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Published on: June 29, 2018
Self-sustaining oscillations in complex networks of excitable elements.
Patrick McGraw1, Michael Menzinger
1Department of Chemistry, University of Toronto, Toronto, Ontario M5S3H6, Canada.
Summary
Random networks with loops can self-organize into coherent oscillations. Excitation circulates in selected pacemaker loops, driving synchronized network behavior.
Area of Science:
- Complex systems
- Network science
- Nonlinear dynamics
Background:
- Excitable media exhibit complex spatio-temporal dynamics.
- Network topology significantly influences emergent behaviors.
- Understanding self-organization in coupled systems is crucial.
Purpose of the Study:
- To investigate the self-organization of oscillating states in random networks.
- To identify the underlying mechanisms of coherent oscillations.
- To characterize the role of network loops and initial conditions.
Main Methods:
- Analysis of symmetrically coupled, excitable elements in random networks.
- Investigation of network structures including abundant loops.
- Examination of system behavior under random initial conditions.
Main Results:
- Random networks self-organize into coherently oscillating states.
- Oscillations involve unidirectional signal propagation.
- Specific network loops act as pacemakers, driving periodic excitation circulation.
Conclusions:
- Network loops are essential for self-organized oscillations in excitable systems.
- Pacemaker loop selection dictates the dynamics of coherent network states.
- The findings provide insights into emergent order in complex networks.
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