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Area of Science:

  • Collective behavior dynamics
  • Mathematical modeling of animal groups
  • Theoretical physics of phase transitions

Background:

  • Schooling fish exhibit complex collective patterns like milling and polarized schooling.
  • Mathematical models show these patterns emerge from local interactions without leadership or memory.
  • A popular model demonstrates collective memory, but its origin is unclear.

Purpose of the Study:

  • To elucidate the mechanisms driving collective memory in fish schooling models.
  • To identify the origin of emergent patterns and phase transitions in collective behavior.
  • To resolve ambiguity regarding the source of collective memory in fish dynamics.

Main Methods:

  • Numerical simulations of fish schooling behavior.
  • Application of bifurcation theory to analyze state transitions.
  • Development of a phenomenological model for group polarization dynamics.

Main Results:

  • The transition from milling to schooling is driven by a noisy transcritical bifurcation.
  • Collective memory and transient milling dynamics are captured by a polarization model.
  • Collective memory arises from noisy bifurcation, not structural bistability.

Conclusions:

  • Collective memory in fish schooling models originates from noisy bifurcations.
  • This finding clarifies the mechanisms behind collective phase transitions.
  • Contributes fundamental understanding to self-organizing systems and emergent behavior.