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Periodic tridiagonal systems modeling competitive-cooperative ecological interactions

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


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