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Phase transitions on a multiplex of swarmalators
Steve J Kongni1, Venceslas Nguefoue1, Thierry Njougouo2
1Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon and MoCLiS Research Group, Dschang, Cameroon.
Physical Review. E
|October 18, 2023
Summary
Bidirectionally coupled swarmalators exhibit distinct synchronization patterns based on vision range and coupling strengths. Researchers identified interlayer static synchronization and analyzed complex phase transitions during dynamic changes.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Swarmalators, hybrid systems combining elements of swarms and oscillators, are crucial for understanding emergent collective behavior.
- Bidirectional coupling introduces complex interactions that can lead to diverse synchronization phenomena.
- Investigating the interplay between attractive and repulsive forces is key to predicting system dynamics.
Purpose of the Study:
- To analyze the dynamics of bidirectionally coupled swarmalators under varying attractive and repulsive coupling strengths.
- To investigate the influence of the vision range (r_c) on interlayer connectivity and emergent patterns.
- To characterize phase transitions and synchronization mechanisms within the swarmalator system.
Main Methods:
- Theoretical analysis of swarmalator dynamics with attractive (σ_a) and repulsive (σ_r) couplings.
- Systematic variation of the vision range (r_c) to observe its effect on connectivity and patterns.
- Numerical simulations and visualization (animations) to support analytical findings and observe transitions.
Main Results:
- Identified and proved the stability of interlayer static synchronization (π).
- Observed first-order transitions for small repulsive coupling (σ_r) or large vision range (r_c).
- Characterized a two-step second-order transition for σ_r=0 and small r_c, involving energy drops and rotating waves in internal phases.
Conclusions:
- The vision range (r_c) significantly dictates interlayer connectivity and emergent patterns in swarmalator systems.
- Complex phase transitions, including first and second-order, are observed and depend critically on coupling parameters and vision range.
- The study reveals intricate dynamics, including rotating waves, leading to synchronization, providing insights into collective behavior in coupled oscillator systems.
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