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Interplay Between Reproduction and Age Selective Harvesting Delays of a Single Population Non-Autonomous System

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  • N. S. N. V. K. Vyshnavi Devi

    (SRM Institute of Science and Technology)

  • Debaldev Jana

    (SRM Institute of Science and Technology)

  • M. Lakshmanan

    (Bharathidasan University)

Abstract

This paper is concerned with an analysis of the dynamics of a non-autonomous, single population age based growth model with harvesting formulation. First, we derive sufficient conditions for permanence and positive invariance. Then, by constructing a scalar function, namely the Lyapunov function, we arrive at a suitable criterion for global attractivity. With the help of Brouwer fixed point and continuation theorems, we obtain constraints for the existence of a positive periodic solution. Then we prove that there exists only one solution which is almost periodic in nature that is distinct from every other solution. Further, we carry out a numerical simulation to support the analytical findings.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0501-x
    DOI: 10.1007/s13226-020-0501-x
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    References listed on IDEAS

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    1. Song, Xiaodong & Bryan, Brett A. & Paul, Keryn I. & Zhao, Gang, 2012. "Variance-based sensitivity analysis of a forest growth model," Ecological Modelling, Elsevier, vol. 247(C), pages 135-143.
    2. Andrew S. MacDougall & Eric Harvey & Jenny L. McCune & Karin A. Nilsson & Joseph Bennett & Jennifer Firn & Timothy Bartley & James B. Grace & Jocelyn Kelly & Tyler D. Tunney & Bailey McMeans & Shin-Ic, 2018. "Context-dependent interactions and the regulation of species richness in freshwater fish," Nature Communications, Nature, vol. 9(1), pages 1-9, December.
    3. 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.
    4. Anders Skonhoft & Niels Vestergaard & Martin Quaas, 2012. "Optimal Harvest in an Age Structured Model with Different Fishing Selectivity," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 51(4), pages 525-544, April.
    5. 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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