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Bifurcations of a singular prey–predator economic model with time delay and stage structure

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  • Zhang, Xue
  • Zhang, Qing-Ling
  • Liu, Chao
  • Xiang, Zhong-Yi

Abstract

This paper studies a singular prey–predator economic model with time delay and stage structure. Compared with other researches on dynamics of prey–predator population, this model is described by differential–algebraic equations due to economic factor. For zero economic profit, this model exhibits three bifurcational phenomena: transcritical bifurcation, Hopf bifurcation and singular induced bifurcation. For positive economic profit, the model undergoes a saddle-node bifurcation at critical value of positive economic profit, and the increase of delay destabilizes the positive equilibrium point of the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results.

Suggested Citation

  • Zhang, Xue & Zhang, Qing-Ling & Liu, Chao & Xiang, Zhong-Yi, 2009. "Bifurcations of a singular prey–predator economic model with time delay and stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1485-1494.
  • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1485-1494
    DOI: 10.1016/j.chaos.2009.03.051
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Singh, Brahampal, 2007. "The dynamics of a food web consisting of two preys and a harvesting predator," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1346-1356.
    2. Gao, Shujing & Chen, Lansun & Sun, Lihua, 2005. "Optimal pulse fishing policy in stage-structured models with birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1209-1219.
    3. Zhang, Lei & Wang, Wenjuan & Xue, Yakui, 2009. "Spatiotemporal complexity of a predator–prey system with constant harvest rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 38-46.
    4. Liu, Zhihua & Yuan, Rong, 2006. "Stability and bifurcation in a harvested one-predator–two-prey model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1395-1407.
    5. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
    6. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
    7. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    8. Rao, Feng & Wang, Weiming & Li, Zhenqing, 2009. "Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1634-1644.
    9. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
    10. Zhang, Xue & Zhang, Qing-ling & Zhang, Yue, 2009. "Bifurcations of a class of singular biological economic models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1309-1318.
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