顾宏宇,魏新

• 1:黑龙江大学数学与统计学院

摘要(Abstract)：

研究了一类带有扩散和Allee效应的May-Holling-Tanner捕食者-食饵模型，其中捕食者既有食饵又有可替代食物来源。首先，对线性化系统进行分析得到Hopf分支存在的条件，后选取扩散系数为分支参数，得到了Turing-Hopf分支的存在性条件。然后，通过对Turing-Hopf分支三阶截断规范型的计算，将系统于该分支点邻域的时空动力学特征进行了深度的剖析。最后，利用数值模拟为理论研究提供支撑。

关键词(KeyWords)： Hopf分支;Turing-Hopf分支;扩散;捕食者-食饵模型

Abstract:

Keywords:

基金项目(Foundation): 黑龙江省自然科学基金资助项目(JQ2023A005,PL2025A013);; 黑龙江省省属本科高校优秀青年教师基础研究支持计划资助(YQJH2025196)

作者(Author): 顾宏宇,魏新

DOI: 10.13482/j.issn1001-7011.2026.04.214

参考文献(References)：

• [1] WANG C,PEI Y,NIU Y,et al.Complex dynamical behavior of Holling-Tanner predator-prey model with cross-diffusion [J].Complexity,2022,2022(1):8238384.
• [2] CHERNIHA R,DAVYDOVYCH V.Symmetries and exact solutions of the diffusive Holling-Tanner prey-predator model [J].Acta Applicandae Mathematicae,2023,187(1):8.
• [3] ROMERO-ORDO??EZ M,P??REZ-N????EZ J,PINO-ROMERO N.Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey [J].Mathematics in Applied Sciences and Engineering,2024,5(4):305-328
• [4] SINGH A,TRIPATHI D,KANG Y.A modified May-Holling-Tanner model:the role of dynamic alternative resource on species’ survival [J].Journal of Biological Systems,2024,32(1):187-218.
• [5] KOROBEINIKOV A.A Lyapunov function for Leslie-Gower predator-prey models [J].Applied Mathematics Letters,2001,14(6):697-699.
• [6] SAHOO B,DAS B,SAMANTA S.Dynamics of harvested-predator-prey model:role of alternative resources [J].Modeling Earth Systems and Environment,2016,2(3):140.
• [7] FREEDMAN H.Deterministic mathematical models in population ecology [J].Canadian Journal of Statistics,2010,10(4):315-315.
• [8] ARIF M,ABODAYEH K,EJAZ A.Stability analysis of fractional-order predator-prey system with consuming food resource [J].Axioms,2023,12(1):64.
• [9] GUIN L,MANDAL P.Effect of prey refuge on spatiotemporal dynamics of the reaction-diffusion system [J].Computers and Mathematics with Applications,2014,68(10):1325-1340.
• [10] GUIN L,MONDAL B,CHAKRAVARTY S.Existence of spatiotemporal patterns in the reaction-diffusion predator-prey model incorporating prey refuge [J].International Journal of Biomathematics,2016,9(6):1650085.
• [11] ZHENG P.On a two-species competitive predator-prey system with density-dependent diffusion [J].Mathematical Biosciences and Engineering,2022,19(12):13421-13457.
• [12] HAN R,GUIN L N,DAI B.Consequences of refuge and diffusion in a spatiotemporal predator-prey model [J].Nonlinear Analysis:Real World Applications,2021,60:103311.
• [13] GUIN L,DJILALI S,CHAKRAVARTY S.Cross-diffusion-driven instability in an interacting species model with prey refuge [J].Chaos,Solitons and Fractals,2021,153:111501.
• [14] WHITE K,GILLIGAN C.Spatial heterogeneity in three species,plant-parasite-hyperparasite,systems [J].Philosophical Transactions of the Royal Society of London.Series B:Biological Sciences,1998,353(1368):543-557.
• [15] TURING A.The chemical basis of morphogenesis [J].Bulletin of Mathematical Biology,1990,52(1):153-197.
• [16] SEGEL L,JACKSON J.Dissipative structure:an explanation and an ecological example [J].Journal of Theoretical Biology,1972,37(3):545-559.
• [17] GIERER A,MEINHARDT H.A theory of biological pattern formation [J].Kybernetik,1972,12(1):30-39.
• [18] HAN R,GUIN L,ACHARYA S.Complex dynamics in a reaction-cross-diffusion model with refuge depending on predator-prey encounters [J].The European Physical Journal Plus,2022,137(1):134.
• [19] LIU Y,WEI X.Turing-Hopf bifurcation analysis of the Sel’kov-Schnakenberg system [J].International Journal of Bifurcation and Chaos,2023,33(1):2350012.
• [20] SONG Y,ZHANG T,PENG Y.Turing-Hopf bifurcation in the reaction-diffusion equations and its applications [J].Communications in Nonlinear Science and Numerical Simulation,2016,33:229-258.