Resonance-Based Subspace Dynamics (RBS-D): Coupled Rotational Systems as an Experimental Platform for State-Based Dynamics – Tetravalent Structure, Regime Transitions, and Threshold Phenomena

This work develops a state-based framework for the description of complex physical systems in which observable structures are interpreted as stable configurations within coupled dynamical state spaces. The focus lies on strongly coupled, nonlinear, and multiscale systems, where stability is not an intrinsic property of isolated objects but emerges entirely from interaction, feedback, and regime-dependent coupling. As an experimental realization, a coupled three-cylinder rotational system is introduced, combining rotating flows, shear gradients, vortex formation, and—under conductive conditions—electromagnetically mediated feedback. This system provides direct access to coupled and decoupled dynamical regimes as well as sharp transitions between structurally distinct states. A central result is the introduction of a tetravalent structural classification, in which system states are categorized according to stability and coupling strength. Linear, nonlinear, hydrodynamic, and magnetohydrodynamic regimes are reinterpreted as limiting projections of a unified coupled state dynamics. Additionally, a dimensionless order parameter Ξ is introduced, integrating phase coherence, rotational structure, geometric constraints, and medium coupling. The system exhibits fundamentally non-continuous response behavior, characterized by threshold-driven transitions between qualitatively different dynamical regimes. Observable signatures include hysteresis, phase locking windows, directional anisotropy, vortex reorganization, and spontaneous restructuring of flow topology. This research direction is motivated by the hypothesis that controlled manipulation of coupled dynamical states may enable new approaches to influencing material behavior, including force redistribution and regime-dependent stabilization effects.