On a property of a generalized Kolmogorov population model

Shair Ahmad; Alan C. Lazer

doi:10.3934/dcds.2013.33.1

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2013, Volume 33, Issue 1: 1-6. Doi: 10.3934/dcds.2013.33.1

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On a property of a generalized Kolmogorov population model

Shair Ahmad^1, and
Alan C. Lazer^2,

1.
Department of Mathematics, University of Texas at San Antonio, San Antonio, Texas 78249
2.
Department of Mathematics, University of Miami, Coral Gables, Miami, Florida 33124

Received: August 2011

Revised: January 2012

Published: January 2013

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Abstract

We consider Kolmogorov-type systems which are not necessarily competitive or cooperative. Our main result shows that such systems cannot have nontrivial periodic solutions whose orbits are orbitally stable. We obtain our results under two assumptions that we consider to be natural assumptions.

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Mathematics Subject Classification: 34C60, 92D25.

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References

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