Generalizing the May-Leonard System to Any Number of Species

  • Genaro de la VegaEmail author
  • Santiago López de Medrano
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 54)


We construct generalizations of the May-Leonard three species Lotka-Volterra system to any number of species, extending the property of cyclic dominance. First we recall the main properties of the May-Leonard system. Then we construct a Lotka-Volterra system for n species which has an invariant attracting polygon. We construct Lotka-Volterra-Kolmogorov deformations of higher degree of this system which have the same attracting polygon and all the properties of the May-Leonard one. We finish with the construction of Lotka-Volterra deformations of the same system which numerically show a curvilinear attracting polygon and the same properties, but the corresponding analytic results are still not complete.


Vector Field Equilibrium Point Invariant Manifold Cyclic Behaviour Cyclic Permutation 
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This work owes much to many years of joint work and long discussions of the second author with Marc Chaperon. The first author received a Conacyt grant for writing his Ph. D. Thesis, part of which is included in this article. The second author was partially supported by Conacyt-CNRS and by the UNAM-DGAPA-Papiit grants IN102009 and IN108112.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Genaro de la Vega
    • 1
    Email author
  • Santiago López de Medrano
    • 1
  1. 1.Instituto de Matemáticas, UNAMUniversidad Nacional Autónoma de MéxicoMéxico, D.F.México

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