Browsing by Autor "Antonio Tineo"

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    A result of Ambrosetti–Prodi type for first-order ODEs with cubic non-linearities. Part II
    (Springer Science+Business Media, 2003) Antonio Tineo
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    The periodic predator-prey Lotka-Volterra model
    (1996) Julián López-Gómez; Rafael Ortega; Antonio Tineo
    In this paper we characterize the existence of coexistence states for the classical Lotka-Volterra predator-prey model with periodic coefficients and analyze the dynamics of positive solutions of such models. Among other results we show that if some trivial or semi-trivial positive state is linearly stable, then it is globally asymptotically stable with respect to the positive solutions. In fact, the model possesses a coexistence state if, and only if, any of the semi-trivial states is unstable. Some permanence and uniqueness results are also found. An example exhibiting a unique coexistence state that is unstable is given.