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（2003）02. Neuronal Dynamics——Activation Models（1/2）

Bidirectional and Unidirectional connection Topologies Bidirectional networks M and N have the same or approximately the same structure.N=MT M=NT Unidirectional network A neuron field synaptically intraconnects to itself. BAM M is symmetric, M=M the unidirectional network is BAM 2002.10.8

2002.10.8 Bidirectional and Unidirectional connection Topologies Bidirectional networks M and N have the same or approximately the same structure. Unidirectional network T M = N M T N = A neuron field synaptically intraconnects to itself. BAM M is symmetric, the unidirectional network is BAM M M T =

Augmented field and augmented matrix Augmented field Rv一，[K] M connects Fx to F,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 T C = C FZ

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）