Non-autonomous version of Lyapunov exponent (EADP)

[rusandris]

In non-autonomous systems with parameter drift, long time averages are less useful to assess chaoticity.

There are several different ways to address this, one is related to the ensemble approach. Here, a new quantity called the Ensemble-averaged pairwise distance (EAPD) is used. An analog of the classical largest Lyapunov exponent can be extracted from the EAPD) function: the local slope can be considered an instantaneous Lyapunov exponent.

See for example here , section 3.3 :

The function of the EAPD in continuous time is defined as $\rho(t) = \langle ln r(t) \rangle$ where the average is taken over an ensemble of trajectories. To any member of the ensemble a test particle is ordered at an initial distance $r_0$ . Quantity $r(t)$ is the dimensionless phase space distance between a test particle and an ensemble member at time $t$.

I was wondering if we could use ParallelDynamicalSystem for handling large ensembles of trajectories of the drifting system. The test particles would just be a copy of the ensemble (can be even inside the same ParallelDynamicalSystem or separately). For estimating the slope, we could use the already existing tools from FractalDimensions.jl FractalDimensions.slopefit.

As far as I know, there isn't a function for this right now. Let me know if this is a good idea, and whether ChaosTools is the right package. (I've seen CriticalTransitions has some functionality for rate-dependent phenomena but seems more niche).