gistfile1.txt

using PseudoArcLengthContinuation, LinearAlgebra, Plots, PyPlot, Optim
const PALC = PseudoArcLengthContinuation

# fonction à annuler

function f(x, alpha)
	resu = zeros(1)
	resu[1]=  alpha*x[1] + x[1]^3 
	return resu
end

function df(x, alpha)
	resu = zeros(1,1)
	resu[1,1] = alpha + 3*x[1]^2
end

# option pour Newton

optnewton = NewtonPar(verbose = true)

sol = zeros(1)
sol[1] = 100.

# résolution

alpha_min = -10.
alpha_max = 10.

alpha_start = -1.

out, _, _ = @time newton( x -> f(x, alpha_start), sol, optnewton)


optcont = ContinuationPar(dsmin = 0.01, dsmax = 0.15, ds= 0.01, pMax = alpha_max , pMin = alpha_min,  newtonOptions = NewtonPar(tol = 1e-9))

br, _ = continuation((x, p) -> f(x, p), out, alpha_start , optcont, plot = true, printSolution = (x,p) -> x[1], plotSolution = (x, p;kwargs...) -> (plot!(x; ylabel="solution",label="",kwargs...)))