The fact that a trajectory in state space spirals toward a strange attractor does not imply that the target system's behavior in physical space is approaching that attractor (except possibly under the perfect model scenario).
An imaginary space that describes all the possible conditions a system can be in; each point in this space represents one possible situation.
Target system(as used in philosophy of science)
The real-world thing you're trying to understand or study, as opposed to a simplified version of it.
Trajectory(as describing how a system evolves from one state to another)
The path or sequence of changes something follows over time.
perfect model scenario(Philosophy of scientific modeling)
A limiting case in which the model is assumed to perfectly represent the target system, under which state space trajectories may correspond directly to physical space behavior.
strange attractor(Used in the context of classical dynamical systems and chaos theory)
A structure in state space characterized by infinitely intricate self-repeating (fractal) geometry that plays a crucial role in chaos explanations
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