2/14 



DYNAMIC SYSTEMS 



graphed, by the method, at positions B, C, and D (Figure 2/13/1). 

 So the system's behaviour corresponds to a movement of the 

 representative point along the line in the phase-space. 



By comparing the Table and the Figure, certain exact corre- 

 spondences can be found. Every state of the system corresponds 



Table 2/13/1. 



uniquely to a point in the plane, and every point in the plane 

 (or in some portion of it) to some possible state of the system. 

 Further, every line of behaviour of the system corresponds 

 uniquely to a line in the plane. If the system has three variables, 

 the graph must be in three dimensions, but each state still corre- 

 sponds to a point, and each line of behaviour to a line in the phase- 

 space. If the number of variables exceeds three, this method of 

 graphing is no longer physically possible, but the correspondence 

 is maintained exactly no matter how numerous the variables. 



2/14. A system's field* is the phase-space containing all the lines 

 of behaviour found by releasing the system from all possible initial 

 states in a particular set of surrounding conditions. 



In practice, of course, the experimenter would test only a repre- 

 sentative sample of the initial states. Some of them will probably 

 be tested repeatedly, for the experimenter will usuallv want to 

 make sure that the system is giving reproducible lines of behaviour. 

 Thus in one experiment, in which dogs had been severely bled 

 and then placed on a standard diet, their body-weight x and the 

 concentration y of haemoglobin in their blood were recorded at 

 weekly intervals. This two- variable system, tested from four 

 initial states by thirty-six primary operations, gave the field shown 

 in Figure 2/14/1. Other examples occur frequently later. 



It will be noticed that a field is defined, in accordance with 



* Some name is necessary for such a representation as Figure 2/13/1, especially 

 as the concept must be used incessantly throughout the book. I hope that a 

 better word than 4 field ' will be found, but I have not found one yet. 



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