具有θ-Logistic增长的捕食种群模型的动力学研究OA
Dynamics of a Predator-Prey Population Model withθ-Logistic Growth
本文考虑一类具有Holling-Ⅱ功能反应和θ-Logistic增长的捕食者-食饵模型,首先,证明了解的正性以及一致有界性;其次,分析了模型平衡点的存在性及稳定性条件,证明了在边界平衡点存在跨临界分支,并且以θ为参数,得到正平衡点处存在Hopf分支的条件;最后,讨论了θ对种群密度的影响.数值模拟验证了理论结果的正确性.
In this paper,we consider a class of predator-prey model with Holling-Ⅱ functional response and θ-Logistic growth.Firstly,the positivity and uniform boundedness of solutions are proved.Secondly,the existence and stability conditions of the equilibrium point are analyzed.It is shown that a transcritical bifurcation occurs at the boundary equilibrium.The conditions of the existence of Hopf bifurcation at the positive equilibrium are obtained with θ as the bifurcation parameter.Finally,the influence of θ on population density is discussed.Numerical simulation further verify the feasibility of our conclusions.
游雪娇;买阿丽
山西师范大学数学科学学院,山西太原 030031运城学院数学与信息技术学院,山西运城 044000
数理科学
θ-Logistic捕食者-食饵模型Holling-Ⅱ功能反应稳定性Hopf分支
θ-LogisticPredator-prey modelHolling-Ⅱ functional responseStabilityHopf bifur-cation
《应用数学》 2026 (3)
743-749,7
国家自然科学基金(1210154712071418)运城学院大学生创新训练计划项目(DC2025077)
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