Not necessarily Lyapunov time. In a higher dimensional model, suppose you have many rooms in a house with various heating sources. This is then modeled by a large matrix of coefficients of heat transfer equations, but such a large system of nonlinear equations is prone to chaotic behavior. Realistically though, the temperatures of many rooms don't fluctuate too rapidly after the house attains some kind of equilibrium but retains some due some from the culmination of many turbulent flows.
How do you quantify this notion of "not too chaotic"? Because the manifolds in the solution space could be very turbulent, but their overall magnitude in proportion to the equilibrium temperature may not be that great.
This sounds like you should just go for the amplitude. You do not seem to actually care about chaoticity (whatever that may be). It doesn’t matter for your application whether the oscillation is periodic, quasiperiodic or chaotic.