研究了一類(lèi)連續(xù)型全反饋人工神經(jīng)網(wǎng)絡(luò)的穩(wěn)定性，通過(guò)求解簡(jiǎn)單的一維微分方程，給出了該類(lèi)神經(jīng)網(wǎng)絡(luò)系統(tǒng)解的解析表達(dá)式，利用解的解析表達(dá)式證明了當(dāng)A的特征值λ≤0，至少有一個(gè)特征值為負(fù)時(shí)，網(wǎng)絡(luò)的一切從Rn中的單位超球內(nèi)出發(fā)的解收斂于原點(diǎn)或單位超球內(nèi)的一點(diǎn)．
關(guān) 鍵 詞 神經(jīng)網(wǎng)絡(luò); 特征值; 特征向量; 穩(wěn)定性

Abstract In this paper the problem of artificial neural network model is studied. The differential equation of an artificial neural network model is solved by solving a simple one imension differential equation. Applying the solution of the neural network model, we proved that all solutions of a network from the unit hypersphere over Rn converge to the origin or a point in the sphere, when all of A's eigenvalues are less than or equal to zero as well as not all of the eigenvalues equal to zero.
Key words neural networks; eigenvalue; eigenvector; stability