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Visualizing Lignification Dynamics in Plants with Click Chemistry: Dual Labeling is BLISS!
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Plant Dynamics, Birth-Jump Processes, and Sharp Traveling Waves.

N Rodríguez1, G Malanson2

  • 1Department of Mathematics, UNC Chapel Hill, Phillips Hall, CB#3250, Chapel Hill, NC, 27599-3250, USA. nrod@unc.edu.

Bulletin of Mathematical Biology
|May 12, 2018
PubMed
Summary

This study introduces a discrete agent-based model for plant growth and dispersal, revealing wave-like solutions. Mathematical analysis confirms the existence and properties of these traveling waves, supported by numerical simulations.

Keywords:
Birth-jump processesDegenerate reaction–diffusion equationTraveling wave solutions

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Area of Science:

  • Mathematical Biology
  • Ecology
  • Computational Science

Background:

  • Understanding plant growth and dispersal dynamics is crucial for ecological studies.
  • Discrete agent-based models offer a framework for simulating complex biological processes.
  • Traveling wave phenomena are observed in various biological systems, including population dynamics.

Purpose of the Study:

  • To introduce and analyze a discrete agent-based model for plant growth and dispersal.
  • To rigorously investigate the existence and properties of traveling wave solutions.
  • To determine the minimum speed of these wave phenomena.

Main Methods:

  • Development of a discrete agent-based model incorporating a birth-jump process.
  • Derivation of the diffusion limit of the discrete model.
  • Analytical proof of traveling wave solutions under logarithmic growth.
  • Variational approach to determine wave speed.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • The discrete model exhibits wave-like solutions representing plant dispersal.
  • Existence of sharp and continuously differentiable traveling wave solutions is proven.
  • A variational speed for the minimum wave propagation speed is established.
  • Numerical experiments confirm the analytical results and model predictions.

Conclusions:

  • The developed agent-based model effectively captures plant growth and dispersal dynamics.
  • The study provides rigorous mathematical evidence for traveling wave solutions in this context.
  • The findings contribute to a deeper understanding of ecological pattern formation.