertainties that occur in the networks with a high degree of accuracy. In particular, this rule enabled the response networks to identify unknown information in the drive networks with a high level of precision by incorporating an adaptive updating mechanism. Finally, a numerical example was provided to elucidate the viability of the ongoing investigation.