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Data-driven exploration of swarmalators with second-order harmonics.

R Senthamizhan1, R Gopal1, V K Chandrasekar1

  • 1Department of Physics, Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, <a href="https://ror.org/032jk8892">SASTRA Deemed University</a>, Thanjavur 613 401, India.

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We studied swarmalators with second-order harmonics, finding active asynchronous states and phase waves. Convolutional neural networks effectively analyzed these complex dynamics and stability boundaries.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Swarmalators combine features of swarming and oscillations.
  • Second-order harmonics introduce complex interactions in phase dynamics.
  • Understanding emergent behaviors in coupled oscillator populations is crucial.

Purpose of the Study:

  • To investigate the dynamical states of swarmalators with second-order phase interactions.
  • To identify and characterize the active asynchronous state and phase wave transitions.
  • To quantify the stability boundary of the active asynchronous state using novel methods.

Main Methods:

  • Simulation of swarmalator populations with second-order harmonic interactions.
  • Application of convolutional neural networks (U-Net architecture) for data-driven stability analysis.
  • Analytical investigation of clustered states' stability.

Main Results:

  • Emergence of active asynchronous states and clustered states was observed.
  • A transition from static asynchronous to active phase wave states via the active asynchronous state was identified.
  • The stability boundary of the active asynchronous state was successfully delineated and quantified using a data-driven approach.

Conclusions:

  • Second-order harmonics in swarmalators lead to rich dynamical behaviors, including active asynchronous and clustered states.
  • Convolutional neural networks provide an effective tool for analyzing the stability of complex dynamical systems.
  • The study demonstrates a powerful synergy between data-driven and analytical methods in understanding emergent phenomena.