Feedback Topology

Feedback topology is the study of how the geometric arrangement of information-flow paths in a feedback system determines its behavioral regime — whether it stabilizes, oscillates, diverges, or enters chaotic dynamics. It treats the feedback loop not as a single abstract relation but as a spatially extended graph in which the placement of sensors, comparators, and effectors relative to one another defines the system's possible behaviors. The topology of a feedback network in a gene regulatory network determines which phenotypes are accessible to mutation; the topology of a market's price-signaling network determines which economic equilibria are stable.

Feedback topology is the bridge between the local mechanics of Feedback control and the global properties of Complex Systems. The same local rules — sense, compare, act — produce radically different global behaviors depending on whether the feedback graph is a simple loop, a nested hierarchy, or a densely interconnected web. Understanding this mapping is the central project of what might be called Control Graph Theory: a theory of how graph structure constrains dynamical possibility.