具有阶段结构的非自治捕食–食饵模型
Non-Autonomous Predator-Prey Model with Stage Structure
DOI: 10.12677/PM.2018.86082, PDF,  被引量   
作者: 卢 旸, 高 晗, 戴娜娜, 尹鑫浩：东北石油大学，数学与统计学院应用数学系，黑龙江 大庆
关键词: 非自治；阶段结构；捕食–食饵模型；一致持久性；灭绝性；Non-Autonomous； Stage Structure； Predator-Prey Model； Uniform Persistence； Extinction
摘要: 研究了一类捕食者具有阶段结构且模型参数为时变系数的非自治捕食–食饵模型。在模型中假设捕食者具有阶段结构，食饵具有指数型增长率，定性分析了当模型中的所有参数为时变系数时的动力学性态。通过定义捕食者的净再生数，运用比较原理分别得到了捕食者的一致持久性和捕食者的灭绝性。最后通过数值模拟验证了理论的正确性。
Abstract: This paper studies a kind of non-autonomous predator-prey model with stage structure and mod el parameters depended on time-varying coefficients. In the model it is assumed that the predator has stage structure, prey has exponential growth rate, and dynamics is analyzed qualitatively when all the parameters on the model parameters depend on time-varying coefficients. By defining the net reproductive number of the predator, a uniform persistence and extinction of the predators are obtained by using the comparison principle, respectively. Finally the correctness of the theory is verified by numerical simulation.
文章引用：卢旸, 高晗, 戴娜娜, 尹鑫浩. 具有阶段结构的非自治捕食–食饵模型[J]. 理论数学, 2018, 8(6): 613-623. https://doi.org/10.12677/PM.2018.86082

