一类具有藻毒素动态影响的水域生态模型的动力学问题研究
Study on the Dynamics of an Aquatic Ecological Model with Dynamic Effects of Algo Toxins
摘要: 在考虑水域中的藻毒素是变量的情况下，构建一类具有藻毒素动态影响的水域生态模型，探索藻毒素对产毒藻类与鱼类生长共存模式的影响机制。数学理论工作主要调查了模型平衡点的存在性、稳定性和Hopf分岔动力学行为，推导出模型诱发Hopf分岔的临界条件。数值模拟工作既验证了理论推导结果的有效性，又阐明模型分岔动力学行为的演化特性，并揭示了过高或过低的藻毒素接触率参数将会导致产毒藻类种群和鱼类种群从常稳态持久生存模式变为周期振荡共存模式。总而言之，希望这些研究结果既有利于促进藻鱼生态系统研究的快速发展，又可为生物操纵控藻技术的应用提供一定的理论基础。
Abstract: Considering that algal toxins in water were variable, an aquatic ecological model with dynamic effects of algal toxins was constructed, which could explore the impact mechanism of algal toxins on the growth coexistence mode of toxin producing algae and fish. The mathematical theory work mainly investigated the existence, stability, and Hopf bifurcation dynamic behavior of model equilibrium points, and derived the critical conditions for the model to induce Hopf bifurcation. The numerical simulation work not only verified the effectiveness of the theoretical derivation results, but also elucidated the evolutionary characteristics of the bifurcation dynamics behavior of the model, and revealed that excessively high or low algal toxin exposure rates would cause the toxic algal population and fish population to shift from a stable coexistence mode to a cyclic oscillation mode. In conclusion, it was hoped that these research results would not only promote the rapid development of algae fish ecosystem research, but also provide a theoretical basis for the application of biological manipulation algae control technology.
文章引用：傅云天. 一类具有藻毒素动态影响的水域生态模型的动力学问题研究[J]. 应用数学进展, 2024, 13(5): 2000-2019. https://doi.org/10.12677/aam.2024.135188

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