一类具有时滞效应的营养盐–浮游植物系统的动力学研究
Dynamic Analysis of a Time Delayed Nutrient-Phytoplankton System
DOI: 10.12677/AAM.2017.62019, PDF, HTML, XML, 下载: 1,929  浏览: 3,008  国家自然科学基金支持
作者: 尚荣忠：温州大学，浙江 温州
关键词: 时滞；平衡点；稳定性；Hopf分支；Time Delays； Equilibrium； Stability； Hopf Bifurcation
摘要: 本文主要在动态建模过程中考虑易感染浮游植物吸收营养盐转化为自身能量所造成的时间滞后和易感浮游植物变为感染浮游植物所造成的时间滞后，进而建立了一类具有时滞效应的营养盐–浮游植物动态系统。在此基础上，主要采用Routh-Hurwitz判据和Lyapunov-Krasovskii函数对该系统内平衡点的稳定性和Hopf分支进行了理论分析，获得了系统具有这些特定动力学行为的临界条件，这些研究结果对预防和控制浮游植物大面积爆发具有一定的指导意义。
Abstract: The paper mainly considered the time lag problem caused by the susceptible phytoplankton absorbing nutrient and translating into energy and susceptible phytoplankton turning into infected phytoplankton, and then, a time delayed nutrient-phytoplankton system will be established. On this basis, the stability of the equilibrium point and the Hopf bifurcation of the system have been analyzed by using the Routh-Hurwitz criterion and the Lyapunov-Krasovskii function, and then the critical conditions of these particular dynamical behaviors have been obtained. Finally, these results have some guiding significance for the prevention and control of large area outbreaks of phytoplankton.
文章引用：尚荣忠. 一类具有时滞效应的营养盐–浮游植物系统的动力学研究[J]. 应用数学进展, 2017, 6(2): 165-173. https://doi.org/10.12677/AAM.2017.62019

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https://doi.org/10.1007/s10255-016-0540-6

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