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The attractor structure of functional connectivity in coupled logistic maps
Venetia Voutsa1, Michail Papadopoulos2, Vicky Papadopoulou Lesta2
1School of Science, Constructor University Bremen, 28759 Bremen, Germany.
Chaos (Woodbury, N.Y.)
|December 7, 2023
Summary
This study reveals how network structure (SC) and dynamics (FC) interact in coupled systems. Cellular automata analysis shows noise can improve SC/FC correlations by better sampling system states.
Area of Science:
- Complex Systems
- Network Science
- Computational Neuroscience
Background:
- Understanding the relationship between network architecture (structural connectivity, SC) and system dynamics (functional connectivity, FC) is crucial across various scientific disciplines.
- Current methods often translate dynamic observations into pairwise node relationships (FC) for comparison with SC.
Purpose of the Study:
- To investigate how SC/FC relationships change with coupling strength in stylized dynamical systems.
- To explore the utility of cellular automata as a data analysis tool for understanding network dynamics.
Main Methods:
- Utilized coupled logistic maps to model dynamical processes on graphs.
- Employed symbolic encoding to map system dynamics onto a cellular automaton.
- Analyzed the attractors of the resulting cellular automaton to understand SC/FC relationships.
- Introduced noise to observe its effect on SC/FC correlations.
Main Results:
- SC/FC relationships in coupled logistic maps are strongly dependent on coupling strength.
- The observed SC/FC behavior is invariant under symbolic encoding and mapping to cellular automata.
- Cellular automaton attractors alone can explain the observed SC/FC variations.
- Noise was found to enhance SC/FC correlations through more uniform attractor sampling.
Conclusions:
- Cellular automata provide a valuable data analysis framework for network dynamics, distinct from simulation.
- The study offers insights into the fundamental interplay between network structure and emergent dynamics.
- Noise can play a beneficial role in revealing underlying network-dynamic relationships.
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