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Time delay can facilitate coherence in self-driven interacting-particle systems.

Yongzheng Sun1, Wei Lin2, Radek Erban3

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Investigating self-propelled particle models with time delays reveals that longer delays increase switching time. This finding helps explain collective animal behavior, like locust group diffusion dynamics.

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Area of Science:

  • Physics
  • Complex Systems
  • Biophysics

Background:

  • Collective animal behavior, such as flocking or swarming, is often modeled using self-propelled particle (SPP) systems.
  • Time delays in interactions can significantly alter the dynamics of such systems, but their precise impact is not fully understood.
  • Experimental observations in animal groups, like locusts, show complex diffusion behaviors that require sophisticated models for explanation.

Purpose of the Study:

  • To investigate the effect of time delays on the directional switching behavior of self-propelled particles.
  • To explore the applicability of SPP models with time delays in explaining experimentally observed collective animal behaviors.
  • To generalize the model to account for heterogeneity in response times within animal groups.

Main Methods:

  • Development and analysis of a self-propelled particle model incorporating delayed interactions.
  • Mathematical derivation of the relationship between time delay and average switching time.
  • Application of the model to explain state-dependent diffusion coefficients in locust groups.

Main Results:

  • The average switching time of the self-propelled particles was found to be a monotonically increasing function of the time delay.
  • The model with time delays successfully explains the state-dependent diffusion coefficient observed in experiments with locust groups.
  • The theory was extended to heterogeneous groups, accommodating varying time delays for individual particles.

Conclusions:

  • Time delays are a crucial factor in the directional switching dynamics of self-propelled particles.
  • Self-propelled particle models with time delays provide a robust framework for understanding complex collective animal behaviors.
  • The inclusion of heterogeneity in time delays enhances the model's ability to capture real-world biological phenomena.