This article aims to investigate the fixed time synchronization of a class of chaotic neural systems by way of adaptive control method. Using Lyapunov stability theory, a new fixed time stability theorem which plays an important role on the synchronization scheme is presented at first. Then, combining the fixed time stability theorem and adaptive control technique, an adaptive control scheme has been developed to achieve the fixed time synchronization of chaotic neural systems. The proposed controllers assure the global convergence of the error dynamics in fixed-time based on the Lyapunov stability theory. Furthermore, the proposed control strategy cannot only provide a fast convergence rate, but also afford a bounded convergence time which is unrelated to the initial values and easy to work out by using the simple time calculation formula. Finally, numerical simulations are presented by taking a typical two-order chaotic neural system as an example to verify and demonstrate the effectiveness of the proposed scheme.

中文翻译：

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基于主动自适应控制的时滞混沌神经网络固定时间同步

本文旨在通过自适应控制方法研究一类混沌神经系统的固定时间同步问题。利用李雅普诺夫稳定性理论，首先提出了一个新的对同步方案起重要作用的固定时间稳定性定理。然后，结合固定时间稳定性定理和自适应控制技术，开发了一种自适应控制方案来实现混沌神经系统的固定时间同步。所提出的控制器确保基于李雅普诺夫稳定性理论的固定时间误差动力学的全局收敛。此外，所提出的控制策略不仅可以提供较快的收敛速度，而且可以提供与初始值无关的有界收敛时间，并且易于使用简单的时间计算公式来计算。