Stuart-Landau Dynamics

Stuart-Landau Dynamics are the nonlinear amplitude equations that govern the homeostasis of the four dimensional layers, describing the passage from a growth regime to a resonance regime. In the book's account of dimensional interaction, once the torus eigenlattice supplies the frequencies and cross-layer resonance produces interference, the layers do not keep proliferating: Stuart-Landau dynamics describe how dimensional proliferation gives way to harmonic regulation. Each layer's amplitude grows while small and saturates as it becomes large, so the four layers settle into a self-regulating balance rather than runaway growth. The current lexicon statement gives the equations as Ȧⱼ = (μⱼ + iωⱼ)Aⱼ − (βⱼ + iγⱼ)|Aⱼ|²Aⱼ + coupling terms, where Aⱼ is the complex amplitude of layer j and Ȧⱼ its rate of change, the first term is the linear growth-and-oscillation term, the second the cubic saturation term that limits large amplitudes, and the coupling terms tie the layers together. Stuart-Landau Dynamics connect to Recursive Toroidal Coupling, UniSpheral Toroidal Mode Spectrum, Interference Patterns, Dimensional Interaction Layers (DILs) and Dimensional Saturation.