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Optimal pulse fishing policy in stage-structured models with birth pulses

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  • Gao, Shujing
  • Chen, Lansun
  • Sun, Lihua

Abstract

In this paper, we propose exploited models with stage structure for the dynamics in a fish population for which periodic birth pulse and pulse fishing occur at different fixed time. Using the stroboscopic map, we obtain an exact cycle of system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate (or pulse fishing time or harvesting effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, period-doubling, multi-period-halving and incomplete period-doubling bifurcation, pitch-fork and tangent bifurcation, non-unique dynamics (meaning that several attractors or attractor and chaos coexist) and attractor crisis. This suggests that birth pulse and pulse fishing provide a natural period or cyclicity that make the dynamical behaviors more complex. Moreover, we show that the pulse fishing has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. An interesting result is obtained that, after the birth pulse, the population can sustain much higher harvesting effort if the mature fish is removed as early as possible.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:chsofr:v:25:y:2005:i:5:p:1209-1219
    DOI: 10.1016/j.chaos.2004.11.093
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    References listed on IDEAS

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    1. 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.
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    Cited by:

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    2. 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.
    3. Wang, Fengyan & Pang, Guoping, 2009. "The global stability of a delayed predator–prey system with two stage-structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 778-785.
    4. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.
    5. Terry, Alan J., 2015. "A population model with birth pulses, age structure, and non-overlapping generations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 400-417.

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