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
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。
Abstract: 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.
文章引用：张琰, 张蒙. 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[J]. 应用数学进展, 2022, 11(8): 6044-6054. https://doi.org/10.12677/AAM.2022.118636

参考文献

[1] 陈兰荪. 害虫治理与半连续动力系统几何理论[J]. 北华大学学报(自然科学版), 2011, 12(1): 1-9.
[2] Liu, B., Tian, Y. and Kang, B. (2012) Dynamics on a Holling II Predator-Prey Model with State-Dependent Impulsive Control. International Journal of Biomathematics, 5, Article ID: 1260006. [Google Scholar] [CrossRef] 
[3] 黄立壮, 刘琼, 陈武大仁, 等. 一类具有状态脉冲反馈控制的害虫治理模型[J]. 广西大学学报(自然科学版), 2020, 45(4): 911-919.
[4] Das, T., Mukherjee, R.N. and Chaudhuri, K.S. (2009) Harvesting of a Prey-Predator Fishery in the Presence of Toxicity. Applied Mathematical Model-ling, 33, 2282-2292. [Google Scholar] [CrossRef] 
[5] Truscott, J.E. and Brindley, J. (1994) Ocean Plankton Populations as Excitable Media. Bulletin of Mathematical Biology, 56, 981-998.
[6] Bhatia, S.K., Chauhan, S. and Agarwal, A. (2017) A Stage-Structured Prey-Predator Fishery Model in the Presence of Toxicity with Taxation as a Control Parameter of Harvesting Effort. Journal of Nonlinear Analysis and Application, 2017, 83-104.
[7] 蓝桂杰, 陈哲文, 魏春金, 等. 污染环境下毒素脉冲输入和心理效应对随机捕食-食饵系统的影响[J]. 系统科学与数学, 2019, 39(12): 2070-2092.
[8] 张茜, 刘兵, 石丽云. 在脉冲污染环境中具有阶段结构的捕食食饵Gompertz模型的动力学性质[J]. 生物数学学报, 2010(2): 9.
[9] 何伟莲. 具有反馈控制和有毒物质的竞争系统的持久性和全局吸引性[J]. 商丘师范学院学报, 2007, 23(12): 31-39.
[10] Wang, F., Meng, X.-Z. and Cheng, H.-D. (2010) Dy-namical Analysis of a Chemostat-Type Competition Model with Pulsed Input in a Polluted Environment. Mathematica Applicata, 23, 204-212.
[11] 陈兰荪, 程惠东. 害虫综合防治建模驱动“半连续动力系统理论”兴起[J]. 数学建模及其应用, 2021, 10(1): 1-16. [Google Scholar] [CrossRef] 

为你推荐