Pattern Formation on Networks: from Localised Activity to Turing Patterns.

ABSTRACT: Networks of interactions between competing species are used to model many complex systems, such as in genetics, evolutionary biology or sociology and knowledge of the patterns of activity they can exhibit is important for understanding their behaviour. The emergence of patterns on complex networks with reaction-diffusion dynamics is studied here, where node dynamics interact via diffusion via the network edges. Through the application of a generalisation of dynamical systems analysis this work reveals a fundamental connection between small-scale modes of activity on networks and localised pattern formation seen throughout science, such as solitons, breathers and localised buckling. The connection between solutions with a single and small numbers of activated nodes and the fully developed s

SUBMITTER: McCullen N 

PROVIDER: S-EPMC4895380 | biostudies-literature | 2016 Jun

REPOSITORIES: biostudies-literature