《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (1): 42-49.doi: 10.6040/j.issn.1671-9352.0.2021.344
• • 上一篇
沈维*,张存华
SHEN Wei*, ZHANG Cun-hua
摘要: 考虑了具有Holling-Ⅲ型功能反应的时滞食饵-捕食模型。通过分析相应特征方程的根在复平面上的分布, 研究了模型正平衡点的稳定性与Hopf分支,最后利用MATLAB软件包对相应的理论结果进行了数值验证。
中图分类号:
[1] BAIRAGI N, JANA D. On the stability and Hopf bifurcation of a delay-induced predator-prey system with habitat complexity[J]. Applied Mathematical Modelling, 2011, 35:3255-3267. [2] 王婷婷, 唐浩彭, 马智慧. 具有生境复杂性效应的时滞捕食-食饵系统[J]. 兰州大学学报(自然科学版), 2018, 54(5):682-690. WANG Tingting, TANG Haopeng, MA Zhihui. Research on a delay-induced predator-prey system with Holling Ⅲ functional response and habitat complexity[J]. Journal of Lanzhou University( Natural Sciences), 2018, 54(5):682-690. [3] YAN Xiangping, SHI Junping. Stability switches in a logistic population model with mixed instantaneous and delayed density dependence[J]. Journal of Dynamics and Differential Equations, 2017, 29:113-130. [4] LI Xiaona. The toxic producing Phytoplankton-Zooplankton interaction with Holling III functional response[J]. Advances in Applied Mathematics, 2019, 8(10):1655-1658. [5] MUKHERIEE D, MAJI C D. Bifurcation analysis of a Holling type II predator-prey model with refuge[J]. Chinese Journal of Physics, 2020, 65:153-162. [6] WANG Shufan, TANG Haopeng, MA Zhihui. Hopf bifurcation of a multiple-delayed predator-prey system with habitat complexity[J]. Mathematics and Computers in Simulation, 2021, 180:1-23. [7] YUAN Rui, JIANG Weihua, WANG Yong. Saddle-node- Hopf bifurcation in a modified Leslie-Gower predator-prey model with time-delay and prey harvesting[J]. Journal of Mathematical Analysis and Applications, 2015, 422:1072-1090. [8] SONG Yongli, HAN Maoan, WEI Junjie. Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays[J]. Physica Dynamics, 2005, 200:185-204. [9] YAN Xiangping, LIU Fangbin, ZHANG Cunhua. Multiple stability switches and Hopf bifurcation in a damped harmonic oscillator with delayed feedback[J]. Nonlinear Dynamics, 2020, 99(3):2011-2030. [10] LI Kai, WEI Junjie. Stability and Hopf bifurcation analysis of a prey-predator system with two delays[J]. Chaos, Solitons and Fractals, 2009, 42:2606-2613. [11] MENG Xinyou, HUO Haifeng, ZHANG Xiaobing. Stability and global Hopf bifurcation in a delayed food web consisting of prey and two predators[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16:4335-4348. |
[1] | 魏立祥,张建刚,南梦冉,张美娇. 具有时滞的磁通神经元模型的稳定性及Hopf分岔[J]. 《山东大学学报(理学版)》, 2021, 56(5): 12-22. |
[2] | 马维凤,陈鹏玉. 状态依赖型时滞微分方程的解流形及其C1-光滑性[J]. 《山东大学学报(理学版)》, 2021, 56(2): 92-96. |
[3] | 马德青,胡劲松. 消费者参考质量存在时滞效应的动态质量改进策略[J]. 《山东大学学报(理学版)》, 2020, 55(9): 101-89. |
[4] | 王静,伏升茂. 带防御机制的捕食者-食饵模型中恐惧因子的作用[J]. 《山东大学学报(理学版)》, 2020, 55(3): 121-126. |
[5] | 章欢,李永祥. 含时滞导数项的高阶常微分方程的正周期解[J]. 《山东大学学报(理学版)》, 2019, 54(4): 29-36. |
[6] | 罗强,韩晓玲,杨忠贵. 三阶时滞微分方程边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2019, 54(10): 33-39. |
[7] | 李乐乐,贾建文. 具有时滞影响的SIRC传染病模型的Hopf分支分析[J]. 《山东大学学报(理学版)》, 2019, 54(1): 116-126. |
[8] | 陈雨佳, 杨和. 一类三阶时滞微分方程在Banach空间中的周期解的存在性[J]. 山东大学学报(理学版), 2018, 53(8): 84-94. |
[9] | 董兴林,齐欣. 基于时滞效应的青岛市两阶段科技投入与产出互动关系[J]. 山东大学学报(理学版), 2018, 53(5): 80-87. |
[10] | 陈丽,林玲. 具有时滞效应的股票期权定价[J]. 山东大学学报(理学版), 2018, 53(4): 36-41. |
[11] | 张道祥,孙光讯,马媛,陈金琼,周文. 带有Holling-III功能反应和线性收获效应的时滞扩散捕食者-食饵系统Hopf分支和空间斑图[J]. 山东大学学报(理学版), 2018, 53(4): 85-94. |
[12] | 高荣,张焕水. 离散时间多输入时滞随机系统的镇定性[J]. 山东大学学报(理学版), 2017, 52(4): 105-110. |
[13] | 鞠培军,王伟. 多输入多输出线性系统的时滞界问题[J]. 山东大学学报(理学版), 2017, 52(11): 60-64. |
[14] | 王双明. 一类具有时滞的周期流行病模型的动力学分析[J]. 山东大学学报(理学版), 2017, 52(1): 81-87. |
[15] | 王亚军,张申,胡青松,刘峰,张玉婷. 具有测量噪声的时滞多智能体系统的一致性问题[J]. 山东大学学报(理学版), 2017, 52(1): 74-80. |
|