Advances in Differential Equations

The periodic predator-prey Lotka-Volterra model

Julián López-Gómez, Rafael Ortega, and Antonio Tineo

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Abstract

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

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

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366896045

Mathematical Reviews number (MathSciNet)
MR1401400

Zentralblatt MATH identifier
0849.34026

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

Citation

López-Gómez, Julián; Ortega, Rafael; Tineo, Antonio. The periodic predator-prey Lotka-Volterra model. Adv. Differential Equations 1 (1996), no. 3, 403--423. https://projecteuclid.org/euclid.ade/1366896045.


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