3*alpha*a^2*B*cos(3*Phi)/(4*omega[0])-f*cos(Phi)/(2*omega[0]) = sigma*a-3*alpha*a*B^2/omega[0]-3*alpha*a^3/(8*omega[0])

systems of Nonlinear equations : 

EQ1 := 0.6250000000e-3*Omega^2*R[2]^6+0.4500000000e-2*Omega^2*R[2]^4+(Omega^4-1.9919*Omega^2+1)*R[2]^2-0.225e-1*Omega^2*R[1]^2 = 0;
EQ2 := (.2916*Omega^6+0.225e-1*U^2)*R[1]^6+(-0.9936e-1*Omega^4*U^2+1.296*Omega^4*U-1.20*Omega^2*U^2+1.20*U^2)*R[1]^4+(16*Omega^4*U^2+0.8464e-2*Omega^2*U^4-.2208*Omega^2*U^3-30.56*Omega^2*U^2+16*U^2)*R[1]^2-2.56*U^2*R[2]^2 = 0;
EQ3 := 0.3164062500e-4*Omega^2*R[1]^8+0.1687500000e-2*Omega^2*(-Omega^2+1)*R[1]^6+0.225e-1*Omega^2*(-Omega^2+1)^2*R[1]^4-0.3600e-2*Omega^2*R[1]^2*R[2]^2+.16*(Omega^2-1)^2*R[2]^4 = 0;