Kinetic‐domain analysis of dendritic population dynamics: Revealing hierarchical kinetic organization

Markovian population dynamics on complex networks can be represented exactly in the site or spectral basis, but neither representation directly organizes the relaxation of a selected observable into sequential kinetic stages. Here we examine this hierarchical kinetic organization using the observable‐specific kinetic‐domain (KD) formulation for population transfer on a regular dendritic network. For homogeneous transfer rates, the KD recursion applied in the full site space establishes a one‐to‐one correspondence between the kinetic domains and the generation shells. The resulting stage‐resolved passage times coincide exactly with the conventional generation‐to‐generation mean first‐passage times. This correspondence provides a particularly transparent demonstration of the hierarchical character of the KD representation, with successive KD stages identified directly with successive generation‐to‐generation passages of the conventional first‐passage description. A representative inhomogeneous realization further shows that the low‐index domains retain a recognizable remnant of the homogeneous radial structure, allowing the homogeneous analytic results to serve as a useful reference for the dominant low‐index kinetics. These results identify the generation‐shell hierarchy as a particularly simple realization of a more general observable‐specific kinetic organization and illustrate the potential of the KD formulation for revealing such organization directly from the underlying rate matrix.