本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Ra...本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.展开更多
Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article give...Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article gives conditions for its Hyers-Ulam-Rassias stability. As a consequence, the authors obtain its Hyers-Ulam stability and prove that the equation has a unique multivalued solution near an approximate multivalued solution.展开更多
文摘本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.
文摘Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article gives conditions for its Hyers-Ulam-Rassias stability. As a consequence, the authors obtain its Hyers-Ulam stability and prove that the equation has a unique multivalued solution near an approximate multivalued solution.
