CHAPTER 16 



The Multistable System 



16/1. The systems discussed in the previous chapter contained 

 no step-functions, and the effect of ultrastability on their pro- 

 perties was not considered. In this chapter, ultrastability will 

 be re-introduced, so we shall now consider what properties will 

 be found in systems which show both ultrastability and dispersion. 



To study the interactions of these two properties we might 

 start by examining the properties of an ultrastable system whose 

 main variables are all part-functions. But it has been found 

 simpler to start by considering a system defined thus : a multi- 

 stable system consists of many ultrastable systems joined main 

 variable to main variable, all the main variables being p art-functions . 



The restriction to part-functions is really slight, for the part- 

 function ranges all the way from the full- to the step-function. 

 It will further be noticed that, as the ultrastable, or ' sub- ', 

 systems are joined main variable to main variable only, each 

 step-function will now be restricted in two ways. The critical 

 states which determine whether a particular step-function shall 

 change value depend only on those main variables that belong 

 to the same subsystem. And when a step -function has changed 

 value, the immediate effect is confined to that subsystem to 

 which it belongs. In the definition of the ultrastable system 

 (S. 8/6) no such limitation was imposed. 



This type of system has been defined, not because it is the 

 only possible type, but because the exactness of its definition 

 makes possible an exact discussion. When we have established 

 its properties, we will proceed on the assumption that other 

 systems, far too varied for individual study, will, if they approxi- 

 mate to the multistable system in construction, approximate 

 to it in behaviour. 



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