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Patterning of Microorganisms and Microparticles through Sequential Capillarity-assisted Assembly
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Pattern formation via intermittence from microscopic deterministic dynamics.

Marco Hernández1, Daniel Escaff, Ricardo Finger

  • 1Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Santiago, Chile.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a lattice model for population dynamics, revealing pattern formation via intermittence. The model offers insights into how discrete systems generate complex spatial structures from disordered states.

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Area of Science:

  • Mathematical modeling
  • Theoretical ecology
  • Complex systems

Background:

  • Population dynamics often exhibit pattern formation in continuous models.
  • The Allee effect describes reduced per capita growth at low population densities.
  • Understanding discrete models is crucial for ecological pattern emergence.

Purpose of the Study:

  • To develop a one-dimensional lattice model incorporating variable coupling and the Allee effect.
  • To investigate pattern formation mechanisms in this discrete system.
  • To analyze the relationship between intermittence, chaos, and model parameters.

Main Methods:

  • Development of a one-dimensional lattice model.
  • Analytical estimation of pattern wavelength.
  • Numerical simulations of pattern formation and fluctuations.
  • Analysis of intermittence and sensitivity to initial conditions.

Main Results:

  • The lattice model exhibits pattern formation from disorder via intermittence.
  • Analytical and numerical methods confirm pattern wavelength estimation.
  • Intermittence is linked to the edge of chaos and initial condition sensitivity.
  • System size influences the intermittent regime, consistent with analytical predictions.

Conclusions:

  • The proposed lattice model successfully simulates population dynamics pattern formation.
  • Intermittence provides a novel mechanism for pattern emergence in discrete systems.
  • The model offers a framework for studying ecological dynamics in discrete environments.