Dynamical Transitions and Bifurcation Structures in Coupled Subspace Systems

Resonance-Based Subspace Dynamics (RBS-D) is a 24-part scientific framework that introduces a structural interpretation of physical systems based on coupled subspaces, resonance phenomena, and nonlinear dynamics. This publication (No. 09 / 24) develops the theory of dynamical transitions within the RBS-D framework by analyzing how coupled subspace systems change their structural behavior under variation of coupling strength, phase relations, and external excitation. The focus lies on transition mechanisms between different resonance regimes, including sudden structural shifts, gradual deformations of attractor states, and bifurcation-like reconfigurations of coupled dynamics. Within the RBS-D framework, physical systems are described in terms of: transition between resonance states bifurcation-like structural changes coupling-driven regime shifts phase coherence reconstruction processes This publication extends the multi-scale architecture (P08) by introducing a formal description of dynamical transitions between hierarchical resonance configurations.