Pattern Formation over Multigraphs.

ABSTRACT: Two of the most common pattern formation mechanisms are Turing-patterning in reaction-diffusion systems and lateral inhibition of neighboring cells. In this paper, we introduce a broad dynamical model of interconnected modules to study the emergence of patterns, with the above mentioned two mechanisms as special cases. Our results do not restrict the number of modules or their complexity, allow multiple layers of communication channels with possibly different interconnection structure, and do not assume symmetric connections between two connected modules. Leveraging only the static input/output properties of the subsystems and the spectral properties of the interconnection matrices, we characterize the stability of the homogeneous fixed points as well as sufficient conditions for the emerg

SUBMITTER: Gyorgy A 

PROVIDER: S-EPMC5839348 | biostudies-literature | 2018 Jan-Mar

REPOSITORIES: biostudies-literature