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The analytical solutions of the harvesting Verhulst’s evolution equation

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  • Miškinis, Paulius
  • Vasiliauskienė, Vaida

Abstract

The Verhulst differential equation is one of the evolutionary equations most widely known in ecology. Its analytical solution is applied to explain the growth dynamics of populations with limited resources. The situation when the harvesting or “influence” function, i.e. the additional term proportional to the population concentration, is controlled by the time-dependent coefficient is analyzed. Several examples when this equation has the analytical solutions whose dependence on the parameters is expressed in an explicit form are presented. The estimation of the influence function in real experiments with bread mold is presented. The stability and harvesting functions in the general case are discussed.

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  • Miškinis, Paulius & Vasiliauskienė, Vaida, 2017. "The analytical solutions of the harvesting Verhulst’s evolution equation," Ecological Modelling, Elsevier, vol. 360(C), pages 189-193.
    • Handle: RePEc:eee:ecomod:v:360:y:2017:i:c:p:189-193
    DOI: 10.1016/j.ecolmodel.2017.06.021
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    References listed on IDEAS

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    1. V.I. Yukalov & E.P. Yukalova & D. Sornette, "undated". "Punctuated Evolution due to Delayed Carrying Capacity," Working Papers CCSS-09-004, ETH Zurich, Chair of Systems Design.
    2. Thornley, John H.M. & Shepherd, John J. & France, J., 2007. "An open-ended logistic-based growth function: Analytical solutions and the power-law logistic model," Ecological Modelling, Elsevier, vol. 204(3), pages 531-534.
    3. Safuan, Hamizah M. & Jovanoski, Zlatko & Towers, Isaac N. & Sidhu, Harvinder S., 2013. "Exact solution of a non-autonomous logistic population model," Ecological Modelling, Elsevier, vol. 251(C), pages 99-102.
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    Cited by:

    1. Cortés, J.-C. & Moscardó-García, A. & Villanueva, R.-J., 2022. "Uncertainty quantification for hybrid random logistic models with harvesting via density functions," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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