# Wrong largest Lyapunov exponent?

I’m calculating the Lyapunov exponents of the Rössler oscillator using chaostools lyapunovspectrum, but I’m getting a weird result:
For the fixed point, the largest Lyapunov exponent (LLE) is smaller than the LLE for the periodic case.

Am I missing something?

Thanks!

Chaotic case (b=0.2):
[0.07292829133282637, -2.236844767689135e-5, -5.144998974835244]
Periodic case (b=1.2):
[-2.9536474906300005e-5, -0.11551781455039102, -5.157491428530996]
Fixed point (b=2.0):
[2.213499351555786e-6, -0.08642708221620443, -5.204999474514104]

Code:

``````
using ChaosTools

function rossler_rule(u, p, t)
α = p[1]; β = p[2]; γ = p[3]
du1 = -u[2] - u[3]
du2 = u[1] + α*u[2]
du3 = β + u[3] * (u[1] - γ)
return SVector{3}(du1, du2, du3)
end

function ross_jacob(u, p, t)
α = p[1]; β = p[2]; γ = p[3]
row1 = SVector(0,-1,-1)
row2 = SVector(1,α,0)
row3 = SVector(u[3],0,u[1]-γ)
return vcat(row1', row2', row3')
end

b_value = parse(Float64,ARGS[1])

ross = CoupledODEs(rossler_rule, fill(6.0,3), [0.2, b_value, 5.7])
tangent = TangentDynamicalSystem(ross; J = ross_jacob)
λ = lyapunovspectrum(tangent, 10000; Δt = 1, Ttr=10000,show_progress=true)
println(λ)
``````

Image from Rössler attractor - Wikipedia :