JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (7): 30-38.doi: 10.6040/j.issn.1671-9352.0.2018.018

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Study of dynamic of a discrete host-parasitoid model

LIU Hua1, YE Yong1, WEI Yu-mei2*, YANG Peng1, MA Ming1, YE Jian-hua1, MA Ya-lei1   

  1. 1. School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China;
    2. The Experiment Center, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Received:2018-01-17 Online:2018-07-20 Published:2018-07-03

Abstract: A host-parasitoid model with Allee effect and Holling Ⅲ functional response function was established, and the local stability and persistence of equilibria was discussed. The influence of the Allee effect on the dynamic behavior of the model is simulated by the computer simulation and the intrinsic growth rate r as the parameter of the bifurcation diagram. We found that the introduction of Allee effect will accelerate the extinction of population in the model with both Allee effect and Holling Ⅲ functional response. When the system is strong Allee, the chaotic dynamics of the system will be reduced.

Key words: stability, persistence, bifurcation diagram, Holling Ⅲ functional response, Allee effect

CLC Number: 

  • O29
[1] ALLEE W C. Animal aggregations: a study in general sociology[M]. Chicago: University of Chicago Press, 1931.
[2] ALLEE W C, EMERSON A E, PARK O, et al. Principles of animal ecology[M]. Philadlphia: W B Saunders, 1949.
[3] COURCHAMP F, BEREC L, GASCOIGNE J. Allee effects in ecology and conservation[M]. Oxford: Oxford University Press, 2008.
[4] LIU Hua, LI Zizhen, GAO Meng, et al. Dynamic complexities in a host-parasitoid model with Allee effect for the host and parasitoid aggregation[J]. Ecological Complexity, 2009, 6(3):337-345.
[5] 蒋芮, 刘华, 谢梅,等. 具有HollingⅡ型功能反应和Allee效应的捕食系统模型[J]. 高校应用数学学报, 2016,31(4):441-450. JIANG Rui, LIU Hua, XIE Mei, et al. A predator-prey system model with Holling II functional response and Allee effect[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4):441-450.
[6] DIN Q. Qualitative analysis and chaos control in a density-dependent host-parasitoid system[J]. International Journal of Dynamics & Control, 2017(3):1-21.
[7] DIN Q. Global stability of Beddington model[J]. Qualitative Theory of Dynamical Systems, 2016, 16(2):1-25.
[8] LIU Xijuan, CHU Yandong, LIU Yun. Bifurcation and chaos in a host-parasitoid model with a lower bound for the host[J]. Advances in Difference Equations, 2018, 2018(1):31(1-15).
[9] MORAN P A P. Some remarks on animal population dynamics[J]. Biometrics, 1950, 6(3):250-258.
[10] RICKER W E. Stock and recruitment[J]. J Fish Res Board Can, 1954(11):559-623.
[11] LV Songjuan, ZHAO Min. The dynamic complexity of a three species food chain model[J]. Chaos Solitons and Fractals, 2006, 10(57):1-12.
[12] BEDDINGTON J R, FREE C A, LAWTON J H. Dynamic complexity in predator-prey models framed in difference equations[J]. Nature, 1975, 255(5503):58-60.
[13] HOLLING C S. The functional response of predators to prey density and its role in mimicry and population regulation[J]. Mem Entomol Soc Can, 1965, 97(45):1-60.
[14] TANG Sanyi, CHEN Lansun. Chaos in functional response host-parasitoid ecosystem models[J]. Chaos Solitons and Fractals, 2002, 13(4):875-884.
[15] MAY R M. Simple mathematical models with very complicated dynamics[J]. Nature, 1976, 261(5560):459-467.
[16] OATEN A, MURDOCH W W. Functional response and stability in predator-prey systems[J]. Am Nat, 1975, 109(967):299-318.
[17] MURDOCH W W, OATEN A. Predation and population stability[J]. Adv ecol Res, 1975, 9:1-131.
[18] CHEN Fengde. Permanence for the discrete mutualism model with time delays[J]. Mathematical & Computer Modelling, 2008, 47(3):431-435.
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