Fig. 21.

Variations of two complex eigenvalues as $({\nu }_c,{\nu }_1)$ moves along segment $P_0{P}_1$ (red), and the HB course (blue) in Fig. 20: a ${\lambda }_{\mathrm{M}}$-branch reaches the imaginary axis at $P_1(0.006,0.06507)$; ${\lambda }_{\mathrm{M}}$-branch along the course, from solid square to hollow square, crosses the imaginary axis at parameter value $P_1$. b ${\lambda }_{\mathrm{m}}$-branches enter into and stay in the left complex plane along $P_0{P}_1$ and the course. A supercritical Hopf bifurcation occurs at ${\nu }_1^{\ast }\approx 0.06507$. ${\lambda }_{\mathrm{Ave}}(P_0):=[{\lambda }_{\mathrm{m}}(P_0)+{\lambda }_{\mathrm{M}}(P_0)]/2$ (Color figure online)