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Two-network Kuramoto-Sakaguchi model under tempered stable Lévy noise
Alexander C Kalloniatis1, Timothy A McLennan-Smith2, Dale O Roberts2
1Defence Science and Technology Group, Canberra, ACT 2600, Australia.
Physical Review. E
|February 21, 2019
Summary
This study explores how tempered stable Lévy noise affects two interacting populations. We found that noise parameters can surprisingly restore order in competitive dynamics, offering insights into complex systems.
Area of Science:
- Complex Systems Dynamics
- Statistical Physics
- Nonlinear Dynamics
Background:
- Investigates competitive dynamics between two interacting populations of phase oscillators.
- Introduces tempered stable Lévy noise as a generalization of Gaussian noise with controllable tail heaviness (parameterized by α and λ).
Purpose of the Study:
- To analyze how phase lag and noise distribution shape system behavior (steady vs. noisy).
- To understand the impact of tempered stable Lévy noise on synchronization and phase advantage in competitive populations.
Main Methods:
- Employs both analytical and numerical approaches to study the system.
- Compares system behavior to dynamics in tilted ratchet potentials.
- Utilizes a measure of noise to analyze transitions in a fitness landscape.
Main Results:
- Changes in the power law exponent (α) away from the Gaussian limit disrupt population locking.
- Increasing the tempering parameter (λ) generally restores locking.
- A surprising nonmonotonic transition is observed: decreasing α to very small values (α≪1) with λ≠0 can restore locking, indicating a return to an ordered regime.
Conclusions:
- The system's bulk behavior is effectively described by tilted ratchet potentials.
- The observed restoration of locking at small α values, mediated by the ratchet mechanism, offers a novel way to guide collective behavior in competitive dynamical systems.
- This finding highlights a counterintuitive mechanism for achieving order in complex systems through specific noise parameter tuning.
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