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Qualitative analysis of one class of population models with commensal interaction

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Abstract

The qualitative analysis of a class of dynamic population models that are in commensal relationships and compete for one substrate is carried out. The stability of all the stationary conditions is analyzed. All the singularities are found analytically and constraints are obtained for species growth characteristics and initial flows of the substrate and product. The qualitative changes in the dynamics due to variations of several system parameters are analyzed and bifurcation diagrams are constructed for all the singular points.

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Authors and Affiliations

  1. Kharkov National University of Radio Electronics, Kharkov, Ukraine

    S. N. Gerasin & I. G. Yalovega

  2. Kharkov Institute of Management, Kharkov, Ukraine

    S. V. Yakovlev

Authors
  1. S. N. Gerasin
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  2. S. V. Yakovlev
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  3. I. G. Yalovega
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Correspondence to S. N. Gerasin.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2012, pp. 42–49.

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Gerasin, S.N., Yakovlev, S.V. & Yalovega, I.G. Qualitative analysis of one class of population models with commensal interaction. Cybern Syst Anal 48, 192–199 (2012). https://doi.org/10.1007/s10559-012-9397-8

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  • DOI: https://doi.org/10.1007/s10559-012-9397-8

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