Cheng Yanzhao, Shi Yanchao, Guo Jun
School of Science, Southwest Petroleum University, Chengdu, 610500 China.
Key Laboratory of Numerical Simulation of Sichuan Provincial Universities, School of Mathematics and Information Sciences, Neijiang Normal Univeristy, Neijiang, 641000 Sichuan Province China.
Cogn Neurodyn. 2024 Aug;18(4):1943-1953. doi: 10.1007/s11571-023-10057-x. Epub 2024 Jan 17.
In this paper, the exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays is discussed. By using the differential inclusion theory and the set-valued map theory, the discontinuous quaternion-valued memristor-based Cohen-Grossberg neural networks are transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With some inequality techniques, several criteria of exponential synchronization for quaternion-valued memristor-based Cohen-Grossberg neural networks are given. Different from the existing results using decomposition techniques, a direct analytical approach is used to study the synchronization problem by introducing an improved one-norm method. Moreover, the activation function is less restricted and the Lyapunov analysis process is simpler. Finally, a numerical simulation is given to prove the validity of the main results.
本文讨论了具有时变延迟的四元数忆阻器型Cohen-Grossberg神经网络的指数同步问题。利用微分包含理论和集值映射理论，将基于四元数忆阻器的不连续Cohen-Grossberg神经网络转化为具有区间参数的不确定系统。设计了一种新颖的控制器来实现控制目标。通过一些不等式技术，给出了基于四元数忆阻器的Cohen-Grossberg神经网络指数同步的几个判据。与现有使用分解技术的结果不同，通过引入改进的一范数方法，采用直接解析方法研究同步问题。此外，激活函数的限制较少，Lyapunov分析过程更简单。最后，给出了数值仿真以证明主要结果的有效性。
