I have a physics background with very little knowledge of graph theory, but a question arose related to directed acyclic graphs (DAGs) and I'm hoping to get hints towards an answer.
Assume we have a system where:
- The interactions between components are described by a DAG.
- The inputs to the system are random and non-periodic.
- The individual components (nodes) do not have inherent periodic behavior.
Under these conditions, is it possible for the system as a whole to exhibit periodic behavior, stable attractors, strange attractors in its output or state?
To clarify, I am interested in understanding whether a system that is implemented based on a DAG structure (e.g., a network of interacting elements) can give rise to oscillatory, asymptotic, or other chaotic dynamics, even though the graph itself does not contain cycles.
If such behavior can emerge in such systems, what are the necessary conditions or mechanisms that could lead to it? Are there any known examples or studies that demonstrate periodic, etc. dynamics in DAG-structured systems?
If it is not possible, is there a proof of that?
I would appreciate any insights or references to relevant literature that can help me understand this problem better. Thank you in advance for your help!