毒素影响下捕食种群具有常数投放率的捕食–食饵模型的动力学研究  

Dynamical Research of a Predator-Prey Model of Predator Population with Constant Release Rate under Toxin Influence

作　　者：张琰 张蒙 

机构地区：[1]北京建筑大学理学院,北京

出　　处：《应用数学进展》2022年第8期6044-6054,共11页Advances in Applied Mathematics

摘　　要：基于水环境污染日益严重,本文建立了一类毒素影响下鱼类具有常数投放的捕食–食饵模型,研究了系统平衡点的存在性与稳定性,利用后继函数法证明了系统阶一周期解存在性,其次利用类Poincaré准则,得到了阶一周期解稳定的条件,最后通过数值模拟验证结论的重要性。In this paper, a predator-prey model of fish with constant release under the influence of toxins is established based on the increasing pollution of water environment. The existence and stability of the equilibrium point of the system are studied, and the existence of the order-1 periodic solution is proved by using the method of successor function. Secondly, the condition of the stability of the or-der-1 periodic solution is obtained by using the analogue of Poincaré’s criterion. Finally, the im-portance of the conclusion is verified by numerical simulation.

关 键 词：毒素 常数投放 阶一周期解 类Poincaré准则 数值模拟 

分 类 号：X52[环境科学与工程—环境工程]