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Bifurcation and bio-economic analysis of a prey-generalist predator model with Holling type IV functional response and nonlinear age-selective prey harvesting

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  • Datta, Jyotiska
  • Jana, Debaldev
  • Upadhyay, Ranjit Kumar

Abstract

In this paper, we have studied the dynamical behaviour of a Leslie-Gower model with Holling type-IV functional response and nonlinear prey harvesting where target prey for harvesting are above a particular age which is called maturation delay. The model system has been studied using qualitative analysis, bifurcation theory, bionomic equilibrium, MSY and optimal harvesting policy. We explain that the interior equilibrium is delay dependent and locally asymptotically stable. The age-selective harvesting system under goes a Hopf-bifurcation with respect to the maturation delay. Conditions for the MSY and existence of bionomic equilibrium are analyzed and Pontryagin's maximum principle has been used to find the path of a singular control. Difficult analytical results are featured by numerical examples to better understand the system in a simple way.

Suggested Citation

  • Datta, Jyotiska & Jana, Debaldev & Upadhyay, Ranjit Kumar, 2019. "Bifurcation and bio-economic analysis of a prey-generalist predator model with Holling type IV functional response and nonlinear age-selective prey harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 229-235.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:229-235
    DOI: 10.1016/j.chaos.2019.02.010
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    References listed on IDEAS

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    1. Henrik Svedäng & Sara Hornborg, 2014. "Selective fishing induces density-dependent growth," Nature Communications, Nature, vol. 5(1), pages 1-6, September.
    2. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar & Samanta, G.P., 2016. "Ecological dynamics of age selective harvesting of fish population: Maximum sustainable yield and its control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 111-122.
    3. Jana, Debaldev & Pathak, Rachana & Agarwal, Manju, 2016. "On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 252-273.
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    Cited by:

    1. Bairagi, Nandadulal & Bhattacharya, Santanu & Auger, Pierre & Sarkar, Biswajit, 2021. "Bioeconomics fishery model in presence of infection: Sustainability and demand-price perspectives," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    2. Das, Parthasakha & Das, Samhita & Upadhyay, Ranjit Kumar & Das, Pritha, 2020. "Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Lan, Heng-you, 2021. "Approximation-solvability of population biology systems based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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