可化为对称情形的具有非对称权阵的连续Hopfield型神经网络

Continuous Hopfield-type neural networks with asymmetric connection weights which can be reduced to the symmetric case

若非线性连续Ｈｏｐｆｉｅｌｄ型神经网络的非对称权阵能够分解为正定对角阵、对称阵与另一正定对角阵的乘积，则该非对称网络经过一个相似变换可化为具有等价的稳定性质且权阵为上述对称阵的神经网络．由此推出，该类非对称神经网络具有全局稳定的吸引子，且为它的非空的平衡点集．另得到了保证该类非对称神经网络具有全局渐近稳定性的一个充分条件．

class of nonlinear continuous Hopfield-type neural network with asymmetric connection weights,which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix and another positive definite diagonal matrix,can be reduced to neural network with the above symmetric matrix through a similarity transformation. The two neural networks have exactly the same stability properties,so the class of asymmetric neural network has a non-empty globally stable equilibrium attractor.A sufficient condition for the global asymptotic stability of the class of asymmetric neural network is also derived.