Age-Structured Population Dynamics with Nonlocal Diffusion
Age-Structured Population Dynamics with Nonlocal Diffusion
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DOI：
10.1007/s10884-020-09860-5
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发表时间：
2020-06-15
影响因子：
1.3
通讯作者：
Yu, Xiao
中科院分区：
文献类型：
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作者：
Kang, Hao;Ruan, Shigui;Yu, Xiao
随机扩散年龄结构种群模型已被许多研究者所研究。尽管与随机扩散过程相比，非局部扩散过程更适用于许多生物和物理问题，但关于年龄结构的非局部扩散种群模型的理论结果却很少。本文的目的是发展具有非局部扩散的年龄结构种群动力学的基本理论。特别地，我们研究了具有非局部扩散的年龄结构模型的线性算子半群，并利用它的无穷小生成元的谱性质来确定零稳态的稳定性。结果表明：(I)当出生率和死亡率都与空间变量无关时，具有非局部扩散的年龄结构模型的半群的结构本质上是由无扩散的年龄结构模型的半群结构和非局部算子决定的；(Ii)当出生率和死亡率都依赖于空间变量时，其渐近行为可以由无穷小生成元的谱界符号来决定；(Iii)当出生率和死亡率都依赖于空间变量和时间时，可以建立弱解和比较原理；(Iv)上述结果可以推广到年龄结构模型。此外，在前两种情况(I)和(II)中，我们将我们的结果与具有拉普拉斯扩散的年龄结构模型进行了比较。
Random diffusive age-structured population models have been studied by many researchers. Though nonlocal diffusion processes are more applicable to many biological and physical problems compared with random diffusion processes, there are very few theoretical results on age-structured population models with nonlocal diffusion. In this paper our objective is to develop basic theory for age-structured population dynamics with nonlocal diffusion. In particular, we study the semigroup of linear operators associated to an age-structured model with nonlocal diffusion and use the spectral properties of its infinitesimal generator to determine the stability of the zero steady state. It is shown that (i) the structure of the semigroup for the age-structured model with nonlocal diffusion is essentially determined by that of the semigroups for the age-structured model without diffusion and the nonlocal operator when both birth and death rates are independent of spatial variables; (ii) the asymptotic behavior can be determined by the sign of spectral bound of the infinitesimal generator when both birth and death rates are dependent on spatial variables; (iii) the weak solution and comparison principle can be established when both birth and death rates are dependent on spatial variables and time; and (iv) the above results can be generalized to an age-size structured model. In addition, we compare our results with the age-structured model with Laplacian diffusion in the first two cases (i) and (ii).