摘要
研究一类基于个体尺度分布的竞争种群系统平衡态的稳定性.利用种群再生数获得了平衡态的存在性条件,借助特征根的分布给出了平衡态的稳定性判据,运用离散化程序展示了两个稳定性实例.
This paper researches the stability of the steady states of a competitive population system, in which the individuals are classified by their body size. Firstly, we establish the existence of equilibria by defining the basic reproductive numbers of the involved populations, and show that the system owns a unique positive steady state if the reproductive numbers of the two populations are greater than one. On the other hand, the trivial solution is always an equilibrium. Secondly, we investi- gate the stability of the equilibria via linearization method, and carefully derive the corresponding characteristic equation. Then we obtain the criterion by a standard argument; that is, a steady state will be asymptotically stable if all the eigenvalues have negative real parts, while unstable if one of the eigenvalues has positive real part. Finally, we explore the stability by numerical simulations since the high com- plexity in the characteristic equation makes a clear and extensive theoretical analysis impossible. Introducing an appropriate difference format and choosing two examples, we present some intuitive demonstrations for the stability of the trivial equilibrium, which agree with the theoretical predictions. In a word, size-structured population models are more realistic for some species, but they bring us more challenges to mathematical analysis. This work offers a helpful effort.
出处
《系统科学与数学》
CSCD
北大核心
2015年第5期566-575,共10页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(11271104)
浙江省教育厅(Y201327022)科研项目资助课题
关键词
个体尺度
竞争系统
特征方程
再生数
稳定性
Body size； competitive system； characteristic equation； reproductive number； stability
