using DifferentialEquations

μ = 0.456
ϵ = 0.0357

function bluesky(du,u,p,t)
    du[1] = u[1]*(2+μ-10(u[1]^2+u[2]^2)) + u[3]^2 + u[2]^2+2u[2]
    du[2] = -u[3]^3-(1+u[2])*(u[3]^2+u[2]^2+2u[2])-4*u[1]+μ*u[2]
    du[3] = (1+u[2])*u[3]^2+u[1]^2-ϵ
end

u0 = [1.0;0.0;0.0]
tspan = (0.0,100.0)
prob = ODEProblem(bluesky,u0,tspan)
sol = solve(prob)

using Plots
plot(sol,vars=(1,2,3))

plt = path3d(1, xlim=(-3,3), ylim=(-3,3), zlim=(-3,3),
                xlab = "x", ylab = "y", zlab = "z",
                title = "Gavrilov-A. Shilnikov model", marker = 1)

# build an animated gif, saving every 10th frame
@gif for i=1:length(sol)
    push!(plt, sol[i][1], sol[i][2], sol[i][3])
end every 3

function displayfile(mimetype, filename)
    open(filename) do f
        base64text = base64encode(f)
        display("text/html", """<img src="data:$mimetype;base64,$base64text">""")
    end
end

displayfile("image/gif","./bluesky.gif")

# ちょっと遅くしたもの
displayfile("image/gif","./bluesky2.gif")

plotly()
plot(sol[1,:],sol[2,:],sol[3,:], size=(500, 500))