红松鼠种群保护状态反馈脉冲控制第二类模型研究
Study on the Second Model of State Feedback Impulsive Model of Red Squirrel Protection
摘要: 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。
Abstract: 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.
文章引用：王烁烁. 红松鼠种群保护状态反馈脉冲控制第二类模型研究[J]. 应用数学进展, 2021, 10(11): 3640-3649. https://doi.org/10.12677/AAM.2021.1011385

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