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On a two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process
1a School of Mathematics and Statistics , Zhaoqing University , Zhaoqing , Guangdong 526061 , People's Republic of China.
This study introduces a two-phase population model with distinct reproductive and non-reproductive stages. The model demonstrates asynchronous exponential growth, offering insights into population dynamics.
Area of Science:
- Population Dynamics
- Mathematical Biology
- Demography
Background:
- Population models are crucial for understanding demographic changes.
- Size-structured models offer detailed insights into population dynamics.
- Distinguishing life stages, like reproductive and non-reproductive, enhances model accuracy.
Purpose of the Study:
- To analyze a two-phase, size-structured population model.
- To investigate population growth with distributed delays in reproduction.
- To compare the two-phase model with a classical one-phase model.
Main Methods:
- Establishing well-posedness of the model.
- Utilizing semigroup theory to analyze population dynamics.
- Employing mathematical analysis for asynchronous exponential growth.
Main Results:
- The two-phase model demonstrates well-posedness.
- Asynchronous exponential growth was proven for the model's solutions.
- A comparison was made between the two-phase and one-phase models under specific conditions.
Conclusions:
- The two-phase size-structured model provides a robust framework for population dynamics.
- The model accurately captures asynchronous exponential growth patterns.
- Further research can explore variations in growth rates between stages.
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