Generation of synchronous patterns in regular coupled networks of cells.

Motivation: Synchronization phenomena are ubiquitous in nature, and therefore also in such diverse fields as natural sciences, engineering, or sociology. The pursuit of synchronous behavior by objects of different types has already stimulated manifold research activities. In addition to other factors, network structures and time delays also play an important role here. The formalism of coupled cell networks provides a general framework for the study of synchronization through the description with coupled systems of ordinary differential equations and their bifurcations. The theory of an equivariant mapping degree is an important topological tool to study fundamental properties of the fixed points or periodic orbits of such systems.
The main objective of the work is to study and analyze the influence of the network structure and the time delay caused by the coupling on the synchronization process. The focus here will be on ideas from coupled cell network theory and equivariant mapping degree theory.
Methods: In the work, various synchronous patterns are to be generated using matrix computation for regular coupled cell networks, various analysis using for the output data of the generated patterns are elaborated. A coupled cell network will be designed to generate specific synchronous behaviors.
Project goals and work packages:
– Literature review on coupled cell networks and classification using synchronous behavior.
– Analysis of the synchronous behavior of a cell network
– Design and self-generation of the coupled cell network