Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication

Proportional delay, which is different from time-varying delays and distributed delay, is a kind of unbounded delay. The proportional delay system as an important mathematical model often rises in some various fields such as control theory, physics and biology systems. This paper is concerned with the finite-time and the fixed-time synchronization problem for a class of inertial neural networks with multi-proportional delays. First, by constructing a proper variable substitution, the original inertial neural networks with multi-proportional delays can be rewritten as a first-order differential system. Second, by constructing Lyapunov functionals and by using analytical techniques, and together with novel control algorithms, some new and effective criteria are established to achieve finite-time and fixed-time synchronization of the master/slave of addressed systems. Finally, several examples and their simulations are given to illustrate the effectiveness of the proposed method. Furthermore, a secure communication synchronization problem is presented to illustrate the effectiveness of the obtained results. (C) 2018 Published by Elsevier B.V.