Fig. 5

Mapping to $(k_1,k_2)$-plane. The curves $E_T({\alpha }_2)$ and $E_N({\alpha }_2)$ show the parametrization of the origin (trivial fixed point) and non-trivial fixed points, respectively, for fixed ${\alpha }_1$. This figure illustrates how some solution branches can regain stability after encountering numerous bifurcations. Blue, fold/transcritical; red, asymmetric Hopf; magenta, symmetric periodic solution; black, parametrization of fixed points.