具恐惧效应与趋避敏感性随机捕食模型动力学
Dynamics of Stochastic Predator-Prey Model with Fear Effect and Predator-Taxis Sensitivity
摘要: 恐惧效应是捕食过程中的一种普遍反应，由食饵对捕食者的恐惧而产生的一系列自我保护行为。首先，通过构造一个合适的随机李雅普诺夫函数，给出了模型正解存在唯一平稳分布的充分条件；然后，通过对模型使用Itô’s公式，得到了模型中捕食者种群在两种情况下分别灭绝的充分条件。
Abstract: Fear effect is a common response in the process of predation, and the prey produces a series of self-protection behaviors because of its fear of predators. Firstly, a sufficient condition for the ex-istence and uniqueness of the ergodic stationary distribution of the positive solution of the model was given by a suitable stochastic Lyapunov function. Then, by using Itô’s formula to the model, the sufficient conditions for the extinction of predator population in the model were obtained in two cases.
文章引用：王欣琦, 张天四. 具恐惧效应与趋避敏感性随机捕食模型动力学[J]. 理论数学, 2022, 12(9): 1399-1410. https://doi.org/10.12677/PM.2022.129153

参考文献

[1] Lotka, A.J. (1925) Elements of Physical Biology. Williams and Wilkins, Baltimore.
[2] Volterra, V. (1926) Variazioni e Fluttuazioni Del Numero d’individui in Specie Animali Conviventi. Memoria della Reale Accademia Nazionale dei Lincei, 2, 31-113.
[3] Jana, A. and Roy, S.K. (2021) Behavioural Analysis of Two Prey-Two Predator Mode. Ecological Complexity, 47, Article ID: 100942. [Google Scholar] [CrossRef] 
[4] Qi, H.K., Meng, X.Z., Hayat, T. and Hobiny, A. (2022) Stationary Distribution of a Stochastic Predator-Prey Model with Hunting Cooperation. Applied Mathematics Letters, 124, Article ID: 107662. [Google Scholar] [CrossRef] 
[5] Liu, Q. and Jiang, D.Q. (2021) Influence of the Fear Factor on the Dynamics of a Stochastic Predator-Prey Model. Applied Mathematics Letters, 112, Article ID: 106756. [Google Scholar] [CrossRef] 
[6] Wang, Z.J., Deng, M.L. and Liu, M. (2021) Stationary Distribution of a Stochastic Ratio-Dependent Predator-Prey System with Regime-Switching. Chaos, Solitons and Fractals, 142, Article ID: 110462. [Google Scholar] [CrossRef] 
[7] Lu, W.J., Xia, Y.H. and Bai, Y.Z. (2020) Periodic Solution of a Stage-Structured Predator-Prey Model Incorporating Prey Refuge. Mathematical Biosciences and Engineering, 17, 3160-3174. [Google Scholar] [CrossRef] [PubMed]
[8] Bhatia, S.K., Sudipa, C.H., Agaewal, A. and Jain, R. (2020) Effect of Stage Structure in Predator-Prey Model with Crowley-Martin Functional Response. International Journal of Applied Mathematics and Statistics, 59, 79-92.
[9] Liu, Q., Jiang, D.Q. and Hayat, T. (2021) Dynamics of Stochastic Predator-Prey Models with Distributed Delay and Stage Structure for Prey. International Journal of Biomathematics, 14, Article ID: 2150020. [Google Scholar] [CrossRef] 
[10] Preisser, E.L. and Bolnick, D.I. (2008) The Many Faces of Fear: Comparing the Pathways and Impacts of Nonconsumptive Predator Effects on Prey Populations. PLOS ONE, 3, Article No. e2465. [Google Scholar] [CrossRef] [PubMed]
[11] Wang, X.Y., Zanette, L. and Zou, X.F. (2016) Modelling the Fear Effect in Predator-Prey Interactions. Journal of Mathematical Biology, 73, 1179-1204. [Google Scholar] [CrossRef] [PubMed]
[12] Dong, Y.X., Wu, D.Y., Shen, C.S. and Ye, L.H. (2022) Influence of Fear Effect and Predator-Taxis Sensitivity on Dynamical Behavior of a Predator-Prey Model. Zeitschrift Für Angewandte Mathematik und Physik, 73, Article No. 25. [Google Scholar] [CrossRef] 
