Three-Dimensional Competitive Lotka-Volterra Systems with no Periodic Orbits

@article{Zeeman1998ThreeDimensionalCL,
  title={Three-Dimensional Competitive Lotka-Volterra Systems with no Periodic Orbits},
  author={Mary Lou Zeeman and Pauline van den Driessche},
  journal={SIAM Journal of Applied Mathematics},
  year={1998},
  volume={58},
  pages={227-234}
}
The following conjecture of M. L. Zeeman is proved. If three interacting species modeled by a competitive Lotka–Volterra system can each resist invasion at carrying capacity, then there can be no coexistence of the species. Indeed, two of the species are driven to extinction. It is also proved that in the other extreme, if none of the species can resist invasion from either of the others, then there is stable coexistence of at least two of the species. In this case, if the system has a fixed… CONTINUE READING

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