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A Contusive Model of Unilateral Cervical Spinal Cord Injury Using the Infinite Horizon Impactor
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Asymptotic State of a Two-Patch System with Infinite Diffusion.

Yuanshi Wang1

  • 1School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People's Republic of China. mcswys@mail.sysu.edu.cn.

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|February 27, 2019
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Summary

Spatial diffusion in heterogeneous environments can increase total population size, contrary to some previous theories. This study extends ecological models to consumer-resource systems, revealing new insights into population dynamics and persistence.

Keywords:
Consumer-resource modelDiffusionLiapunov stabilitySpatially distributed populationUniform persistence

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Area of Science:

  • Mathematical Biology
  • Theoretical Ecology
  • Population Dynamics

Background:

  • Mathematical models predict larger population sizes in heterogeneous environments due to diffusion.
  • Previous theory focused on simple diffusion, not extended to consumer-resource systems with external input.

Purpose of the Study:

  • To extend diffusion theory to consumer-resource systems with external resource input.
  • To analyze a two-patch diffusion model characterizing a recent experiment.
  • To investigate the impact of spatial diffusion on population abundance and persistence.

Main Methods:

  • Analysis of a two-patch mathematical model with diffusion.
  • Demonstration of nonnegativity and boundedness of model solutions.
  • Complete exhibition of global dynamics for subsystems.
  • Rigorous mathematical analysis of equilibrium points and stability.

Main Results:

  • Homogeneously distributed resources yield higher carrying capacity than heterogeneous ones, aligning with experiments but refuting some theory.
  • Spatial diffusion increases total equilibrium population abundance in heterogeneous environments, confirming prior theory and data.
  • Stable positive equilibria exist for large diffusion rates, converging to a single point as diffusion increases.

Conclusions:

  • Spatial diffusion enhances population abundance in heterogeneous environments, a finding supported by data and theory.
  • The study provides novel predictions regarding source-sink populations and consumer diffusion rates affecting persistence.
  • Ecological models can be extended to complex systems, offering new insights into population dynamics.