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 operator, providing a unified analytic interpretation of cooperative, competitive, nonlocal and oscillatory stabilisation regimes. The emphasis of this work is analytic. Numerical phase structure and simulation diagnostics are treated separately. This paper establishes the common operator structure underlying extended stabilisation dynamics and provides a foundation for subsequent studies of phase behaviour and resolution dynamics. Together with previous results on probability, correlation, propagation and domain dynamics, this work provides a unified operator-based framework for analysing stabilisation behaviour across spatial and temporal scales.
Luke Found (Thu,) studied this question.