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Related Concept Videos

Toroids01:27

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Multilators on a 3-Torus: A framework for high-dimensional coupled oscillators.

Porikshit Mondal1,2, Rakshita Sharma1, V K Chandrasekar3

  • 1Indian Institute of Science Education and Research, School of Physics, Thiruvananthapuram-695551, Kerala, India.

Physical Review. E
|May 16, 2026
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Summary
This summary is machine-generated.

We introduce a new oscillator model with three or more coupled variables, extending the swarmalator concept. This framework analyzes complex collective dynamics on a 3-torus manifold, applicable to various scientific fields.

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Area of Science:

  • Complex Systems
  • Dynamical Systems Theory
  • Mathematical Modeling

Background:

  • Classical Kuramoto oscillators use a single phase variable.
  • Swarmalators extend this to two variables: position and phase.
  • Many natural systems exhibit interactions with three or more coupled variables.

Purpose of the Study:

  • To develop a generalized oscillator model for systems with at least three mutually coupled state variables.
  • To analyze the collective dynamics of such systems within a mathematically tractable framework.
  • To explore the applicability of this model to diverse scientific domains.

Main Methods:

  • Introduction of a novel oscillator model with three or more variables, each evolving on a circle.
  • Mathematical analysis of system dynamics constrained to a 3-torus manifold (T³).
  • Identification and characterization of distinct collective states and behaviors.

Main Results:

  • The proposed model successfully accommodates systems with multiple coupled state variables.
  • The 3-torus framework enables analytical treatment of complex collective behaviors.
  • A variety of emergent collective dynamics were revealed.

Conclusions:

  • The generalized oscillator model provides a powerful framework for understanding systems with intricate multi-variable interactions.
  • This approach has broad applicability in fields such as sociology, collective animal motion, and neuroscience.
  • The study opens new avenues for analyzing complex emergent phenomena in coupled systems.