6 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



Furthermore, when 



i) a < b , cuj> > by it is always exciting in activity and transiently 



exciting at rest; 

 ii) a < b , 04 < by it is transiently inhibiting in activity, tran- 

 siently exciting at rest (Figure 1) ; 



Figure 2 



iii) a > b , a<j> > by it is always exciting in activity, transiently 

 inhibiting at rest (Figure 2). 

 The case a > b , cuj> < by is inconsistent with <£ > y> . 

 b) Asymptotically inhibiting whenever 



Furthermore, when 



<f> <xp 



i) a > b , cuj) < by it is always inhibiting in activity and tran- 

 siently inhibiting at rest; 

 ii) a > b , cuf> > by it is transiently exciting in activity, transient- 

 ly inhibiting at rest; 

 iii) a < b , a$ < by it is always inhibiting in activity, transiently 

 exciting at rest. 



The case a < b , a</> > by is inconsistent with <£ < \p . 



We have tacitly assumed that the <j at any synapse is affected only 

 by neurons terminating, not at all by these originating, at this syn- 

 apse. We further suppose that if several neurons terminate on the 

 same neuron, the </s of all of them combine linearly. It is now ap- 

 parent that with these simple assumptions, results of considerable 

 complexity are possible. We shall attempt first of all to explore some 

 of these complexities in the abstract, and next to relate a few of them 

 to concrete psychological processes. 



