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State-dependent effective interactions in oscillator networks through coupling functions with dead zones
Peter Ashwin1, Christian Bick1, Camille Poignard1
1EPSRC Centre for Predictive Modelling in Healthcare and Centre for Systems, Dynamics & Control, Department of Mathematics, University of Exeter, Exeter, Devon, UK.
Summary
Networks of coupled oscillators with
Area of Science:
- Complex systems
- Network dynamics
- Nonlinear dynamics
Background:
- The behavior of interacting dynamical systems is determined by their coupling mechanisms.
- Coupling functions with 'dead zones' (where coupling is zero) present unique challenges in analyzing network dynamics.
Purpose of the Study:
- To formalize the concepts of dead zones and effective interactions in networks of oscillatory units.
- To investigate how coupling functions influence and shape effective interaction schemes.
- To analyze the temporal evolution of effective interactions in these networks.
Main Methods:
- Analysis of oscillatory units with coupling functions exhibiting dead zones.
- Formalization of 'dead zones' and 'effective interactions' concepts.
- Examination of the relationship between coupling function properties and emergent interaction dynamics.
Main Results:
- Effective interactions, rather than fixed structural connectivity, are crucial for understanding network dynamics.
- Oscillators can effectively decouple based on their phase configurations.
- Effective interactions are not static and can evolve over time along system trajectories.
Conclusions:
- Dead zones in coupling functions lead to dynamic and evolving effective interactions.
- The structure of the coupling function dictates the possible schemes of effective interaction.
- Understanding effective interactions is key to predicting the behavior of complex networks.
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