Wilson–Cowan E–I dynamics

τE dE/dt = −E + S(wEEE − wIEI + Iext) τI dI/dt = −I + S(wEIE) S(u) = 1 / (1 + e−10(u−0.5))

Phase plane

Click the plane to start from there
attractor
transient
dE/dt = 0
dI/dt = 0
● stable  ○ unstable  × saddle
start
now
Arrow excites, bar inhibits. Width shows strength; brightness shows current activity.
Regime
–
Fixed point
–
(E*, I*)
Period
–
time units per cycle
E amplitude
–
peak − trough

Time series