一类具有抑制效应的浮游生态模型的时空动力学问题研究
Spatiotemporal Dynamics of a Planktonic Ecological Model with Inhibitory Effect
DOI: 10.12677/AAM.2019.812236, PDF,   
作者: 姬圈利:温州大学浙江省水环境与海洋生物资源保护重点实验室,浙江 温州
关键词: 抑制效应平衡点稳定性霍普夫分支图灵失稳Inhibitory Effect Equilibrium Stability Hopf Bifurcation Turing Instability
摘要: 依据藻类水华监测数据与浮游生态学理论,构建一类具有抑制效应的浮游生态动力学模型,对其定性理论与数值工作进行研究。理论工作主要研究了模型解的正性与有界性、平衡点的存在性与稳定性,并给出模型发生霍普夫分支与图灵失稳的临界条件。数值工作主要验证了理论推导工作的有效性与临界条件的可行性。这些研究结果对浮游生态系统非线性动力学问题研究具有一定的促进作用。
Abstract: Based on monitoring data of algae blooms and planktonic ecological theory, a planktonic ecological dynamical model with inhibitory effect has been established, and its qualitative theory and numerical simulations have been investigated. Theoretical studies mainly have considered the positivity and boundedness of model solutions, the existence and stability of equilibria, and the critical conditions for the Hopf bifurcation and Turing instability. Numerical simulations mainly have verified the effectiveness of the theoretical derivation and the feasibility of critical conditions. The obtained results can be very helpful to deepen and expand the research of nonlinear dynamics of such plankton ecosystem.
文章引用:姬圈利. 一类具有抑制效应的浮游生态模型的时空动力学问题研究[J]. 应用数学进展, 2019, 8(12): 2050-2061. https://doi.org/10.12677/AAM.2019.812236

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