7 06 Dr. B. van der Pol on Oscillation Hysteresis in a 



It may here be noticed that stable oscillations are only 

 possible when both a' and y' as defined by (1 a) are positive. 

 No further terms are needed in this series to enable us to 

 account for the hysteresis phenomenon under consideration, 

 though, naturally, in order to obtain a more exact numerical 

 result in all details, further terms may be necessary. 



We further write 



a 2 " =a 2 , 



P. 



o, 



Ci 



=/3, 



and assume, in agreement with the usual circuit dimensions, 

 that the initial logarithmic increment of the total primary 

 (triode included) and the logarithmic decrement of the 

 secondary are small compared with unity, i. e. that 



(X-^l, 0<- 2 ^l. 



ft)! G> 3 



On making these substitutions in (1) we arrive at 



+ (1-P)(ft> 1 2 « 2 - co^u,)- + (l-P)co l Wv 



6^ 



f2 



r J 8 ^ 2 <7 ^ 



... (2) 



On neglecting small terms in (2) this equation can further 

 be simplified, and we obtain as the fundamental differential 

 equation of our problem 



+ {| + ^(l-P)|}(^ + ^) + (a2 - aj )J 



(IV 



+ (l-P)(ft> 1 2 a2 -ft) 2 2 « 1 )^=0 (3) 



