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Asynchronous exponential growth for a two-phase size-structured population model and comparison with the

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  • 1a School of Mathematics and Statistics Sciences , Zhaoqing University , Zhaoqing , 526061 Guangdong , People's Republic of China.

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Summary

This study introduces a two-phase population model with distinct active and resting stages and distributed birth delays. The model demonstrates asynchronous exponential growth, differing from simpler one-phase models.

Keywords:
35A0235B4035Q92Size-structured populationsasynchronous exponential growthdistributed delay

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Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Theoretical Ecology

Background:

  • Population models are crucial for understanding species dynamics.
  • Size-structured models offer detailed insights into population development.
  • Incorporating life-stage transitions, like active and resting phases, enhances model realism.

Purpose of the Study:

  • To analyze a two-phase, size-structured population model with distributed delays in reproduction.
  • To investigate the impact of distinct 'active' and 'resting' life stages on population growth.
  • To compare the long-term behavior of the two-phase model with a one-phase model.

Main Methods:

  • Utilizing the theory of semigroups to establish global well-posedness.
  • Analyzing the asymptotic behavior of population densities.
  • Comparing the dynamics of the two-phase model against a simplified one-phase model.

Main Results:

  • The two-phase model is globally well-posed.
  • Solutions exhibit asynchronous exponential growth.
  • Asymptotic behaviors differ significantly between the two-phase and one-phase models.

Conclusions:

  • The inclusion of distinct life stages and distributed delays in population models leads to unique dynamic properties.
  • The two-phase model provides a more nuanced understanding of population growth compared to one-phase models.
  • This research contributes to the theoretical framework of complex population dynamics.