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红松鼠种群保护状态反馈脉冲控制第二类模型研究
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Abstract:
英国本土红松鼠因外来灰松鼠的入侵而面临灭绝危机，为了保护红松鼠的生存量，英国政府提出既保护了英国本土红松鼠达到人们所希望的数量而灰松鼠也能保留人们所希望的种群规模，针对目前的情况，文章根据疱疹病毒对两种松鼠影响程度的差异，建立非Lota-Volterra竞争模型，详细分析了无脉冲时的正平衡点的情况，建立带有状态反馈的脉冲模型。利用后继函数法和微分方程的有关理论，研究了系统阶一周期解的存在性和稳定性。所得结论为红松鼠的保护工作提供了一定的理论依据。
Native red squirrels in the UK are facing the danger of extinction due to the invasion of alien grey squirrels. In order to protect the stock of red squirrels, the British government proposed that the number of native red squirrels in the UK could be protected to the desired number while the population size of grey squirrels could be retained. In view of the present situation, according to the difference of herpes virus influence degree on two squirrels, the non-Lota-Volterra competition model is established, and the positive equilibrium point is analyzed in detail under the condition of no pulse, and the pulse model with state feedback is established. The existence and stability of first-order periodic solutions of the system are studied by using the method of successive functions and the theory of differential equations. The conclusions provided a theoretical basis for the conservation of red squirrels.
| [1] | 陈兰荪. 数学生态学模型与研究方法(第二版), 生物数学丛书, 第19卷[M]. 北京: 科学出版社, 2017. |
| [2] | 马知恩, 周义仓, 李承治. 常微分方程定性与稳定性方法[M]. 第2版. 北京: 科学出版社, 2015. |
| [3] | Liu, Q., Zhang, M. and Chen, L.S. (2019) State Feedback Impulsive Therapy to SIS Model of Animal Infectious Disease. Physica A, 516, 222-232. https://doi.org/10.1016/j.physa.2018.09.161 |
| [4] | Laksbmikantham, V., Bainov, D. and Simeonov, P. (1989) Theory of Impulsive Differential Equations. World Scientific, Singapore. https://doi.org/10.1142/0906 |
| [5] | Wang, L.M., Liu, Z.J., et al. (2007) Impulsive Diffusion in Single Species Model. Chaos, Solitons & Fractals, 33, 1213-1219. https://doi.org/10.1016/j.chaos.2006.01.102 |
| [6] | Liu, K.Y. and Chen, L.S. (2007) Harvesting Control for a Stage-Structured Predator-Prey Model with Ivlev’s Functional Response and Impulsive Stocking on Prey. Discrete Dynamics in Nature and Society, 2007, Article ID: 086482. |
| [7] | 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. |
| [8] | 陈兰荪. “半连续动力系统”理论及应用[J]. 玉林师范学院学报, 2013, 34(2): 2-10. |
| [9] | Wang, T.Y. and Chen, L.S. (2011) Nonlinear Analysis of a Microbial Pesticide Model with Impulsive State Feedback Control. Nonlinear Dynamics, 65, 1-10. https://doi.org/10.1007/s11071-010-9828-x |
| [10] | 陈兰荪. 半连续动力系统理论及应用[J]. 玉林师范学院学报, 2013, 34(2): 1-9. |
| [11] | 桂占吉, 王凯华, 陈兰荪. 病虫害防治的数学理论与计算[M]. 北京: 科学出版社, 2014. |
| [12] | 叶彦谦, 等. 极限环论[M]. 上海: 上海科学技术出版社, 1984. |
| [13] | Zhang, M., Chen, L.S. and Li, Z.Y. (2019) Homoclinic Bifurcation of a State Feedback Impulsive Controlled Prey-Predator System with Holling-II Functional Response. Nonlinear Dynamics, 98, 929-942.
https://doi.org/10.1007/s11071-019-05235-8 |
| [14] | Fu, J.-B. and Chen, L.-S. (2018) Modelling and Qualitative Analysis of Water Hyacinth Ecological System with Two State-Dependent Impulse Controls. Complexity, 2018, Article ID: 4543976. https://doi.org/10.1155/2018/4543976 |
| [15] | Liu, Q., Zhang, M. and Chen, L.S. (2019) State Feedback Impulsive Therapy to SIS Model of Animal Infectious Diseases. Physica A: Statistical Mechanics and its Applications, 516, 222-232.
https://doi.org/10.1016/j.physa.2018.09.161 |
| [16] | Zhang, M., Liu, K.Y., Chen, L.S. and Li, Z.Y. (2018) State Feedback Impulsive Control of Computer Worm and Virus with Saturated Incidence. Mathematical Biosciences & Engineering, 15, 1465-1478.
https://doi.org/10.3934/mbe.2018067 |
| [17] | Chen, L.S., Liang, X.Y. and Pei, Y.Z. (2018) The Periodic Solution of the Impulsive State Feedback Dynamical System. Communication in Mathematical Biology and Neuroscience, 2018, Article No. 14. |
