IV 



THE DYNAMICS OF SIMPLE CIRCUITS 



If the terminus of a single neuron is brought into coincidence 

 with its origin, or the final terminus of a chain into coincidence with 

 the initial origin, the result is a simple circuit. Circuits are of com- 

 mon occurrence in the central nervous system, and, in fact, Lorente 

 de No (1933) asserts that for every neuron or chain of neurons pass- 

 ing from one given cell-complex to another given cell-complex, there 

 is also a neuron or a chain of neurons passing in the reverse direc- 

 tion. O'Leary (1937) notes the frequent occurrence of circuits in the 

 olfactory cortex of the mouse. A circuit composed of only excitatory 

 fibers may have the effect of prolonging a state of activity after the 

 withdrawal of the stimulus, of enhancing the activity due to a pro- 

 tracted but weak stimulus, or, perhaps, of providing a permanent 

 reservoir of activity through perpetual self-stimulation. Thus Kubie 

 (1930) has discussed their possible role in the production of spon- 

 taneous sensations and movements. Prolongation and enhancement 

 will not, of course, occur when one member of the circuit is inhibi- 

 tory, but besides the possible modulating effects that such circuits 

 might have, they provide, perhaps less obviously, for the possibility 

 of regular fluctuations in the response to a persistent, constant stim- 

 ulus. 



Fluctuation, prolongation and enhancement, permanent reser- 

 voirs of activity, are all more or less directly observable within the 

 central nervous system. Whether any or all of these can be attributed 

 to mechanisms of precisely this type is a question to be decided by 

 the comparison of experiment with theory. We proceed therefore to 

 develop some of the consequences to be expected if this is indeed the 

 case. 



The simplest circuit is that formed by a single self-stimulating 

 neuron (Landahl and Householder, 1939) of the simple excitatory 

 type. The total stimulus acting upon the neuron at any time consists 

 of a part a = e , due to the activity of the neuron itself, and of a part 

 S coming from other neurons or receptors. If we may disregard the 

 conduction time — this is always quite small— let 



£ = S-h, (1) 



and consider ^ as a function of the excess of stimulus over threshold, 

 equation ( 1 ) of chapter i takes the form 



de/dt = a\_<f>(£ + e) - e]. (2) 



22 



