DYNAMIC SYSTEMS 2/10 



Two states are equal if and only if the corresponding pairs of 

 numerical values are all equal. 



2/10. A line of behaviour is specified by a succession of states 

 and the time-intervals between them. The first state in a line of 

 behaviour will be called the initial state. Two lines of behaviour 

 are equal if all the corresponding pairs of states are equal, and 

 if all the corresponding pairs of time-intervals are equal. One 

 primary operation yields one line of behaviour. 



There are several ways in which a line of behaviour may be 

 recorded. 



m 



B 



Time — *- 



Figure 2/10/1 : Events during an experiment on a conditioned reflex in 

 a sheep. Attached to the left foreleg is an electrode by which a shock 

 can be administered. Line A records the position of the left forefoot. 

 Line B records the sheep's respiratory movements. Line C records 

 by a rise (E) the application of the conditioned stimulus : the sound 

 of a buzzer. Line D records by a vertical stroke (F) the application of 

 the electric shock. (After Liddell et al.) 



The graphical method is exemplified by Figure 2/10/1. The 

 four variables form, by definition, the system that is being 

 examined. The four simultaneous values at any instant define 

 a state. And the succession of states at their particular intervals 

 constitute and specify the line of behaviour. The four traces 

 specify one line of behaviour. 



Sometimes a line of behaviour can be specified in terms of 

 elementary mathematical functions. Such a simplicity is con- 

 venient when it occurs, but is rarer in practice than an 



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