Stabilisation Dynamics VII: An Operator Framework for Extended Stabilisation Dynamics

This paper develops a unified operator framework for three key extensions of continuum stabilisation dynamics. Building on the local continuum stabilisation field theory, we analyse coupled stabilisation fields, nonlocal spatial coupling and delayed stabilisation response. We show that these extensions can be understood as structured deformations of a common linear stabilisation response operator. Coupled fields introduce multiple response channels, nonlocal kernels modify spatial propagation through finite-range interactions, and delay introduces temporal memory effects that can reorganise stabilisation behaviour. Within this framework, system behaviour is governed by the spectral properties of the underlying…