An Improved Finite-Time and Fixed-Time Stable Synchronization of Coupled Discontinuous Neural Networks

This article focuses on the finite-time and fixed-time synchronization of a class of coupled discontinuous neural networks, which can be viewed as a combination of the Hindmarsh–Rose model and the Kuramoto model. To this end, under the framework of Filippov solution, a new finite-time and fixed-time stable theorem is established for nonlinear systems whose right-hand sides may be discontinuous. Moreover, the high-precise settling time is given. Furthermore, by designing a discontinuous control law and using the theory of differential inclusions, some new sufficient conditions are derived to guarantee the synchronization of the addressed coupled networks achieved within a finite-time or fixed-time. These interesting results can be seemed as the supplement and expansion of the previous references. Finally, the derived theoretical results are supported by examples with numerical simulations.