Fig. 10: Fitzhugh–Nagumo (FN) model for simultaneous advancing and receding traveling waves and Turing patterns [with f3(u) and g3(u)].
From: Acetylcholine waves and dopamine release in the striatum
![Fig. 10: Fitzhugh–Nagumo (FN) model for simultaneous advancing and receding traveling waves and Turing patterns [with f3(u) and g3(u)].](http://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41467-023-42311-5/MediaObjects/41467_2023_42311_Fig10_HTML.png?as=webp)
a Phase plane. Arrangement (Left) of fixed-points (e.g., u+ > u0 and v+ > v0) and nullclines [e.g., area between nullclines adjacent to (u+,v+) is larger] that give rise to simultaneously expanding “activated” states (Right). b Same as panel a, except that area between nullclines adjacent to (u0,v0) is larger, giving rise to simultaneously receding activated states Insets: space-time plots. c Phase diagram of FN model, demonstrates that it supports both advancing and receding waves, and in a subset of the receding wave regime it is possible to observe Turing patterns (provided the Du /Dv is sufficiently small). d Cross-correlation function [of u(x0,t) and v(x0,t)] during a traveling wave is always symmetrical. Parameters correspond to black and yellow asterisks in (c). e Space-time plot and snapshots of a receding wave leaving Turing patterns in its wake. Parameters correspond to black asterisk in (c).
