Global Synchronization in the Finite Time for Variable-Order Fractional Neural Networks with Discontinuous Activations

Abstract

In this paper, we focus the global synchronization in the finite time for variable-order fractional neural networks with discontinuous activation functions. Global Mittag–Leffler synchronization and synchronization in the finite time. Firstly, the order α(t) of the fractional derivative of Caputo is changed with time, the α(t) is designed and improved, which plays an important role in the synchronization analysis. Secondly, the fractional Lyapunov method and the Mittag–Leffler function are applied, the linear matrix inequalities (LMI) are used to guarantee the conditions for satisfying the finite time synchronization. With this method finite-time synchronization and time estimation can be achieved simultaneously. Finally, the effectiveness of the method is verified by two examples.