有限资源下杀虫剂具有残留作用的害虫综合控制的数学模拟研究
Mathematical Simulations of Integrated Pest Control with Pesticide Residues under Limited Resources
摘要: 本文考虑到杀虫剂的残留作用、喷洒前后对种群的作用方式的改变以及天敌资源的有限性,首先建立并系统地研究了资源有限下杀虫剂具有残留作用的固定时刻的害虫控制切换系统,分析关键参数对害虫灭绝阈值的影响;其次建立资源有限下依赖于害虫种群数量的状态害虫控制切换系统,通过数值模拟分析在规定的时间内影响杀虫剂的使用频率的因素。
Abstract: Considering the residual effect of pesticides, the change of the mode of action of the population be-fore and after spraying pesticides and the limitation of natural enemy resources, firstly, a fixed-time pest control switching system with residual effect of pesticides under limited resources is estab-lished and systematically studied, and the influence of key parameters on the pest eradication threshold is analyzed. Secondly, a state pest control switching system that is dependent on the amount of pest populations under limited resources is established, and the factors that affect the frequency of pesticide use in the specified time are analyzed by numerical simulations.
文章引用:唐玲碧, 刘晓虎, 刘兵, 李金洋. 有限资源下杀虫剂具有残留作用的害虫综合控制的数学模拟研究[J]. 应用数学进展, 2022, 11(7): 4509-4518. https://doi.org/10.12677/AAM.2022.117477

参考文献

[1] Gao, S.J., Luo, L., Yan, S.X. and Meng, X.Z. (2018) Dynamical Behavior of a Novel Impulsive Switching Model for HLB with Seasonal Fluctuations. Complexity, 2018, Article ID: 2953623. [Google Scholar] [CrossRef
[2] Liu, B., Ying, Z. and Chen, L.S. (2004) The Dynamics of a Preda-tor-Prey Model with Ivlev’s Functional Response Concerning Integrated Pest Management. Acta Mathematicae Applica-tae Sinica, 20, 133-146. [Google Scholar] [CrossRef
[3] Gao, S.J., Guo, J., Xu, Y., Tu, Y.B. and Zhu, H.P. (2021) Mod-eling and Dynamics of Physiological and Behavioral Resistance of Asian Citrus Psyllid. Mathematical Bioscience, 340, Article ID: 108674. [Google Scholar] [CrossRef] [PubMed]
[4] Lan, G.J., Fu, Y.J., Wei, C.J. and Zhang, S.W. (2018) A Research of Pest Management SI Stochastic Model Concerning Spraying Pesticide and Releasing Natural Enemies. Communica-tions in Mathematical Biology and Neuroscience, 2018, 3648. http://scik.org/index.php/cmbn/article/view/3648
[5] Liang, J.H., Tang, S.Y. and Cheke, R.A. (2016) Beverton-Holt Discrete Pest Management Models with Pulsed Chemical Control and Evolution of Pesticide Resistance. Communica-tions in Nonlinear Science and Numerical Simulation, 36, 327-341. [Google Scholar] [CrossRef
[6] Tian, Y., Tang, S.Y. and Cheke, R.A. (2019) Dynamic Complex-ity of a Predator-Prey Model for IPM with Nonlinear Impulsive Control Incorporating a Regulatory Factor for Predator Releases. Mathematical Modelling and Analysis, 24, 134-154. [Google Scholar] [CrossRef
[7] Tang, S.Y., Tang, B., Wang, A.L. and Xiao, Y.N. (2015) Holling II Predator-Prey Impulsive Semi-Dynamic Model with Com-plex Poincaré Map. Nonlinear Dynamics, 81, 1575-1596. [Google Scholar] [CrossRef
[8] Zhang, Q.Q., Tang, B., Cheng, T.Y. and Tang, S.Y. (2020) Bifurcation Analysis of a Generalized Impulsive Kolmogorov Model with Applications to Pest and Disease Control. SIAM Journal on Applied Mathematics, 80, 1796-1819. [Google Scholar] [CrossRef
[9] Tang, S.Y., Li, C.T., Tang, B. and Wang, X. (2019) Global Dynamics of a Nonlinear State-Dependent Feedback Control Ecological Model with a Multiple-Hump Discrete Map. Communica-tions in Nonlinear Science and Numerical Simulation, 79, Article ID: 104900. [Google Scholar] [CrossRef
[10] Tang, S.Y., Liang, J.H., Tan, Y.S. and Cheke, R.A. (2013) Threshold Conditions for Integrated Pest Management Models with Pesticides That Have Residual Effects. Journal of Mathematical Biology, 66, 1-35. [Google Scholar] [CrossRef] [PubMed]
[11] Kang, B.L., Liu, B. and Tao, F.M. (2018) An Integrated Pest Management Model with Dose Response Effect of Pesticides. Journal of Biological System, 26, 59-86. [Google Scholar] [CrossRef
[12] Liu, B., Tao, F.M., Kang, B.L. and Hu, G. (2021) Modelling the Effects of Pest Control with Development of Pesticide Resistance. Acta Mathematicae Applicatae Sinica, English Se-ries, 37, 109-125. [Google Scholar] [CrossRef
[13] Li, C.T. and Tang, S.Y. (2018) Analyzing a Generalized Pest-Natural Enemy Model with Nonlinear Impulsive Control. Open Mathematics, 16, 1390-1411. [Google Scholar] [CrossRef