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Swarmalators with frequency-weighted interactions
R Senthamizhan1, R Gopal1, V K Chandrasekar1
1SASTRA Deemed University, Department of Physics, Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, Thanjavur 613 401, India.
Heterogeneous coupling in swarmalators drives distinct collective states and abrupt transitions. This study precisely determines conditions for these dynamical shifts, enhancing swarmalator theory.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Swarmalators exhibit complex collective behaviors.
- Understanding frequency-weighted interactions is crucial for swarmalator dynamics.
- Heterogeneity in natural frequencies impacts collective states.
Purpose of the Study:
- Investigate frequency-weighted interactions in a solvable one-dimensional swarmalator model.
- Identify and characterize distinct collective states under heterogeneous coupling.
- Determine conditions for abrupt dynamical transitions.
Main Methods:
- Analysis of a solvable model of one-dimensional swarmalators on a ring.
- Scaling spatial and phase couplings by heterogeneous natural frequencies.
- Self-consistency analysis to determine transition conditions.
Main Results:
- Identified three collective states: asynchronous, phase-wave, and bistrip mixed.
- Established heterogeneous coupling as the driver of abrupt transitions.
- Precisely determined conditions for dynamical transitions among states.
Conclusions:
- Heterogeneous interaction rules significantly influence swarmalator dynamics.
- Theoretical predictions align well with numerical simulation results.
- Extended understanding of swarmalator collective behavior under frequency-weighted coupling.
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