Fractional Order Qi System

Since the Qi chaotic system is depicted as:

\[\begin{cases} \dot{x_1}=a(x_1-x_2)+x_2x_3\\ \dot{x_2}=cx_1-x_2-x_1x_3\\ \dot{x_3}=x_1x_2-bx_3 \end{cases}\]

We can also obtain the fractional order Qi chaotic system:

\[\begin{cases} D^\alpha x_1=a(x_1-x_2)+x_2x_3\\ D^\alpha x_2=cx_1-x_2-x_1x_3\\ D^\alpha x_3=x_1x_2-bx_3 \end{cases}\]

using FractionalDiffEq, Plots
function Qi!(du, u, p, t)
    a, b, c, d, r = 35, 8/3, 80, -1, 1
    du[1] = -a*u[1]+a*u[2]+r*u[2]*u[3]
    du[2] = c*u[1]+d*u[2]-u[1]*u[3]
    du[3] = -b*u[3]+u[1]*u[2]
end

alpha = [0.98, 0.98, 0.98]
h=0.001
tspan = (0, 50)
x0=[0.1, 0.2, 0.3]
prob=FODESystem(Qi!, alpha, x0, tspan)
sol = solve(prob, h, GL())

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

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