A Phenomenological Interaction Index for Attraction–Repulsion Transitions in Dynamic Systems

This paper proposes a phenomenological interaction index to characterize attraction–repulsion behavior between interacting systems under varying distance and dynamic conditions. Unlike fundamental force laws, the proposed formulation does not attempt to describe universal physical forces. Instead, it introduces a dimensionally consistent interaction index that incorporates distance, interaction rate, and system dynamics to capture observed transitions between attraction-dominated and repulsion-dominated regimes in complex systems. The model is applicable to non-equilibrium, flow-driven, or mediated interactions where classical inverse-distance assumptions may not adequately describe system behavior. A phenomenological interaction index is proposed to model attraction–repulsion transitions in dynamic systems under varying distance and interaction conditions. This study proposes a new phenomenological interaction index that integrates distance, interaction rate, and system dynamics to characterize attraction–repulsion transitions in complex, non-equilibrium systems. The formulation is not intended as a fundamental force law but as a context-dependent analytical framework that complements existing physical models...........please check the attachment for details