Collective dynamics of heterogeneous networks of active elements

• Applicant: Dr. Matthias Wolfrum
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Mathematics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 429828445

The collective activity of large networks of coupled active elements has gained much attention in different fields of modern science, ranging from physics, biology and chemistry to social sciences and technology. An important feature which may have fundamental influence on a network’s collective behavior is the heterogeneity of its properties. Heterogeneity may manifest itself as diversity of the nodal intrinsic (local) parameters (dynamical heterogeneity) and/or via complex connectivity patterns (structural heterogeneity). A typical consequence of the network heterogeneity is a splitting of the nodes into subgroups with different behavior. However, it is a highly nontrivial problem to predict the features of the resulting partition given the particular form of heterogeneity, as well as to determine the dynamics of the ensuing groups. The main goal of the present project is to systematically investigate the relationship between the various types of network heterogeneity and its collective dynamics. Within this general framework, we will consider three sets of problems. Firstly, we intend to contribute to the theory of macroscopic excitability in a diverse population of coupled oscillatory and excitable units. Secondly, we will study partial synchronization and the formation of complex patterns due to heterogeneous connectivity in adaptive networks. Finally, we will investigate how the scenarios for the onset of complex activity patterns depend on the interplay between structural and dynamical heterogeneity, considering the effects of correlation between the nodal parameters and the distribution of their connectivity degrees.

• DFG Programme: Research Grants
• International Connection: Russia
• Partner Organisation: Russian Foundation for Basic Research
• Cooperation Partner: Professor Dr. Vladimir Nekorkin