DynamicalSystems.jl and CUDA.jl

Hello!
Can i use CUDAj.jl and DynamicalSystems.jl together?
I calculate map of spectrum Lyapunov exponents with inheritance of initial conditions. I manage to parallelize calculations using Threads.@threads for loop. But it takes quite a long time.
I wanted to try to calculate the initial conditions for each point on the map with paralleling by Threads.@threads. Then run the calculation of the Lyapunov exponents spectrum for each point on the GPU.

My second question
Can I get a message that an instability has been detected in the form of some code when I use the trajectory? When I began to calculate the initial conditions for each point on the map, the message about unstability appeared, but I don’t quite understand how to track at what parameter values this happened.

Thank you for helps!