Self-organized collective patterns on graphs

featured image caption


Over the last few years, diverse studies have established that many forms of dynamics self-organize on networks to give rise to large-scale collective patterns. The dynamical pattern is then a consequence of the parameters defining the dynamics as well as the network architecture. Examples include Turing patterns on graphs arising from reaction-diffusion systems, self-organized waves around hubs arising in excitable dynamics and synchronization of modules arising in coupled oscillators. In some cases, changing a parameter of the dynamics can trigger a transition from one pattern to another.  These self-organized, collective behaviours are in the focus of ESR3. The work will involve studying such behaviours in model simulations and searching for evidence of such behaviours in the data available within the ITN for the diverse application projects in two example case studies.

Example 1:
To use anatomical connectivity to provide the spatial measure of propagation of activity from key nodes in a neuronal network in healthy (stimulus processing) and pathological scenario (epilepsy, schizophrenia) or severely impaired conditions (blind and paraplegic subjects); the analysis will use anatomical connectivity in a similar way the inclusion of air travel connectivity between cities helped to better understand the (wave-like propagation of) disease spreading. Here, MEG data will be provided by AI (AAISCS) and will relate to training provided in Advanced Courses 2 and 5.

Example 2:
To explore waves of sediment movement through river networks. This is affected by the connectivity between the channel and hillslope sediment sources, and also the downstream connectivity between different channel types (e.g. alternating alluvial and bedrock sections). For a given arrangement of channel reaches, how does the downstream sediment movement change as a function of the rate and type of sediment supply (continuous vs. episodic)? Here, spatio-temporal laser scanning datasets of river channels will be used and will be provided by RAH (UDur) and will link to those used in Advanced Course 5.

Expected Results

Expected Results

The project will provide a thorough theoretical understanding of self-organized collective patterns on graphs and facilitate the use of this knowledge in the various application scenarios. The results from these projects will not only provide a better understanding of the way brain activity propagates in the brain under specific task demands, but could also help develop novel learning biomarkers (developed from the knowledge accumulated through complex connectivity analysis of sophisticated data recorded with expensive instrumentation) derived from simple and widely available hardware.


Host Months Aim



Familiarization/selection of what data to use and discussions about possible analysis scenario, and (month 34) run analysis on tomographic solutions of selected MEG data.



Exploitation of Graph Theoretical tools for the theoretical modelling and understanding of self-organized collective patterns on graphs.


23 - 25

Construction and simulation of human brain network models of epileptic patients. These models will mimic the organization of individual patients’ epilepsy including their epileptogenic seizure onset zones and seizure propagation patterns. Correlates of the ictal organization will be identified within the non-ictal pattern dynamics of the resting state and quantified via SC/FC

UDur (RAH)


Modelling waves of sediment movement through river networks.

Other Positions in Network Graphs


Jacobs University (Germany)

Minimal models of dynamics on networks to study generic SC/FC relationships


Jacobs University (Germany)

Self-organized collective patterns on graphs


Masaryk University (Czech Republic)

Catastrophic transitions: Regime shifts in network topology resulting in novel systems