变时滞四元数值Cohen-Grossberg神经网络全局µ稳定性分析  

Globalµ-stability Analysis of Quaternion-valued Cohen-Grossberg Neural Networks with Time-varying Delays

作　　者：杨艳平 陈展衡 YANG Yanping;CHEN Zhanheng(School of Mathematics and Statistics,Yili Normal University,Yining 835000)

机构地区：[1]伊犁师范大学数学与统计学院,伊宁835000

出　　处：《工程数学学报》2024年第6期1041-1052,共12页Chinese Journal of Engineering Mathematics

基　　金：新疆维吾尔自治区自然科学基金(2024D01C196)。

摘　　要：研究了具有变时滞的四元数值Cohen-Grossberg神经网络的全局µ稳定性。首先,将变时滞概念引入神经网络模型,从而构建了一个能更精确反映神经元动态特性的模型。接着,通过应用同胚映射定理,探讨了平衡点存在的唯一性,并确定了系统存在唯一平衡点的充分条件。鉴于四元数乘法的非交换特性,研究将四元数值神经网络系统分解为四个等价的实值神经网络系统。在此基础上,通过构造合适的Lyapunov函数,得到了系统全局µ稳定的充分条件。最终,通过数值仿真实验,验证了该系统的全局µ稳定性,从而证实了理论结论的有效性和准确性。This research investigates the globalµ-stability of a quaternion-valued CohenGrossberg neural network with time-varying delays.The study first introduces the concept of time-varying delays into the neural network model,thereby constructing a more precise model that reflects the dynamic characteristics of neurons.Subsequently,by applying the theorem of homeomorphism,the uniqueness of equilibrium points is discussed,and the sufficient conditions for the existence of a unique equilibrium point in the system are determined.In view of the non-commutativity property of quaternion multiplication,the quaternion-valued neural network system is decomposed into four equivalent real-valued neural network systems.On this basis,by constructing an appropriate Lyapunov function,the sufficient conditions for the globalµ-stability of the system are obtained.Finally,through numerical simulation experiments,the globalµ-stability of the system is verified,thereby confirming the effectiveness and accuracy of the theoretical conclusions.

关 键 词：四元数 µ稳定 COHEN-GROSSBERG神经网络 LYAPUNOV函数 

分 类 号：O175.13[理学—数学]