【摘要】 目的研究Hopfeild型神经网络的几乎处处稳定性。方法应用构造密度函数的方法和线性化方法。结果得到了Hopfield神经网络几乎处处稳定的充分条件和必要条件。结论当平衡点的稳定集在Rn中的补集为零Lebesgue测度集时,此平衡点相对于Lebesgue测度是几乎全局稳定的;当系统的平衡点几乎处处稳定时,系统方向场函数在平衡点的散度非正。更多还原

【Abstract】 Aim The almost stability of Hopfield-type neural networks is studied.Methods By applying density-function-constructing and linearizing methods.Results The sufficient condition and necessary condition of the almost stability is obtained.Conclusion For the equilibrium of Hopfield neural network,when the complete of the stable set in Rn is of zero Lebesgue measure,it is almost globally stable;and if it is almost stable,the divergence of the direction field function in the equilibrium point is not positive.更多还原