WANG Xihao,WEI Yuming.Dynamic analysis of a delayed predator - prey model with fear effect and generalized Holling type Ⅲ functional response[J].Journal of Yanbian University,2023,(04):288-297.
一类具有恐惧效应的时滞广义Holling Ⅲ型捕食者- 食饵模型的动力学分析
- Title:
- Dynamic analysis of a delayed predator - prey model with fear effect and generalized Holling type Ⅲ functional response
- 文章编号:
- 1004-4353(2023)04-0288-10
- Keywords:
- generalized Holling type Ⅲ predator - prey model; fear effect; equilibrium point; delay; persistence; extinction
- 分类号:
- O175
- 文献标志码:
- A
- 摘要:
- 研究了一类具有恐惧效应的时滞广义Holling Ⅲ型捕食者- 食饵模型的动力学行为.首先,通过计算模型平衡点的Jacobian矩阵研究了平衡点的稳定性,并分析了时滞对正平衡点的稳定性影响; 其次,在确定性模型中通过引入白噪声将系统转变为随机模型,并通过构造Lyapunov函数研究了随机模型正解的性质; 再次,在一些假设条件下,利用伊藤公式建立了模型在平均意义下的持续生存和灭绝的充分性条件; 最后,通过数值模拟验证了恐惧效应、时滞和随机因素对捕食者和食饵种群密度的影响.
- Abstract:
- The dynamical behavior of a generalized delayed Holling type Ⅲ predator - prey model with fear effects was investigated.Firstly, the stability of the equilibrium was studied by calculating the Jacobian matrix of the equilibria of the model, and the effect of delay on the stability of the positive equilibrium point was analyzed.Secondly, the system was transformed into a stochastic model by introducing white noise into the deterministic model, and the nature of the stochastic positive solution was studied by constructing the Lyapunov function.Thirdly, under some assumptions, the It? formula was used to establish the model sufficiency conditions for extinction and persistence in the mean.Finally, the effects of fear effects, delay and stochastic factors on predator and prey population densities were verified by numerical simulations.
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相似文献/References:
[1]刘英姿,李忠,何梦昕.具有恐惧效应和食饵避难所的Leslie - Gower捕食者-食饵模型的动力学分析[J].延边大学学报(自然科学版),2022,(02):112.
LIU Yingzi,LI Zhong,HE Mengxin.Dynamics analysis of a Leslie - Gower type predator - prey model with fear effect and prey refuge[J].Journal of Yanbian University,2022,(04):112.
[2]王逸勤,施春玲.具有常数避难所和恐惧效应的HollingⅡ类功能性反应捕食食饵系统的定性分析[J].延边大学学报(自然科学版),2023,(02):116.
WANG Yiqin,SHI Chunling.Qualitative analysis of a predator-prey system with Holling type Ⅱ functional response incorporating fear effct and a constant prey refuge[J].Journal of Yanbian University,2023,(04):116.
备注/Memo
收稿日期: 2023-05-21
基金项目: 国家自然科学基金(11961074)
第一作者: 王檄豪(1998—),男,硕士研究生,研究方向为生物数学.
通信作者: 韦煜明(1974—),男,博士,教授,研究方向为生物数学.