双脉冲阶段结构的种群系统动力学特性

doi:10.6040/j.issn.1671-9352.0.2021.179

摘要/Abstract

摘要： 研究了具有生育脉冲和收获脉冲的阶段结构种群系统的复杂动力学特性。通过频闪映射确定系统的离散动力模型,并讨论了平衡点的存在性和稳定性,应用中心流形理论研究了平衡点的倍周期分岔。数值仿真发现,随着参数的改变一系列的倍周期分岔级联串联在一起形成Feigen-baum树联,并且在二维参数空间这些Feigen-baum树形成的周期岛拓扑是按照Stern-Brocot树排列,而不是熟悉的Farey树。

关键词: 种群系统, 倍周期分岔, 法理数, 混沌

Abstract: This paper studies the complex dynamics of the stage structure population system with birth pulse and harvest pulse. The discrete dynamical model of the system is determined by stroboscopic mapping, and the existence and stability of the equilibrium point are discussed. The central manifold theory is available to study the period-doubling bifurcation of the equilibrium point. By light of numerical simulation, it is revealed that a series of period-doubling bifurcation cascades connects together to form a Feigen-baum tree link(anti-monotonicity)with the parameters varying. What is the most interesting thing is that the topology of the periodic island formed by these Feigen-baum trees in the two-dimensional parameter space is arranged according to the Stern-Brocot tree instead of the familiar Farey tree.

Key words: population system, eriod doubling bifurcation, Farey tree, chaos

中图分类号:

O441.4

吕宁. 双脉冲阶段结构的种群系统动力学特性[J]. 《山东大学学报(理学版)》, 2021, 56(12): 100-110.

LYU Ning. Dynamics of the stage-structured population system with two kinds of pulses[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 100-110.

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