Appendix 2—figure 31. Periodic and excitable regimes in the FHN model.

(A) Nullcline $\dot{w}=0$ (red dash-dot line) intersects with $\dot{v}=0$ (green dash line) in its first piece ${\displaystyle (v_{ss}<v_0)}$. The system is excitable in this case. (B) With nullclines shown in (A), it requires strong enough noise to pass over the threshold so end the competent telogen. When noise is not strong enough, the system stays in competent telogen for a long time. Stochastic trajectory (black line) presented. (C) Nullcline $\dot{w}=0$ (red dash-dot line) intersects with $\dot{v}=0$ (green dash line) in its second piece ${\displaystyle (v_0<v_{ss}<v_1)}$. The system is periodic in this case. (D) With nullclines shown in (C), the system undergoes cyclic dynamics automatically without help from noise, as there is no threshold to pass over. Deterministic trajectory (black line) presented.

DOI: http://dx.doi.org/10.7554/eLife.22772.073