[13] Alabacy, Z.K. and Majeed, A.A. (2021) The Fear Effect on a Food Chain Prey-Predator Model Incorporating a Prey Refuge and Harvesting. Journal of Physics: Conference Series, 1804, Article ID: 012077. [Google Scholar] [CrossRef] 
[14] Xie, B.F. and Zhang, N. (2022) Influence of Fear Effect on a Holling Type III Prey-Predator System with the Prey Refuge. AIMS Mathematics, 7, 1811-1830. [Google Scholar] [CrossRef] 
[15] Yousef, A., Thirthar, A.A., Alaoui, A.L., Panja, P. and Abdeljawad, T. (2022) The Hunting Cooperation of a Predator under Two Prey’s Competition and Fear-Effect in the Prey-Predator Fractional-Order Model. AIMS Mathematics, 7, 5463-5479. [Google Scholar] [CrossRef] 
[16] Souna, F., Djilali, S. and Lakmeche, A. (2021) Spatiotemporal Behavior in a Predator-Prey Model with Herd Behavior and Cross-Diffusion and Fear Effect. The European Physical Journal Plus, 134, Article No. 474. [Google Scholar] [CrossRef] 
[17] Liu, Q., Jiang, D.Q., Hayat, T. and Alsaedi, A. (2018) Sta-tionary Distribution and Extinction of a Stochastic Predator-Prey Model with Herd Behavior. Journal of the Franklin Institute, 355, 8177-8193. [Google Scholar] [CrossRef] 
[18] Zhao, X. and Zeng, Z.J. (2020) Stationary Distribution of a Stochastic Predator-Prey System with Stage Structure for Prey. Physica A: Statistical Mechanics and Its Applications, 545, Article ID: 123318. [Google Scholar] [CrossRef] 
[19] Liu, Q., Jiang, D.Q., Hayat, T., Alsaedi, A. and Ahmad, B. (2020) Dynamical Behavior of a Stochastic Predator-Prey Model with Stage Structure for Prey. Stochastic Analysis and Applications, 38, 647-667. [Google Scholar] [CrossRef] 
[20] Liu, Q. and Jiang, D.Q. (2019) Stationary Distribution and Extinction of a Stochastic One Prey Two Predator Model with Holling Type II Functional Response. Stochastic Analysis and Applications, 37, 321-345. [Google Scholar] [CrossRef] 
[21] Xu, D.S., Liu, M. and Xu, X.F. (2020) Analysis of a Sto-chastic Predator-Prey System with Modified Leslie-Gower and Holling-Type IV Schemes. Physica A: Statistical Me-chanics and Its Applications, 537, Article ID: 122761. [Google Scholar] [CrossRef] 
[22] Zhao, X. and Zeng, Z.J. (2020) Stationary Distribution and Ex-tinction of a Stochastic Ratio-Dependent Predator-Prey System with Stage Structure for the Predator. Physica A: Sta-tistical Mechanics and Its Applications, 545, Article ID: 123310. [Google Scholar] [CrossRef] 
[23] Ji, C.Y., Jiang, D.Q. and Shi, N.Z. (2009) Analysis of a Preda-tor-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes with Stochastic Perturbation. Journal of Mathematical Analysis and Applications, 359, 482-498. [Google Scholar] [CrossRef] 
[24] Dalal, N., Gerrnhalgh, D. and Mao, X.R. (2008) A Stochastic Model for Internal HIV Dynamics. Journal of Mathematical Analysis and Applications, 341, 1084-1101. [Google Scholar] [CrossRef] 
[25] Mao, X. (1997) Stochastic Differential Equations and Applications. Horwood Publishing, Chichester.
[26] Khasminskii, R. (1980) Stochastic Stability of Differential Equations. Sijthoff and Noordhoff, Alphen aan den Rijn.
[27] Ji, C.Y. and Jiang, D.Q. (2014) Threshold Behaviour of a Stochastic SIR Model. Applied Mathematical Modelling, 38, 5067-5079. [Google Scholar] [CrossRef] 

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