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### 融合空间扩散与年龄等级结构的种群模型

1. 杭州电子科技大学运筹与控制研究所,杭州  310018
• 出版日期:2021-10-25 发布日期:2021-12-24

HE Zerong , QIN Wanyu. Analysis of a Population Model Incorporating Spatial Dispersal into Hierarchical Age-Structure[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(10): 2684-2697.

### Analysis of a Population Model Incorporating Spatial Dispersal into Hierarchical Age-Structure

HE Zerong ,QIN Wanyu

1. Insititute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018
• Online:2021-10-25 Published:2021-12-24

Assuming that the internal competition environment is decided by individual's age, we formulate and analyze a class of population model combining the spatial diffusion with the age hierarchy, which is described by the second-order integro-partial differential equation. Based upon some rational assumptions on the model parameters, the existence, uniqueness, non-negativity and boundedness of solutions to the model are established by means of the approach of Banach's fixed-points and the corresponding result in linear systems. In order to go through the process, we first freeze the environment variable in the vital rates and introduce a linear model. Then we make the key technic estimation for the solution mapping, which enables us to define the equivalent norm on the space of the object functions. The fixed point of the solution mapping is exactly the solution for the hierarchical population model. Furthermore, we derive the comparison principle and analyze the separable form of the solutions. The results obtained not only extend some existing works in the literature, but also provide a necessary foundation for the study of stability, controllability and optimal control problems.
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