摘要
目的:研究等级年龄结构模型解的性质以及模型平衡态的稳定性。方法:运用上下解理论对等级年龄结构模型解进行存在性、唯一性的分析,建立微分方程对平衡态的存在性条件进行讨论。结果:运用上下解方法证明了等级年龄结构模型解的存在性、唯一性,通过微分方程以及基本再生数给出平衡态的存在性条件,借助特征线方法,给出模型平衡态稳定和不稳定条件。结论:利用平衡态的稳定性判别条件,可以根据实际需要来调节生物个体的参数来控制生物种群数量或种群密度。
Aims: This paper aims to study the nature of the solution of the graded age structure model and the stability of the equilibrium state of the model. Methods: The existence and uniqueness of the solution of the hierarchical age structure model was analyzed by using the upper and lower solution theory. The differential equation was established to discuss the existence condition of the equilibrium state. Results: The existence and uniqueness of the solution of the hierarchical age structure model were proved by the upper and lower solution method. The existence condition of the equilibrium state was given by the differential equation and the basic reproduction number. With the help of the characteristic line method, the stable and unstable conditions of the model equilibrium state were given. Conclusions: By using the stability judgment condition of the equilibrium state, the parameters of biological individuals can be adjusted according to actual needs to control the biological population quantity or population density.
作者
夏洪涛
刘炎
XIA Hongtao;LIU Yan(College of Sciences,China Jiliang University,Hangzhou 310018,China)
出处
《中国计量大学学报》
2019年第4期524-530,共7页
Journal of China University of Metrology
基金
国家自然科学基金项目(No.11401549)
关键词
计量
等级年龄结构模型
上下解理论
平衡态
稳定性
metrology
hierarchical age-structure model
upper and lower solution theory
equilibrium state
stability
