Researchers in the Complex Systems Laboratory use the methods of statistical physics to investigate evolutionary game theoretic models and dynamic phenomena on various lattices and graphs. These models offer a general mathematical background to multidisciplinary research areas (biology, economics, behaviour research, etc.). They extended the analysis of relatedness of folk music and genetics of various ethnical groups in directions that allow the joint investigation of spatial and temporal processes.
- In evolutionary game theory they use mathematical models to pursue investigations to explore processes, strategies and relationship systems, developing between selfish individuals, which support cooperation advantageous for the community. Among the punitive strategies they have found variations that efficiently help the prevalence of a behaviour representing the common interest in spatial “Tragedy of the commons” games. Model studies also justified the communal usefulness of exchanging information that comes at a cost, if a sufficient number of players willing to sacrifice are present in the community.
- In evolutionary game theoretic models depth analysis is based on the ability to decompose interactions described in matrix form into the linear combination of four basic games. Systematic investigation of the coordination components cast light on the existence of social trap situations which are similar to phase-changes known in solid-state physics. At the level of pair interactions, mathematical analysis of the components causing the tragedy of commons clearly indicated that the frequency (and with it the significance) of the separation of individual and collective interests grows with the increase of the number of strategies in the case of potential games, which represent a significant subset of matrix games strongly related to physics.
- They studied numerically the duration time distribution of avalanche-like failures in models developed for studying power grids. Models suitable to describe the spread of activity were used in modular networks to quantify the effect of the topological features of networks on the dynamics of brain models.
- They continued to develop self-learning algorithms suitable to identify clusters observable in the space of folk music tunes and hereditary genetic codes characterizing ethnic groups, and to more accurately quantify the measure of relatedness. The continuous expansion of the folk music and genetic databases and their completion by archaeological data may even provide a background for the historical analysis of the migration of peoples.