Advances in Differential Equations

The periodic predator-prey Lotka-Volterra model

Julián López-Gómez, Rafael Ortega, and Antonio Tineo

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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.

Article information

Adv. Differential Equations, Volume 1, Number 3 (1996), 403-423.

First available in Project Euclid: 25 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C25: Periodic solutions
Secondary: 92D25: Population dynamics (general)


López-Gómez, Julián; Ortega, Rafael; Tineo, Antonio. The periodic predator-prey Lotka-Volterra model. Adv. Differential Equations 1 (1996), no. 3, 403--423.

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