A kind of non-traditional biomanipulation model with constant releasing fish
A kind of non-traditional biomanipulation model with constant releasing fish
复制标题
一种非传统的恒放鱼生物操控模型
DOI：
10.1002/mma.4340
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发表时间：
2017
影响因子：
2.9
通讯作者：
Song Xinyu
中科院分区：
文献类型：
--
作者：
Guo Hongjian;Chen Lansun;Song Xinyu
基于淡水水体非传统生物调控的思想，提出了一种营养-藻类鱼类模型，用于研究鱼类持续释放对营养物质和藻类的影响。通过讨论边界平衡的稳定性，得到了藻类灭绝的阈值条件。通过讨论正平衡点的存在性和稳定性，得到了藻鱼共存的条件。此外，还考虑了放鱼量的参数，对系统的Hopf分叉进行了分析。在此基础上，提出了一类优化问题，并利用庞特里亚金极大值原理给出了最优解存在的必要条件。最后，通过数值仿真对数学结果进行了验证。数学结果表明，放流鱼存在一个临界量，超过这个临界量，放流鱼的活动可以控制藻类的生长，进一步降低水华发生的概率，但不能降低水体的富营养化水平。版权所有©2017 John Wiley&Sons，Ltd.
On the basis of the ideas of non‐traditional biomanipulation control in fresh water body, a kind of nutrient–algae fish model is presented to investigate the effects of constant releasing fish on the nutrient and the algae. The threshold conditions for the extinction of the algae are obtained by discussing the stability of boundary equilibrium. The conditions for the coexistence of the algae and the fish are obtained by discussing the existence and stability of positive equilibrium. Besides, Hopf bifurcation is also analyzed by considering the parameter about the amount of the released fish. Furthermore, a kind of optimal problem is presented, and the necessary condition for the existence of the optimal solution is given by Pontryagin maximum principle. Finally, the mathematical results are verified by numerical simulations. The mathematical results show that there is a threshold amount of the released fish, above which the activity of releasing fish can control the growth of the algae and further reduce the probability of the algae bloom, but can not decrease the eutrophication level of the water body. Copyright © 2017 John Wiley & Sons, Ltd.