西安电子科技大学：《神经网络与模糊系统 Neural Networks and Fuzzy Systems》课程PPT课件讲稿（2004）Chapter 03 Neuronal Dynamics 2：Activation Models

Augmented field and augmented matrix Augmented field xy一[K] M connects Fx to Fy,N connects Fy to Fx then the augmented field Fz intraconnects to itself by the square block matrix B 2002.10.8

2002.10.8 Augmented field and augmented matrix Augmented field M connects to ,N connects to then the augmented field intraconnects to itself by the square block matrix B     = Y X Z F F F FX FY FZ FX FY FY FX         = 0 0 N M B

Augmented field and augmented matrix In the BAM case,when N=MT then B=BT hence a BAM symmetries an arbitrary rectangular matrix M. In the general case, c= P P is n-by-n matrix. Q is p-by-p matrix. If and only if,N=MT P=PTO=O'the neurons in Fz are symmetrically intraconnected C=C 2002.10.8

2002.10.8 Augmented field and augmented matrix In the BAM case,when then hence a BAM symmetries an arbitrary rectangular matrix M. In the general case, P is n-by-n matrix. Q is p-by-p matrix. M T N = T B = B         = N Q P M C If and only if, the neurons in are symmetrically intraconnected M T N = T P = P T Q = Q FZ T C = C

3.3 ADDITIVE ACTIVATION MODELS Define additive activation model n+p coupled first-order differential equations defines the additive activation model =Ay+s,(,m+, (3-15) 文-Ax+2s心y,m+1 (3-16) i=1 2002.10.8

2002.10.8 3.3 ADDITIVE ACTIVATION MODELS Define additive activation model n+p coupled first-order differential equations defines the additive activation model = • = + + p j j j j i i S y n I 1 x -A x ( ) i i i = • = + + p j i i i j j S x m I 1 y -A y ( ) j j j （3－15） （3－16）

additive activation model define The additive autoassociative model correspond to a system of n coupled first-order differential equations 文=-AX+2S,(,m+1, (3-17) 2002.10.8

2002.10.8 additive activation model define The additive autoassociative model correspond to a system of n coupled first-order differential equations  （3－17） = • = + + p j j j j i i S x m I 1 i i xi - A x ( )

additive activation model define A special case of the additive autoassociative model C- ● +∑+1， (3-18) +s,,m+ (3-19) Ri where R is (3-20)》 measures the cytoplasmic resistance between neurons i and j. 2002.10.8

2002.10.8 additive activation model define A special case of the additive autoassociative model (3-18) (3-19)  + − = − + • j i i j j i i i i i I r x x R x C x = − + + j j j i j i i i S x m I R x ( ) ' Ri ' = + （3-20） n i i j ij R R r 1 1 1 where ' measures the cytoplasmic resistance between neurons i and j. ij r is