Advances in Differential Equations

The periodic predator-prey Lotka-Volterra model

Julián López-Gómez, Rafael Ortega, and Antonio Tineo

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

Permanent link to this document

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.

Export citation