chaos



In [1]:
using DifferentialEquations
using ParameterizedFunctions
using Plots

In [2]:
g = @ode_def Lin begin
    dx = μ - x^2
    dy = -y
end μ=> 1.5
u0 = [0.5,0.1]
tspan = (0.,15.)
plot(solve(ODEProblem(g,u0,tspan),Rosenbrock23()))


WARNING: Hessian could not invert
Out[2]:
DiffEqBase.ODESolution{Array{Array{Float64,1},1},Array{Float64,1},Array{Array{Array{Float64,1},1},1},DiffEqBase.ODEProblem{Array{Float64,1},Float64,true,ParameterizedFunctions.Lin},OrdinaryDiffEq.Rosenbrock23{0,true,Base.LinAlg.#lufact!},OrdinaryDiffEq.InterpolationData{ParameterizedFunctions.Lin,Array{Array{Float64,1},1},Array{Float64,1},Array{Array{Array{Float64,1},1},1},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23ConstantCache{Float64,Base.#identity,Base.#identity},OrdinaryDiffEq.TimeGradientWrapper{OrdinaryDiffEq.VectorF{ParameterizedFunctions.Lin,Tuple{Int64}},Array{Float64,1},Array{Float64,1}},OrdinaryDiffEq.UJacobianWrapper{OrdinaryDiffEq.VectorFReturn{ParameterizedFunctions.Lin,Tuple{Int64}},Float64},Base.LinAlg.#lufact!,ForwardDiff.JacobianConfig{2,Float64,Tuple{Array{ForwardDiff.Dual{2,Float64},1},Array{ForwardDiff.Dual{2,Float64},1}}}}}}(Array{Float64,1}[[0.5,0.1],[0.502858,0.0997714],[0.531073,0.0975136],[0.56166,0.0950623],[0.619872,0.0903729],[0.678064,0.0856257],[0.759049,0.0788526],[0.834516,0.0722581],[0.918315,0.0644232],[0.990271,0.0569972]  …  [1.22474,0.000170875],[1.22474,0.000107981],[1.22474,6.45988e-5],[1.22474,3.58977e-5],[1.22474,1.80009e-5],[1.22474,7.77052e-6],[1.22474,2.64875e-6],[1.22474,5.88232e-7],[1.22474,4.07282e-8],[1.22474,1.07429e-8]],[0.0,0.00228885,0.0251774,0.0506361,0.10122,0.155171,0.237554,0.324863,0.439571,0.561969  …  6.35001,6.80495,7.31303,7.89204,8.56845,9.38353,10.4073,11.7714,13.7661,15.0],Array{Array{Float64,1},1}[Array{Float64,1}[[2.34301e-314,0.0]],Array{Float64,1}[[1.24916,-0.099933],[1.24857,-0.0998857]],Array{Float64,1}[[1.23878,-0.099107],[1.23272,-0.0986403]],Array{Float64,1}[[1.20839,-0.0967919],[1.20144,-0.0962853]],Array{Float64,1}[[1.16515,-0.0936745],[1.15081,-0.0927075]],Array{Float64,1}[[1.09432,-0.088967],[1.0786,-0.0879884]],Array{Float64,1}[[1.00727,-0.0836083],[0.983034,-0.0822154]],Array{Float64,1}[[0.88932,-0.0768865],[0.864369,-0.0755309]],Array{Float64,1}[[0.760914,-0.0699093],[0.730542,-0.0683025]],Array{Float64,1}[[0.61613,-0.0621936],[0.587882,-0.0606716]]  …  Array{Float64,1}[[6.99017e-7,-0.000231346],[5.85712e-7,-0.000213634]],Array{Float64,1}[[2.35352e-7,-0.000150783],[1.944e-7,-0.000138247]],Array{Float64,1}[[7.00138e-8,-9.39935e-5],[5.67884e-8,-8.5384e-5]],Array{Float64,1}[[1.75634e-8,-5.52321e-5],[1.39185e-8,-4.95692e-5]],Array{Float64,1}[[3.44646e-9,-2.99618e-5],[2.65022e-9,-2.64585e-5]],Array{Float64,1}[[4.59327e-10,-1.45317e-5],[3.39481e-10,-1.25514e-5]],Array{Float64,1}[[2.89111e-11,-5.978e-6],[2.02542e-11,-5.00288e-6]],Array{Float64,1}[[-3.26114e-13,-1.8926e-6],[-2.1202e-13,-1.51056e-6]],Array{Float64,1}[[2.58482e-14,-3.71305e-7],[1.51244e-14,-2.74481e-7]],Array{Float64,1}[[-5.8889e-15,-2.99161e-8],[-4.06084e-15,-2.43004e-8]]],DiffEqBase.ODEProblem{Array{Float64,1},Float64,true,ParameterizedFunctions.Lin}(ParameterizedFunctions.Lin,[0.5,0.1],(0.0,15.0)),OrdinaryDiffEq.Rosenbrock23{0,true,Base.LinAlg.#lufact!}(lufact!),OrdinaryDiffEq.InterpolationData,true,0)

In [3]:



Out[3]:

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