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Related Experiment Video

Updated: Jan 19, 2026

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On an age structured population model with density-dependent dispersals between two patches.

Chang-Yuan Cheng1, Shyan-Shiou Chen2, Xing Fu Zou3

  • 1Department of Applied Mathematics, National Pingtung University, Pingtung, ROC 90003, Taiwan.

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Summary

This study introduces a new population model with density-dependent dispersal and delayed births. While density-dependent dispersal doesn't affect extinction, it influences long-term population dynamics and spatial patterns.

Keywords:
age structuredelay differential equationdensity-dependent dispersalglobal convergencepatchuniform persistence

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Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Ecological Modeling

Background:

  • Existing age-structured population models often assume constant dispersal rates.
  • Density-dependent dispersal and delayed births are crucial factors in real-world population dynamics.

Purpose of the Study:

  • To develop and analyze a modified age-structured population model incorporating density-dependent dispersal and delayed non-local birth terms.
  • To investigate the theoretical implications of immature individuals' mobility between patches.

Main Methods:

  • Derivation of a modified population model with nonlinear dispersal and delayed birth terms.
  • Theoretical analysis including well-posedness, existence of positive equilibrium, and extinction/persistence thresholds.
  • Investigation of positive invariant sets and global convergence properties.

Main Results:

  • The model's well-posedness was confirmed.
  • Criteria for the existence of a positive equilibrium were established.
  • A threshold for population extinction versus persistence was determined.

Conclusions:

  • Density-dependent dispersal does not influence extinction/persistence outcomes.
  • Density-dependent dispersal significantly impacts long-term population dynamics, including temporal-spatial patterns and final population sizes when the population persists.