Periodic tridiagonal systems modeling competitive-cooperative ecological interactions

Mats Gyllenberg; Yi Wang

doi:10.3934/dcdsb.2005.5.289

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2005, Volume 5, Issue 2: 289-298. Doi: 10.3934/dcdsb.2005.5.289

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Periodic tridiagonal systems modeling competitive-cooperative ecological interactions

Mats Gyllenberg¹ and
Yi Wang^2,

1.
Department of Mathematics and Statistics, University of Helsinki, FIN-00014 Helsinki
2.
Department of Mathematics, University of Turku, FIN-20014 Turku

Received: October 31, 2003

Revised: June 30, 2004

Published: April 2008

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Abstract

The dynamics of the Poincaré map, associated with a periodic tridiagonal system modeling cooperative-competitive ecological interactions, is investigated. It is shown that the limit-set is either a fixed point or is contained in the boundary of the positive cone and itself contains a cycle of fixed points. Furthermore, the dynamics is trivial if the number of interactive species is not greater than 4.

Keywords:

Periodic Kolmogorov tridiagonal systems,
Cooperative-Competitive.

Mathematics Subject Classification: 34C15, 34C25, 92D25, 92D40.

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