114 



TEMPORAL ORGANIZATION IN CELLS 



approximate values for Z^. in the limits of very small /3 (equation (37)). For 

 jS->0, we have 



and 



'9i 



'^2 



71 



yi 



_J _ L 



Win " Wi . 



(63) 



The Statistical Characteristics of Strongly Coupled Oscillators 



and subharmonic resonance 



The first difference which we see between the system with strong inter- 

 action and that without is in the most probable values of Xj and a'2. We have 

 by definition 



where the dash means that the integration is performed over all variables 

 except x^. This reduces to 



Px.dx^ =^- J e-^""''^' 



dxj 



Writing 

 this becomes 



e-^\.^.V.Xi 



pz J 



g-p[2h,,x,.x^2+h^^.x^-] ^j^ 



•T2 





(/S)i/2z^ 



'p% 



I 



e-''dt 



The maximum value of this expression occurs at the root of the equation 



-)5[-T.+(/,, ./ A„) X. ]» (^-j 1 ' 2 ''ii _ ^^l-^l^'l 



00 



/ 



e'"dt = 



//22 /'22 



W'=I-T,+(/t.,/A2,)A-.I 

 00 



i.e. di'2e-Plr,-ih^,"'„)^^.'hi2-2\H\xi J e-''dt = Q 



It is clear that ati = is not a root except when 6 = 0, and that the equation is 

 satisfied only for some position value of Xi which increases as 6 increases. 



