Fundamental complexity and networks

In the Centre for Complexity Science, we study a range of different systems to find general principles behind the dynamics and the emergent structures we see. We use concepts and approaches from statistical mechanics and information theory to produce better tools to monitor systems and to improve our overall understanding of complex systems. Since complex systems consist of many parts, network theory is central to our activities and we develop new network tools for our applications. Some examples of our work are discussed below with references at the bottom of the page.

Complexity science can be seen as the systematic study of emergent phenomena. It aims to identify general features of emergence in many different types of complex systems, such as configurational structures and modes of the dynamics. Commonly one encounters long range correlation (Palmieri & Jensen, 2020) and intermittent dynamics (Jensen, 2018).  This can lead to power law like probability distributions and to tipping points in the evolution of the systems (Caroli, Piovani & Jensen, 2020).  To analyse interdependence between parts of complex systems new approaches of information theory is asked for (Tempesta & Jensen, 2020; Rosas et al, 2020; Rosas, Mediano, Gastpar & Jensen, 2019). 

The emergent structure in complex systems can often be best described and analysed in terms of network theory. This motivates our search for better network tools to describe systems and new network models that demonstrate key features. When networks are constrained, either by space (Sood, Hilton & Evans 2020) or time (Evans, Calmon & Vasiliauskaite 2020), then new models and techniques are needed.


A. Caroli, D. Piovani, and H.J. Jensen, Forecasting transitions in systems with high dimensional stochastic complex dynamics: A Linear Stability Analysis of the Tangled Nature Model. Phys. Rev. Lett. 113, 264102 (2014).

B. Hilton, A. P. Sood, and T. S. Evans, “Predictive limitations of spatial interaction models: a non-Gaussian analysis,” Scientific Reports, 2019.

T. S. Evans, L. Calmon, and V. Vasiliauskaite, “The Longest Path in the Price Model,Scientific Reports, vol. 10, p. 10503, 2020. 

H.J. Jensen, Tangled Nature: A model of emergent structure and temporal mode among co-evolving agents. European Journal of Physics 40, 014005 (2018). 

Fernando E. Rosas, Pedro A.M. Mediano, Henrik J. Jensen,  Anil K. Seth, Adam B. Barrett, Robin L. Carhart-Harris, and Daniel Bor, Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data. To Appear in PLOS Computational Biology.

Fernando Rosas, Pedro A.M. Mediano, Michael Gastpar, and Henrik J. Jensen, Quantifying high-order interdependencies via multivariate extensions of the mutual information, Phys. Rev. E. 100, 032306 (2019). 2019.

Lorenzo Palmieri and Henrik J Jensen, The Forest Fire Model: The subtleties of criticality and scale invariance. Frontiers in Physics. 8, 257, (2020). 

Piergiulio Tempesta and Henrik J Jensen, Universality Classes and Information-Theoretic Measure of Complexity via Group Entropies. Scientific Reports  10, 5952 (2020).