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Selective harvesting of two competing fish species in the presence of toxicity with time delay

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  • Pal, D.
  • Samanta, G.P.
  • Mahapatra, G.S.

Abstract

In this paper, we have considered a two competing fish species with the delay due to gestation, each of which obeys the law of logistic growth and releases a substance toxic to the other. We also consider the selective harvesting of fishes above a certain age or size by incorporating a time delay in the harvesting term. The dynamical behavior of the exploited system is examined in the presence and absence of delay. Boundedness, local and global stabilities are addressed. The possibility of the existence of a dynamic equilibrium and the optimal harvesting policy is studied in the absence of delay. It is shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Extensive numerical simulations are performed using analytical results for a hypothetical set of parameter values.

Suggested Citation

  • Pal, D. & Samanta, G.P. & Mahapatra, G.S., 2017. "Selective harvesting of two competing fish species in the presence of toxicity with time delay," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 74-93.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:74-93
    DOI: 10.1016/j.amc.2017.05.069
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Robert M. Solow, 1974. "The Economics of Resources or the Resources of Economics," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 12, pages 257-276, Palgrave Macmillan.
    4. Pal, D. & Mahapatra, G.S., 2016. "Effect of toxic substance on delayed competitive allelopathic phytoplankton system with varying parameters through stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 109-124.
    5. Zhao, Hongyong & Huang, Xuanxuan & Zhang, Xuebing, 2015. "Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 300-315.
    6. Liu, Meng & Bai, Chuanzhi, 2016. "Optimal harvesting of a stochastic mutualism model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 301-309.
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    Cited by:

    1. Yuan, Manman & Wang, Weiping & Luo, Xiong & Liu, Linlin & Zhao, Wenbing, 2018. "Finite-time anti-synchronization of memristive stochastic BAM neural networks with probabilistic time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 244-260.
    2. Sahoo, Banshidhar & Poria, Swarup, 2019. "Dynamics of predator–prey system with fading memory," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 319-333.
    3. Jeong, Yong Dam & Kim, Sangil & Jung, Il Hyo & Cho, Giphil, 2021. "Optimal harvesting strategy for hairtail, Trichiurus Lepturus, in Korea Sea using discrete-time age-structured model," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    4. Ye, Luhong & Zhao, Hongyong & Wu, Daiyong, 2023. "Spatial movement with memory-induced cross-diffusion effect and toxin effect in predator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 68-91.

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