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Winner-take-all in a phase oscillator system with adaptation.
Oleksandr Burylko1, Yakov Kazanovich2, Roman Borisyuk2,3
1Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, 01601, Kyiv, Ukraine. burylko@yahoo.co.uk.
Scientific Reports
|January 12, 2018
Summary
This study introduces a generalized phase oscillator system exhibiting winner-take-all dynamics. Researchers identified conditions for this regime and a novel bifurcation type, aiding optimal parameter selection for synchronization.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Conventional phase oscillator models, like the Kuramoto type, focus on synchronization dynamics.
- Existing models often lack the inclusion of dynamic natural frequencies and variable connection strengths.
- Understanding competition and synchronization in coupled oscillator systems is crucial for various scientific fields.
Purpose of the Study:
- To introduce and analyze a generalized phase oscillator system with dynamic variables including natural frequency and connection strengths.
- To investigate the emergence of winner-take-all behavior in this system.
- To characterize the conditions and bifurcations associated with the winner-take-all regime.
Main Methods:
- Development of a generalized phase oscillator model with a central element and radial connections.
- Derivation of conditions for winner-take-all behavior in both stationary and non-stationary dynamics.
- Bifurcation analysis to study transitions between dynamic regimes.
- Computer simulations for parameter optimization.
Main Results:
- The generalized system demonstrates winner-take-all behavior, where peripheral oscillators compete for synchronization with the central element.
- Conditions for achieving the winner-take-all regime were mathematically derived.
- A novel bifurcation, Saddle Node on Invariant Torus (SNIT), was identified and described.
- Optimal parameters for implementing winner-take-all dynamics were determined through simulations.
Conclusions:
- The generalized phase oscillator system offers a new framework for studying competitive synchronization.
- The identified winner-take-all conditions and SNIT bifurcation provide deeper insights into complex system dynamics.
- This research facilitates the design of systems exhibiting targeted synchronization and competition.
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