A trajectory in state space is a way of gaining useful information about the target system via the faithful model assumption, but it is different from trajectories of how an actual system's properties change with respect to time.
The path or sequence of changes something follows over time.
faithful model assumption(Pushed to its extreme limit as a thought experiment to test the limits of confirmation)
The assumption that a model perfectly represents the system it describes
model(Possible worlds interpretation of S5 adapted for modal nonmonotonic logic)
A pair <I, S> where I is a set of literals (a state description / possible world) and S is a set of complete, consistent sets of literals (interpretations) with I ∈ S
Suppose we appealed to strange attractors in our models or in state space reconstruction techniques. Would this be evidence that there is a strange attractor in the target system’s behavior? Modulo worries raised in §5.1, even if the presence of a strange attractor in the state space was both a necessary and sufficient condition for the model being chaotic, this would not amount to an explanation of chaotic behavior in the target system. First, the strange attractor is an object in state space