/* 
amp^2 for hopf bifn formula for 
x'=alpha*x+beta*x(t-T)+a1*x^2+a2*x*x(t-T)+a3*x(t-T)^2+b1*x^3+etc.
T=tcr+mu
That is,
x approx= amp*cos(omega*t)
where omega=w+O(e)
where w=linear freq at T=tcr
*/


-4*BETA^3*(BETA-ALPHA)*(BETA+ALPHA)^2*(5*BETA-4*ALPHA)*MU
 /(15*B4*BETA^6*TCR+5*B2*BETA^6*TCR+3*ALPHA*B4*BETA^5*TCR
		   -15*ALPHA*B3*BETA^5*TCR+ALPHA*B2*BETA^5*TCR
		   -15*ALPHA*B1*BETA^5*TCR-22*A3^2*BETA^5*TCR
		   -7*A2*A3*BETA^5*TCR-14*A1*A3*BETA^5*TCR
		   -3*A2^2*BETA^5*TCR-7*A1*A2*BETA^5*TCR
		   -4*A1^2*BETA^5*TCR-12*ALPHA^2*B4*BETA^4*TCR
		   -3*ALPHA^2*B3*BETA^4*TCR+6*ALPHA^2*B2*BETA^4*TCR
		   -3*ALPHA^2*B1*BETA^4*TCR+12*A3^2*ALPHA*BETA^4*TCR
		   +37*A2*A3*ALPHA*BETA^4*TCR
		   +30*A1*A3*ALPHA*BETA^4*TCR+7*A2^2*ALPHA*BETA^4*TCR
		   +19*A1*A2*ALPHA*BETA^4*TCR
		   +18*A1^2*ALPHA*BETA^4*TCR+12*ALPHA^3*B3*BETA^3*TCR
		   +2*ALPHA^3*B2*BETA^3*TCR+12*ALPHA^3*B1*BETA^3*TCR
		   +4*A3^2*ALPHA^2*BETA^3*TCR
		   -20*A2*A3*ALPHA^2*BETA^3*TCR
		   -16*A1*A3*ALPHA^2*BETA^3*TCR
		   -12*A2^2*ALPHA^2*BETA^3*TCR
		   -26*A1*A2*ALPHA^2*BETA^3*TCR
		   -8*A1^2*ALPHA^2*BETA^3*TCR-8*ALPHA^4*B2*BETA^2*TCR
		   -4*A2*A3*ALPHA^3*BETA^2*TCR
		   +8*A2^2*ALPHA^3*BETA^2*TCR
		   +8*A1*A2*ALPHA^3*BETA^2*TCR+5*B3*BETA^5
		   +15*B1*BETA^5-15*ALPHA*B4*BETA^4+ALPHA*B3*BETA^4
		   -15*ALPHA*B2*BETA^4+3*ALPHA*B1*BETA^4
		   -4*A3^2*BETA^4-9*A2*A3*BETA^4-18*A1*A3*BETA^4
		   -A2^2*BETA^4-9*A1*A2*BETA^4-18*A1^2*BETA^4
		   -3*ALPHA^2*B4*BETA^3+6*ALPHA^2*B3*BETA^3
		   -3*ALPHA^2*B2*BETA^3-12*ALPHA^2*B1*BETA^3
		   +26*A3^2*ALPHA*BETA^3+19*A2*A3*ALPHA*BETA^3
		   +30*A1*A3*ALPHA*BETA^3+11*A2^2*ALPHA*BETA^3
		   +33*A1*A2*ALPHA*BETA^3+12*A1^2*ALPHA*BETA^3
		   +12*ALPHA^3*B4*BETA^2+2*ALPHA^3*B3*BETA^2
		   +12*ALPHA^3*B2*BETA^2-8*A3^2*ALPHA^2*BETA^2
		   -32*A2*A3*ALPHA^2*BETA^2-12*A1*A3*ALPHA^2*BETA^2
		   -14*A2^2*ALPHA^2*BETA^2-18*A1*A2*ALPHA^2*BETA^2
		   -8*ALPHA^4*B3*BETA-8*A3^2*ALPHA^3*BETA
		   +8*A2*A3*ALPHA^3*BETA+4*A2^2*ALPHA^3*BETA
		   +8*A2*A3*ALPHA^4);