How to get the state of a dynamic system during integration?

General Usage
1

Hello everyone, I am calculating Lyapunov exponents for my system using lyapunovspectrum from DynamicalSystems. Can I somehow get the state of the system during integration? For another system, I wrote this code:

check = 0
condition(u,t,integrator) = t==4
function affect!(integrator)
    global check = integrator.u[1]
end
cb = DiscreteCallback(condition,affect!)

sol = solve(prob,Tsit5(),callback=cb, tstops=[4.0])
Plots.plot(sol)

As a result, in the check variable, I get the state value I need. I tried using the same on my system when calculating lyapunov exponents with diffeq:

qq = 0
condition(u,t,integrator) = t==4
function affect!(integrator)
    global qq = integrator.u[1]
end
cb = DiscreteCallback(condition,affect!)
test = lyapunovspectrum(ds,10; Δt = 0.001, diffeq=(callback=cb, tstops=[4.0]))

But nothing is written to the variable qq, can I somehow fix this?

2

I’d try

@show integrator.u[1]
global qq = integrator.u[1]
@show qq

What happens?

3

Does not work, qq also remains zero

4

Does it show something in the REPL? If not your callback might not get called?

5

It does not show anything in REPL, it displays the vector of Lyapunov exponents as usual:

6-element Vector{BigFloat}:
 -0.084004423986244
  0.53101598407193
 -0.3037323622757
 -4.1028902584876
 -1.4216653152434
 -5.3503278350181
6

I didn’t quite understand what you mean

7

I meant this is not a problem of the global variable, but affect!(integrator) never gets called by lyapunovspectrum in the first place. That could be either not implemented or a problem with your parameterization of lyapunovspectrum.

8

Now I understand, thanks. Do you know if there is any other way to get the state of the system in this case?

9

Following the documentation I’d try

lyapunovspectrum(ds,10; Δt = 0.001, diffeq=(tstops=[4.0]), callback=cb)
10

It turns out such an error and again nothing is written to qq.

┌ Warning: Direct propagation of keyword arguments to DifferentialEquations.jl is deprecated.
│ From now on pass any DiffEq-related keywords as a `NamedTuple` using the
│ explicit keyword `diffeq` instead.
└ @ ChaosTools C:\Users\semenjuta.e\.julia\packages\ChaosTools\Xe6aI\src\chaosdetection\lyapunovs.jl:79

If I write like this:

lyapunovspectrum(ds,10; Δt = 0.001, diffeq=(tstops=[4.0], callback=cb))

then there are no errors, but in qq it still remains zero

11

OK, I tried to check the example: it is (obviously) not complete. So one more remark: what happens if you use

condition(u,t,integrator) = true

?

12

Nothing happens, everything works the same

13

OK, I tried the example instead and got for

@show t, n

the result

(Float64[], Float64[])

This doesn’t look right to me. Maybe file an issue?

14

And I tried the example and everything works correctly. But for my case:

saved_values = SavedValues(Float64, Tuple{BigFloat,BigFloat, BigFloat, BigFloat, BigFloat, BigFloat})
cb = SavingCallback((u,t,integrator)->tr(u), saved_values)

test1 = lyapunovspectrum(ds,10; Δt = 0.001, callback=cb)

println(saved_values.saveval)
println(saved_values.t)

the result is wrong again:

NTuple{6, BigFloat}[]
Float64[]
15

You tried an example from DifferentialEquations.jl. The link I gave refers to DynamicalSystems.jl of which lyapunovspectrum is part of.

16

In this example, I have the same error as you.