Finite-time stability and finite-time synchronization of neural network - Dual approach

In this paper we develop new dual tools to study finite-time stability and finite-time synchronization for nonlinear neural networks with functions defining network depending on time. First we study a stability in finite time of the Hopfield neural networks where the activation functions and the strength functions depend on time. Next we deal with a nonlinear coupled network containing the nonlinear coupling function and prove using just duality tools that it synchronizes in finite time with the reference trajectory. We do not use any controller as it is done in most papers on synchronization. We just build a dual Lyapunov function in a dual space and then in the dual space we study the stability and synchronization in the way similar to classical finite type stability. However, the dual Lyapunov function is quite different than the classical one and therefore the obtained results are both different and new.