Adaptive rewiring is the driving force of brain plasticity to form modular, small-world connectivity structure. Highly simplified models for adaptive rewiring represent the dynamic activity of neural masses by coupled logistic maps. Such models have thus far used uniform parametrizations, preventing any cognitive functionality. In order to enable cognitive functions, adaptive rewiring must be robust to non-uniformity of parameters. Moreover, it should enable function-specific structures to emerge from such parameterization. Coupled logistic maps are characterized by two parameters, namely turbulence (constraining node activation) and coupling strength between nodes. We study five parameterization conditions of an adaptively rewiring coupled map network. A baseline condition with uniform values for these parameters is compared with four conditions in which either of the parameters of a subset deviates from the remaining units. To describe the evolution of model network structure, clustering coefficient, average path length, small-worldness, modularity, degree assortativity, edge density, and rich club coefficient are calculated. Different conditions are compared by representing networks as multivariate distributions of local network statistics. The results show that highly modular, small-world structures evolve from random initial conditions, while the structures evolving in different conditions show considerable differentiation. This study offers computational support for robustness of adaptive rewiring algorithm under symmetry-breaking conditions regarding the dynamic evolution of properties characteristic to brain networks. Furthermore, function-specific structures and behaviors emerge from such deviations, implying that functional and structural differentiation can be used to identify functional components in a network, upholding the use of structural and functional connectivity measures in neuroimaging.