Ttr lyapunovspectrum DynamicalSystems.jl

Specific Domains Modelling & Simulations
1

I have code:

lyapunovspectrum(ds, 300000.0;
                    Ttr = 200000.0,
                    diffeq = (alg = Vern9(),
                              abstol = 1e-11, reltol = 1e-11, dense = false,  maxiters = 10000000) )

How correctly use Ttr. I need to start algorithm when transient process is ended. The transition process can last quite a long time. Is there any way to make sure it has been completed?

Spectrum:
image

2

nope, unfortunately no system agnostic way to know this. Perhaps you should de-dimensionalize your equations so the time units aren’t so huge.

3

Is there no way to set Tr so that the algorithm starts at 60% of the specified time?

4

I have a more theoretical question related to the algorithm. If the system has multistability, then how should the spectrum be calculated so that it corresponds to the required attractor.

For example attractor with regular mode

image
image1600×600 125 KB

image
image800×800 79 KB

When i calculate spectrum with initial condition from this attractor i have result how for another attractor, which hyperchaotic
Is it solely related to the system or maybe it’s the algorithm