Fractional Order Chen System

Fractional orderChen system:

\[\begin{cases} D^{\alpha_1}x=a(y-x)\\ D^{\alpha_2}y=(c-a)x-xz+cy\\ D^{\alpha_3}z=xy-bz \end{cases}\]

Behave chaotic property when $a=35$, $b=3$, $c=28$.

using FractionalDiffEq, Plots

h=0.005
alpha = [0.9, 0.9, 0.9]
x0 = [-9, -5, 14]
tspan = (0, 100)
function Chen!(du, u, p, t)
    a, b, c, d = 35, 3, 28, -7
    du[1] = a*(u[2]-u[1])
    du[2] = d*u[1]-u[1]*u[3]+c*u[2]
    du[3] = u[1]*u[2]-b*u[3]
end
prob = FODESystem(Chen!, alpha, x0, tspan)
sol = solve(prob, h, GL())

plot(sol, vars=(1,2,3), title="Fractional Order Chen System")

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