Infinitely long dendrite. (A) Ca spikes propagate. (A1) Bifurcation diagram of traveling Ca-spike solutions. Propagating fronts between R and P subthreshold to Ca spikes are found in Ω (♦); (•), emergence of traveling Ca spikes trains. (A2) (Left) Enlarged view of the “▪” box. (Right) Samples of unitary traveling Ca spikes from branches S1-2 and S5-6 (branches S3-4 are unstable). (A3) Plateau and valley duration (d) in S1 and S6 versus Idc. (B) R ↔ P fronts propagate. (B1) Enlarged view of the “♦” box; uf: unstable fronts, sf: stable fronts. (B2) Examples of RP1 and PR1 fronts. Dashed lines indicate the M state voltage. (C) Plateaus and valleys cannot propagate. V (green) and Vξ (red) nullclines and stable and unstable manifolds (blue) of steady states of the 2D simplified model rewritten in the ξ reference frame, for different Idc values (nA/cm2): 15 (C1) and 33 (C2) inside Ω, and 0 (C3) and 45 (C4) outside Ω. In C1, orange and yellow unstable manifolds are for θ = 0.45 and 0.55 cm/s, and the blue one is for 0.497 cm/s. θ = 0.23 in C2 and 1.00 in C3-4.