参考文献

[1] Fan, M. and Kuang, Y. (2004) Dynamics of a Non-Autonomous Predator-Prey System with the Beddington-DeAngelis Functional Response. Journal of Mathematical Analysis and Applications, 295, 15-39.
[Google Scholar] [CrossRef] 
[2] Hsu, S.B., Hwang, T.M. and Kuang, Y. (2003) Global Analysis of Michae-lis-Menten Type Ratio-Dependent Predator-Prey System. Journal of Mathematical Biology, 42, 489-506.
[Google Scholar] [CrossRef] [PubMed]
[3] Jost, C. and Ellner, S. (2000) Testing for Predator Dependence in Predator-Prey Dynamics: A Nonparametric Approach. Proceedings of the Royal Society of London. Series B, 267, 1611-1620.
[Google Scholar] [CrossRef] [PubMed]
[4] Rui, X., Davidson, F.A. and Chaplain, M.A.J. (2002) Persistence and Stability for a Two-Species Ratio-Dependent Predator-Prey System with Distributed Time Delay. Journal of Mathematical Analysis and Applications, 269, 256-277.
[Google Scholar] [CrossRef] 
[5] Wang, Y., Wu, H. and Sun, S. (2012) Persistence of Pollination Mutual-isms in Plant Pollinator-Robber. Theoretical Population Biology, 81, 243-250.
[Google Scholar] [CrossRef] [PubMed]
[6] Abrams, A. and Ginzburg, L.R. (2000) The Nature of Predation Prey Dependent, Ratio Dependent or Neither. Trends Ecology Evolution, 15, 337-341.
[Google Scholar] [CrossRef] 
[7] Huang, C.-Y., Zhao, M. and Zhao, L.-C. (2010) Permanence of Periodic Predator-Prey System with Two Predators and Stage Structure for Prey. Nonlinear Analysis: Real World Applications, 11, 503-514.
[Google Scholar] [CrossRef] 
[8] Beddington, J.R. (1975) Mutual Interference between Parasites or Predators and Its Effect on Searching Efficiency. Journal of Animal Ecology, 44, 331-340.
[Google Scholar] [CrossRef] 
[9] Deangclis, D.L., Coldstein, R.A. and Neill, R.V. (1975) A Model for Trophic Interaction. Ecology, 56, 881-892.
[Google Scholar] [CrossRef] 
[10] Skalski, G.T. and Filliam, J.F. (2001) Functional Responses with Predator Inter-Ference: Viable Alternatives to the Holling Type Ii Model. Ecology, 82, 3083-3092.
[Google Scholar] [CrossRef] 
[11] Cantrell, R.S. and Cosner, C. (2001) On the Dy-namics of Predator-Prey Model with the Beddington-DeAngelis Functional. Journal of Mathematical Analysis and Applications, 257, 206-222.
[Google Scholar] [CrossRef] 
[12] Hwang, Z.W. (2003) Global Analysis of the Predator-Prey System with Beddington-DeAngelis Functional Response. Journal of Mathematical Analysis and Applications, 281, 395-401.
[Google Scholar] [CrossRef] 
[13] Liu, S. and Zhang, J. (2008) Coexistence and Stability of Predator-Prey Model of Bedding-DeAngelis Functional Response. Journal of Mathematical Analysis and Applications, 342, 446-460.
[Google Scholar] [CrossRef] 
[14] Aiello, W. and Freedman, H.I. (1990) A Time-Delay Model of Single-Species Growth with Stage Structure. Mathematical Biosciences, 101, 139-153.
[Google Scholar] [CrossRef] 
[15] Al-omari, J. and Gourley, S. (2003) Stability and Traveling Fronts in Lotka-Volterra Competition Models with Stage Structure. SIAM Journal on Applied Mathematics, 63, 2063-2086.
[Google Scholar] [CrossRef] 
[16] Liu, S., Chen, L., Luo, G. and Jiang, J. (2002) Asymptotic Behavior of Competitive Lotka-Volterrta System with Stage Structured. Journal of Mathematical Analysis and Applications, 271, 124-138.
[Google Scholar] [CrossRef] 
[17] Liu, S., Chen, L. and Agarwal, R. (2002) Recent Progress on Stage-Structured Population Dynamics. Mathematical and Computer Modelling, 36, 1319-1360.
[Google Scholar] [CrossRef] 
[18] Ou, L., Luo, Y., Jiang, Y. and Li, Y. (2003) The Asymptotic Behaviors of a Stage-Structured Autonomous Predator-Prey System with Time Delay. Journal of Mathematical Analysis and Applications, 283, 534-548.
[Google Scholar] [CrossRef] 
[19] Liu, S. and Edoardo, B. (2010) Predator-Prey Model of Bedding-ton-DeAngelis Type with Maturation and Gestation Delays. Nonlinear Analysis, 11, 4072-4091.
[Google Scholar] [CrossRef] 
[20] Liu, S. and Edoardo, B. (2006) A Stage-Structured Predator-Prey Model of Beddington-DeAngelis Type. SIAM Journal on Applied Mathematics, 4, 1001-1129.
[Google Scholar] [CrossRef] 
[21] Cushing, J.M. (1977) Periodic Time-Dependent Predator-Prey System. SIAM Journal on Applied Mathematics, 32, 82-95.
[Google Scholar] [CrossRef] 
[22] Yang, S.J. and Shi, B. (2008) Periodic Solution for a Three-Stage-Structured Predator-Prey System with Time Delay. Journal of Mathematical Analysis and Applications, 341, 287-294.
[Google Scholar] [CrossRef] 
[23] Zhang, T. and Teng, Z. (2007) On a Non-Autonomous Seirs Model in Epide-miology. Bulletin of Mathematical Biology, 69, 2537-2559.
[Google Scholar] [CrossRef] [PubMed]
[24] Song, X. and Chen, L. (2001) Optimal Harvesting and Stability for a Two-Species Competitive System with Stage-Structure. Mathematical Biosciences, 170, 173-186.
[Google Scholar] [CrossRef] 
[25] Niu, X., Zhang, T. and Teng, Z. (2011) The Asymptotic Behavior of a Non-Autonomous Eco-Epidemic Model with Disease in the Prey. Applied Mathematical Modelling, 35, 457-470.
[Google Scholar] [CrossRef] 
[26] Gourley, S.A. and Kuang, Y. (2004) A Stage-Structured Predator-Prey Model and Its Dependence on Through-Stage Delay and Death Rate. Journal of Mathematical Biology, 49, 188-200.
[Google Scholar] [CrossRef] [PubMed]

为你推荐