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On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting

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  • Jana, Debaldev
  • Pathak, Rachana
  • Agarwal, Manju

Abstract

Age-selective harvesting where harvesting of species after a certain age is a scientific strategy with respect to biological and economical point of views. By this method we can overcome the unexpected extinction risk of any harvested population due to random harvesting below its maturation (age, body size or weight). The objective of this paper is to study dynamic behavior of preypredator system with alternative form of time delay in harvesting. Arino et al. [2] have given alternative expression for a delayed logistic equation. Using this expression of time delay, a preypredator system with Holling type III functional response and independent age-selective harvesting is proposed and analyzed. We find out the critical values of delay parameters under different dynamical situations and observe that system is stable and unstable when the delay parameters are bellow and above the critical values respectively and there is Hopf bifurcation when delay parameters cross the critical values. System shows these interesting dynamical features under different critical parametric restrictions. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations illustrate the analytical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:83:y:2016:i:c:p:252-273
    DOI: 10.1016/j.chaos.2015.12.008
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    1. Lv, Yunfei & Pei, Yongzhen & Wang, Yong, 2019. "Bifurcations and simulations of two predator–prey models with nonlinear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 158-170.
    2. Devi, Sapna & Gupta, Nivedita, 2019. "Effects of inclusion of delay in the imposition of environmental tax on the emission of greenhouse gases," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 41-53.
    3. Wang, Jingjing & Zheng, Hongchan & Jia, Yunfeng, 2021. "Dynamical analysis on a bacteria-phages model with delay and diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. 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.
    5. 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.
    6. Yang, Ruizhi & Ma, Jian, 2018. "Analysis of a diffusive predator-prey system with anti-predator behaviour and maturation delay," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 128-139.
    7. 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.
    8. N. S. N. V. K. Vyshnavi Devi & Debaldev Jana & M. Lakshmanan, 2020. "Interplay Between Reproduction and Age Selective Harvesting Delays of a Single Population Non-Autonomous System," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1857-1891, December.

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