Bifurcation analysis of a host–parasitoid ecological model with the beddington-deangelis functional response
-
2014-05-13 https://doi.org/10.14419/gjma.v2i2.2405 -
Abstract
In this paper, a two species host-parasitoid model system is considered. The global dynamic behavior of the model is investigated through (local) stability results for its equilibriums and large time computer simulations. Many forms of complex dynamics such as chaos, periodic windows etc. are observed. The Hopf point and attractor crises exist for different set of parameter values.
Keywords: Predator-Prey; Bifurcation; Chaos; Stability.
-
References
- W.R. Thompson, On the relative value of parasites and predators in the biological control of insect pests, Bull Entomol Res 19 (1929) 343-350.
- V.A. Bailey, A.J. Nicholson and E.J. Williams, Interaction between hosts and parasites when some host individuals are more difficult to find than others, J Theor Biol. 3 (1962) 1-18.
- D.J. Rogers, Random search and insect population models, J Animal Ecol. 41 (1972)369-383.
- M.P. Hassell, D.J. Rogers, Insect Parasite Response in the Development ofPopulation Model. Journal of Animal Ecology 41 (1972)661-676.
- S.R.J. Jang, Discrete-time host parasitoid models with Allee effects: Densitydependence versus parasitism. Journal of Difference Equations and Applications 17(2011) 525-539.
- J.R. Beddington, C.A. Free, J.H. Lawton, Dynamic complexity in predator-preymodels framed in difference equations, Nature 225 (1975) 58-60.
- R.M. May, Limit cycles in predator-prey communities, Science 177 (1972) 900-902.
- Y. Xiao, S. Tang S, The effect of initial density and parasitoid intergenerational survival rate on classical biological control, Chaos, Solitons and Fractals 37 (2008) 1048-1058.
- C. Xu. M.S. Boyce, Dynamic complexities in a mutual interference hostparasitoid model, Chaos, Solitons and Fractals 24 (2005) 175-182.
- L. Zhu, M. Zhao, Dynamic complexity of host-parasitoid ecological modelwith the Hassell growth function for the host, Chaos, Solitons and Fractals, 39 (2009) 1259-1269.
- S. Tang, L. Chen, Chaos in functional response host-parasitoid ecosystemModels, Chaos, Solitons and Fractals, 13 (2002) 875-884.
- A.J. Nicholson, V.A. Bailey, The balance of animal populations, Part1.ProcZoolSocLondan, (1935) 551-598
- S. Sahney, M.J. Benton, P.A. Ferry, Links between global taxonomic diversity, ecological diversity and the expansion of vertebrates on land, Biology Letters 6 (2010) 544-547.
- R. M. May, Simple mathematical models with very complicated dynamics.Nature1976; 261:459-67.
- M. P. Hassell, The dynamics of arthropod predator-prey systems. Princeton: University Press Princeton NJ; 1978.
- S. R. Jang, S. L. Diamond, A host–parasitoid interaction with Allee effects on the host. Comput Math Appl 2007; 53:89–103.
- R. Kon, Y. Takeuchi, Permanence of host–parasitoid systems. Nonlinear Anal 2001; 47:1383–93.
- E. G. Gu, The nonlinear analysis on a discrete host–parasitoid model with pesticidal interference. Commun Nonlinear Sci Numer Simul 2009; 14:2720–7.
- Y. N. Xiao, D. Z. Cheng, S. Y. Tang, Dynamic complexity in predator prey ecosystem models with age structure for predators. Chaos, Solitons and fractals 2002; 14:1403-11.
- G. Sugihara,R. M. May, Nonlinear forecasting as a way of distinguishingchaos from measurement error in time series, Nature 344 (1990) 734-741.
-
Downloads
-
How to Cite
Agrawal, T. (2014). Bifurcation analysis of a host–parasitoid ecological model with the beddington-deangelis functional response. Global Journal of Mathematical Analysis, 2(2), 65-69. https://doi.org/10.14419/gjma.v2i2.2405Received date: 2014-04-10
Accepted date: 2014-05-09
Published date: 2014-05-13