21/7 DESIGN FOR A BRAIN 



done, the second dominates the first. If parameters in each are 

 equated to variables in the other, then a two-way interaction 

 occurs. For instance, suppose we start with the 2-variable 

 system 



dx/dt = fJx, y; a)\ , .. „ . . . _ . _ 



, ,, _ // \ fand the 1 -variable system dz/dt = 6(z; b) 

 ay /at — j 2 (x, y) j 



then the diagram of immediate effects is 



a— > x+±y b—> z 



If we put a = z, the new system has the equations 



dx/dt =f 1 {x, y; z)\ 



dy/dt =f 2 {x, y) > 



dz/dt = cf>(z ; b) J 

 and the diagram of immediate effects becomes 



b — > z — ► x ^=t y. 

 If a further join is made by putting b = y, the equations become 



dx/dt —fiix, y; z) 

 dy/dt =f 2 (x, y) 

 dz/dt = <j>(z ; y) 

 and the diagram of immediate effects becomes 



In this method each linkage uses up one parameter. This is 

 reasonable ; for the parameter used by the other system might 

 have been used by the experimenter for arbitrary control. So 

 the method simply exchanges the experimenter for another 

 system. 



This method of joining does no violence to each system's 

 internal activities : these proceed as before except as modified by 

 the actions coming in through the variables which were once 

 parameters. 



21/7. The stabilities of separate systems do not define the 

 stability of the system formed by joining them together. 



In the general case, when the/'s are unrestricted, this propo- 

 sition is not easily given a meaning. But in the linear case (to 



230 



