(⁠|$a$|⁠) Sketch of the stability diagram for case I- with |$A<0$| in |$(\nu ,\mu )$|-plane and (⁠|$b$|⁠) the corresponding bifurcation diagram from DK, where the panel (⁠|$b$|⁠)(i) represents the bifurcation above the diagonal in the |$(\nu ,\mu )$|-plane and (⁠|$b$|⁠)(ii) represents the bifurcation below the diagonal in the |$(\nu ,\mu )$|-plane. (⁠|$c$|⁠) Plot of solutions obtained through time stepping (3.12) with parameters values |$Q_1=0.8, Q_2=0.5,C_1=-1, C_2=-0.1,C_3=-1, C_4=-0.1,C_5=-5$| and |$b=2$| for radius |$0.1$|⁠, |$0.7$| and |$0.9$|⁠. A Hopf bifurcation occurs at |$\theta =270^{\circ }$| and a pitchfork bifurcation occurs at |$\theta =180^{\circ }$| and |$\theta =0^{\circ }$|⁠. The blue |$+$| and red |$\times $| refer to stable extended TW and SS solutions, respectively. The half line |$L_m$| is the line from the normal form at which the bifurcation from TW to SS occurs, at |$\theta \approx 153.3^{\circ }$|⁠.