WU Luoyi,ZHENG Hang.Periodic solution of delayed predator - prey model with stage – structured[J].Journal of Yanbian University,2020,46(04):289-294,325.
一类具有阶段结构的时滞捕食系统的正周期解
- Title:
- Periodic solution of delayed predator - prey model with stage – structured
- 文章编号:
- 1004-4353(2020)04-0289-07
- 分类号:
- O175
- 文献标志码:
- A
- 摘要:
- 以捕食者有附加食物、食饵有阶段结构和避难所的时滞捕食系统为研究对象,利用迭合度理论得到了该系统存在正周期解的充分条件,并利用数值模拟验证了所得条件的正确性.
- Abstract:
- A delayed predator -prey model with additional food for predator,stage -structured and refuge for prey is studied. We employ the coincidence degree theory to obtain the sufficient conditions of the positive periodic solution. In the end, the numerical simulation is given to show the validity of the obtained conditions.
参考文献/References:
[1] LOTKA A. Analytical note on certain rhythmic relations in organic systems[J]. Proc Natl Acad Sci USA,1920(6):410-415.
[2] VOLTERRA V. Variazionie fluttuazioni del numero dindividui in specie animal conviventi[J]. Mem R Accad Naz Lincei, 1926,6(2):31-113.
[3] HSU S B, HWANG T W. Global analysis of the Michaelis -Menten type ratio -dependent predator -prey system[J]. Math Biol, 2001,42:489-506.
[4] LIAO X, OU YANG Z, XHOU S. Permanence of species in non -autonomous discrete Lotka -Volterra competitive system with delays and feedback control[J]. Appl Math, 2008,211:1-10.
[5] 范猛,王克.一类具有Holling H型功能性反应的捕食者-食饵系统全局周期解的存在性[J].数学物理学报,2001,21A(4):492-497.
[6] FAN M, WANG Q, ZOU X, et al. Dynamics of a non -autonomous ratio -dependent predator -prey system[J]. Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2003,133(1):97-118.
[7] 傅金波.一类具有相互干扰的食饵-捕食者系统的定性分析[J].系统科学与数学,2017,37(4):1166-1178.
[8] XIA Y H, CAO J, CHENG S S. Multiple periodic solutious of prelayed stage -tructured predator -prey model with non -monotone functional responses[J]. Comput Apple Math, 2014,258:87-98.
[9] 杨英钟.具有阶段结构和反馈控制的非自治单种群系统的正周期解[J].沈阳大学学报(自然科学版),2018,30(6):511-515.
[10] 陈凤德,陈晓星,张惠英.捕食者具有阶段结构Holling Ⅱ类功能性反应的捕食系统正周期解的存在性以及全局吸引性[J].数学物理学报,2006(1):93-103.
[11] WEI F, FU Q. Hopf bifurcation and stability for predator -prey systems with Beddington -DeAngelis type functional response and stage structure for prey incorporating refuge[J]. Appl Math Model, 2016,40:126-134.
[12] SRINIVASU P, PRASAD B, VENKATESULU M. Biological control through provision of additional food to predators: a theoretical study[J]. Theor Popul Biol, 2007,72:111-120.
[13] BAI Y Z, LI Y Y. Stability and Hopf bifurcation for a stage -structured predator -prey model incorporating refuge for prey and additional food for predator[J]. Advances in Difference Equations, 2019,42:1-20.
[14] GAINES R E, MAWHIN T L. Coincidence Degree and Nonlinear Differential Equations[M]. Berlin:Springer -Verlag, 1977.
相似文献/References:
[1]吴罗义.一类具有附加食物的Leslic - Gower捕食者-食饵模型的定性分析[J].延边大学学报(自然科学版),2022,(02):118.
WU Luoyi.Qualitative analysis of a Leslic - Gower type predator - prey model with additional food[J].Journal of Yanbian University,2022,(04):118.
备注/Memo
收稿日期: 2020-10-03 作者简介: 吴罗义(1978—),男,讲师,研究方向为生物数学.
基金项目: 福建省中青年教师教育科研项目(JT180558); 武夷学院校科研资金资助项目(XL201509)