The attractor structure of functional connectivity in coupled logistic maps

Stylized models of dynamical processes on graphs allow us to explore the relationships between network architecture and dynamics, a topic of relevance in a range of disciplines. One strategy is to translate dynamical observations into pairwise relationships of nodes, often called functional connectivity (FC), and quantitatively compare them with network architecture or structural connectivity (SC). Here, we start from the observation that for coupled logistic maps, SC/FC relationships vary strongly with coupling strength. Using symbolic encoding, the mapping of the dynamics onto a cellular automaton, and the subsequent analysis of the resulting attractors, we show that this behavior is invariant under these transformations and can be understood from the attractors of the cellular automaton alone. Interestingly, noise enhances SC/FC correlations by creating a more uniform sampling of attractors. On a methodological level, we introduce cellular automata as a data analysis tool, rather than a simulation model of dynamics on graphs. (c) 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

Stylized models of dynamical processes on graphs provide insights into the relationship between network architecture and dynamics across different disciplines. By translating dynamical observations into functional connectivity (FC) and comparing them quantitatively with structural connectivity (SC), we find that SC/FC relationships vary significantly with coupling strength in coupled logistic maps. Interestingly, noise enhances SC/FC correlations by creating a more uniform sampling of attractors. In terms of methodology, we introduce cellular automata as a data analysis tool for dynamics on graphs.