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May  2005, 5(2): 289-298. doi: 10.3934/dcdsb.2005.5.289

Periodic tridiagonal systems modeling competitive-cooperative ecological interactions

Mats Gyllenberg 1, and  Yi Wang 2,

1. 

Department of Mathematics and Statistics, University of Helsinki, FIN-00014 Helsinki, Finland
2. 

Department of Mathematics, University of Turku, FIN-20014 Turku, Finland

Received  November 2003 Revised  July 2004 Published  February 2005

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: Cooperative-Competitive., Periodic Kolmogorov tridiagonal systems.
Mathematics Subject Classification: 34C15, 34C25, 92D25, 92D4.
Citation: Mats Gyllenberg, Yi Wang. Periodic tridiagonal systems modeling competitive-cooperative ecological interactions. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 289-298. doi: 10.3934/dcdsb.2005.5.289
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