Topology-Mediated Amplification in Adaptive Systems

Instability, adaptation and emergence are often examined within separate theoretical traditions, including dynamical systems theory, critical-transition theory, complex adaptive systems and network science. This paper advances a unifying interpretation in which these phenomena arise from a common underlying process: the amplification of local variability through network topology. Building on Shannon's information-theoretic treatment of entropy, established network science, and an existing entropy–constraint formulation of instability, the paper proposes that topology acts as the mechanism that converts local variability into system- level behaviour (Shannon, 1948; Newman, 2010; Watts and Strogatz, 1998; Barabási and Albert, 1999; Hollands, 2026a). A topology-mediated amplification operator, A_G, is introduced to formalise this transformation, and a topology-dependent amplification exponent, α(T), is used to characterise propagation efficiency. The manuscript also strengthens the argument by linking it explicitly to predictive-processing, cortical-entropy and connectome literature, which together suggest that variability is not merely scalar noise but a network-organised property whose consequences depend on topology (Friston, 2005, 2010; Keller and Mrsic-Flogel, 2018; Carhart- Harris and Friston, 2019; Liu et al., 2020; Hong et al., 2019). Under this framework, stability, adaptation, emergence and instability become operating regions of a single amplification process rather than separate phenomena.