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具有状态反馈脉冲控制的叶螨–捕植螨系统的动力分析
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Abstract:
叶螨取食重要农业植物的叶和果实，是田间农作物的一大害虫，人们利用捕植螨对其进行控制。本文建立了Smith增长且具有Beddington-DeAngelis型功能反应的叶螨–捕植螨系统，并对该系统的有界性，极限环不存在以及平衡点的类型和其稳定性进行了分析。同时，基于这个模型又建立了具有脉冲控制的状态反馈脉冲模型，证明了其阶一周期解的存在性。
The spider mites feed on leaves and fruits of important agricultural plants and are a major pest to crops in the field. People use phytoseiidae mites to control them. In this paper, a Smith increased spider mite-phytoseiidae mites system with Beddington-Deangelis functional response is established. The boundedness, the existence of the limit cycle, the types of equilibrium points and their stability of the system are analyzed. At the same time, based on the model, a state feedback impulse model is established to prove the existence of its order-1 periodic solution.
| [1] | Hoyt, S.C. and Caltagirone, L.E. (1971) The Developing Programs of Integrated Control of Pests of Apples in Washington and Peaches in California. Springer, 1-11. |
| [2] | Hoy, M.A., Roush, R.T. and Smith, K.B. (1979) Spider Mites and Predators in San Joaquin Valley Almond Orchards. California Agriculture, 33, 11-13. |
| [3] | McMurtry, J.A. and van de Vrie, M. (1973) Predation Byamblyseius Potentillae (Garman) Onpanonychusulmi (Koch) in Simple Ecosystems (Acarina: Phytoseiidae, Tetranychidae). Hilgardia, 42, 17-33. |
| [4] | Rabbinge, R and Vrie, M.V.D. (1977) Application of the Process Simulation Technique in Biological Control of the Fruit Tree Red Spider Mite, Panonychus ulmi (Koch). |
| [5] | Beddington, J.R. (1975) Mutual Interference between Parasites or Predators and Its Effect on Searching Efficiency. The Journal of Animal Ecology, 44, 331-340. https://doi.org/10.2307/3866 |
| [6] | DeAngelis, D.L., Goldstein, R.A. and O’Neill, R.V. (1975) A Model for Tropic Interaction. Ecology, 56, 881-892. https://doi.org/10.2307/1936298 |
| [7] | Morozov, A. and Arashkevich, E. (2008) Patterns of Zooplankton Functional Response in Communities with Vertical Heterogeneity: A Model Study. Mathematical Modelling of Natural Phenomena, 3, 131-148. https://doi.org/10.1051/mmnp:2008061 |
| [8] | Zhang, H., Georgescu, P. and Chen, L. (2008) On the Impulsive Controllability and Bifurcation of a Predator-Pest Model of IPM. Biosystems, 93, 151-171. https://doi.org/10.1016/j.biosystems.2008.03.008 |
| [9] | Sivakumar, M., Sambath, M. and Balachandran, K. (2015) Stability and Hopf Bifurcation Analysis of a Diffusive Predator–prey Model with Smith Growth. International Journal of Biomathematics, 8, 1550013. https://doi.org/10.1142/s1793524515500138 |
| [10] | 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. |
| [11] | Meng, X., Song, Z. and Chen, L. (2007) A New Mathematical Model for Optimal Control Strategies of Integrated Pest Management. Journal of Biological Systems, 15, 219-234. https://doi.org/10.1142/s0218339007002143 |
| [12] | Jiao, J., Chen, L. and Luo, G. (2008) An Appropriate Pest Management SI Model with Biological and Chemical Control Concern. Applied Mathematics and Computation, 196, 285-293. https://doi.org/10.1016/j.amc.2007.05.072 |
