Description Adaptive systems continuously encounter perturbations that must be integrated into their internal state structure. Maintaining stability therefore requires the ability to incorporate new states while preserving internal coherence. This work introduces Coherence Complexity (Ck), a structural measure describing the integration effort required to harmonize a system state relative to a persistent reference structure within the state space. Ck is defined through a distance function between system states and a reference integration core and can be formulated within a variational framework. The resulting formulation provides a geometric perspective on adaptive integration processes in dynamical systems. A numerical simulation illustrates the emergence of attractor structures and the gradient-driven evolution of system states within the resulting coherence landscape. Additional material:This record also contains the Python simulation code used to generate the coherence landscape and trajectory examples shown in the paper figures. The script reproduces the potential landscape and the gradient-driven trajectory dynamics presented in the publication.
Steven William Baxmeier (Sun,) studied this question.