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Swarmalators with frequency-weighted interactions.

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Summary
This summary is machine-generated.

Heterogeneous coupling in swarmalators drives distinct collective states and abrupt transitions. This study precisely determines conditions for these dynamical shifts, enhancing swarmalator theory.

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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.