Calculating Lyapunov Exponents in a different manner

I started on a non-linear dynamics project. And am using DifferentialEuations.jl to generate the trajectory. Over this I would like to numerically estimate the Lyapunov exponent for arbitrary trajectories.

I have seen how this could be done using the DynamicalSystems.jl library by calling lyapunovs function, but for my project, I wish to customise it such that the trajectory integration and the estimation of lyaounov exponent runs simultaneosly and aim to terminate the integration once the lyapunov exponent becomes almost fixed against further integration of the trajectory .

So, are there any sophistcated ways of doing this effectively ?
Thanks ahead!