Hopfield连续神经网络局部稳定性分析

利用微分几何的方法,将非线性Hopfield神经网络在平衡点附近精确线性化,使之变换成线性系统。通过分析神经网络的n阶李导数,给出并证明了Hopfield神经网络的局部稳定性定理。定理表明,当神经网络满足精确线性化条件时,系统的可控矩阵的非奇异性充分决定了神经网络吸引子的局部稳定范围。

ON THE LOCAL STABILITY OF THE HOPFIELD''S CONTINUOUS NEURAL NETWORKS

The Hopfield's nonlinear neural network is linearized in the neighborhood of a stability point into a linear system by applying the method of differential geometry. A local stability theorem of the Hopfield's neural networkis given and proved through analysing the n-th order Lie derivative of the neural networks,which shows that the nonsingularity of the controllable matrix of the system fully determines the local stability range of the attractor of the neural network under certain exact linearization conditions.