Pascanu, Razvan; Mikolov, Tomas; Bengio, Yoshua (21 November 2012). "On the difficulty of training Recurrent Neural Networks". arXiv:1211.5063 [cs.LG].

Plotted in Julia.

```julia using Makie using StatsFuns

width, height = 800, 800 scene = Figure(resolution = (width, height)) Axis(scene[1,1], backgroundcolor = "white")

xs = LinRange(-3, -2, 40) ys = LinRange(0, 1, 40) xlims!(-3, -2) ylims!(0, 1)

vectors = df.(xs, ys)

us = [0 for x in xs, y in ys] vs = [-y + logistic(5y + x) for x in xs, y in ys] strength = vec(sqrt.(us .^ 2 .+ vs .^ 2)) strength /= maximum(strength)/20

arrows!(xs, ys, us, vs, arrowsize = strength, lengthscale = 0.3,

   arrowcolor = strength, linecolor = strength)

1. plot attractors

ys = LinRange(0, 1, 400) xs = [log(y/(1-y))-5y for y in ys] lines!(xs, ys, linewidth = 5, color="black")

1. scene

save("one-neuron recurrent network bifurcation diagram.png", scene)