In this paper, a class of coupled nonlinear reaction–diffusion complex network system are investigated with finite-time synchronization based on the event-triggered control. The study aims to develop nonlinear complex network systems with partial differential terms under Dirichlet’s boundary conditions by combining the distributed event-triggered control protocol with the Lyapunov stability theorem, Green formula, matrix inequality, and partial differential equation theory. Several sufficient conditions for the system to achieve finite-time synchronization with or without time delay are obtained. Furthermore, the upper bound of time can be estimated to achieve synchronization. Finally, numerical simulation is used to prove the effectiveness of the theory.

本文研究了一类基于事件触发控制的有限时间同步非线性反应扩散扩散复杂网络系统。该研究旨在通过将分布式事件触发控制协议与Lyapunov稳定性定理，Green公式，矩阵不等式和偏微分方程理论相结合，在Dirichlet边界条件下开发具有偏微分项的非线性复杂网络系统。获得了几个足够的条件，以使系统在有或没有时间延迟的情况下实现有限时间同步。此外，可以估计时间的上限以实现同步。最后，通过数值模拟证明了该理论的有效性。