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.
作者
杨艳平
陈展衡
YANG Yanping;CHEN Zhanheng(School of Mathematics and Statistics,Yili Normal University,Yining 835000)
出处
《工程数学学报》
CSCD
北大核心
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)。
作者简介
杨艳平(1998-),男,硕士生.研究方向:神经网络动力学;通讯作者:陈展衡,E-mail:czh918czh@163.com。
