Stability is determined by evaluating the Jacobian of (7) at the steady state (x 1 , y 1 , x 2 , y 2 ) = 0. At the Hopf bifurcation, the real part of the largest eigenvalue crosses zero, with nonzero imaginary part. The roots of the characteristic polynomial f (λ) of the Jacobian are the eigenvalues {λ}. The four eigenvalues are