A trajectory-free framework for analysing multiscale systems

• A trajectory-free method to test for multiscale dynamics.
• Isolates the fast dynamics and determines the reduced slow dynamics.
• Based on the spectral properties of the transfer and Koopman operators.

We develop algorithms built around properties of the transfer operator and Koopman operator which (1) test for possible multiscale dynamics in a given dynamical system, (2) estimate the magnitude of the time-scale separation, and finally (3) distill the reduced slow dynamics on a suitably designed subspace. By avoiding trajectory integration, the developed techniques are highly computationally efficient. We corroborate our findings with numerical simulations of a test problem.