Is there some way of determining, whether the orbits, given some starting parameters, _at some point_ will become stable? I probably mean periodic. And I probab

Is there some way of determining, whether the orbits, given some starting parameters, _at some point_ will become stable? I probably mean periodic. And I probably mean mostly periodic, with only slight deviation from orbits. And I don't necessarily mean that we can calculate/predict what they will look like in a stable form. This reminds me of Langtons Ant, that has very simple rules, but at first still seems very chaotic. Then after some number of iterations it just shoots away in a regular endlessly regular repeating pattern. "Order came from chaos." So it makes me think, maybe there is not a way to tell, whether the orbits "stabilize" at some point, but maybe they will, and we simply don't know when or how to tell?