应用数学进展  >> Vol. 6 No. 7 (October 2017)

一类具有双时滞效应的溶解氧-浮游生物模型的动力学分析
Dynamic Analysis of a Dissolved Oxygen-Plankton Model with Two Time Delays

DOI: 10.12677/AAM.2017.67099, PDF, HTML, XML, 下载: 826  浏览: 1,029  国家自然科学基金支持

作者: 郭庆:温州大学,浙江 温州

关键词: 溶解氧浮游生物时滞Hopf分支稳定性Dissolved Oxygen Plankton Two Time Delays Hopf Bifurcation Stability

摘要: 基于海洋生态系统内在动态变化特性和海洋生物种群之间的动态作用机制,本论文构建了一类具有双时滞效应的溶解氧-浮游生物动态模型,并对其相关动力学性质进行理论分析,解析出模型内平衡点具有局部渐近稳定性和发生Hopf分支的阈值条件,并详细探析了Hopf分支的相关动力学性质。本研究成果有利于从动力学的角度揭示溶解氧与海洋浮游生物之间的相互作用机制,有助于深入理解时滞效应如何影响海洋生态系统的动态运行趋势,为进一步研究海洋浮游生物之间相互制约、相互协调的生长动态机制提供一定的理论支撑。
Abstract: Based on the internal dynamic characteristics of marine ecosystem and the dynamic mechanism of marine biological population, this paper constructed a dissolved oxygen-plankton dynamic model involving two time delays, and made theoretical analysis of corresponding dynamics. We obtained the locally asymptotic stability of positive equilibrium and the threshold conditions of occurring Hopf bifurcation were gained. Therefore, we analyzed the dynamics of Hopf bifurcation in detail. This result provides a great help for the interaction between dissolved oxygen and marine plankton in dynamics, and is helpful to deeply understand how the delay affects the dynamic trend of the marine ecosystem, and furthermore provide certain theoretical support for the study of dynamic growth mechanism of mutual restriction and mutual coordination in marine plankton.

文章引用: 郭庆. 一类具有双时滞效应的溶解氧-浮游生物模型的动力学分析[J]. 应用数学进展, 2017, 6(7): 816-830. https://doi.org/10.12677/AAM.2017.67099

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