Finite-time synchronization for fuzzy shunting inhibitory cellular neural networks

Finite-time synchronization is a critical problem in the study of neural networks. The primary objective of this study was to construct feedback controllers for various models based on fuzzy shunting inhibitory cellular neural networks (FSICNNs) and find out the sufficient conditions for the solutions of those systems to reach synchronization in finite time. In particular, by imposing global assumptions of Lipschitz continuous and bounded activation functions, we prove the existence of finite-time synchronization for three basic FSICNN models that have not been studied before. Moreover, we suggest both controllers and Lyapunov functions that would yield a feasible convergence time between solutions that takes into account the chosen initial conditions. In general, we consecutively explore models of regular delayed FSICNNs and then consider them in the presence of either inertial or diffusion terms. Using criteria derived by means of the maximum-value approach in its different forms, we give an upper bound of the time up to which synchronization is guaranteed to occur in all three FSICNN models. These results are supported by 2D and 3D computer simulations and two respective numerical examples for $2\times 2$ and $2\times 3$ cases, which show the behavior of the solutions and errors under different initial conditions of FSICNNs in the presence and absence of designed controllers.