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Bifurcation Analysis of a Predator–Prey System with Generalised Holling Type III Functional Response

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Abstract

We consider a generalised Gause predator–prey system with a generalised Holling response function of type III: \(p(x) = \frac{mx^2}{ax^2+bx+1}\). We study the cases where b is positive or negative. We make a complete study of the bifurcation of the singular points including: the Hopf bifurcation of codimensions 1 and 2, the Bogdanov–Takens bifurcation of codimensions 2 and 3. Numerical simulations are given to calculate the homoclinic orbit of the system. Based on the results obtained, a bifurcation diagram is conjectured and a biological interpretation is given.

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Authors and Affiliations

  1. Collège Édouard-Montpetit, Longueuil, QC, Canada, J4H 3M6

    Yann Lamontagne & Caroline Coutu

  2. Département de Mathématiques, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, QC, Canada, H3C 3J7

    Christiane Rousseau

Authors
  1. Yann Lamontagne
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  2. Caroline Coutu
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  3. Christiane Rousseau
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Correspondence to Christiane Rousseau.

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Lamontagne, Y., Coutu, C. & Rousseau, C. Bifurcation Analysis of a Predator–Prey System with Generalised Holling Type III Functional Response. J Dyn Diff Equat 20, 535–571 (2008). https://doi.org/10.1007/s10884-008-9102-9

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  • DOI: https://doi.org/10.1007/s10884-008-9102-9

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