Advances in Differential Equations
- Adv. Differential Equations
- Volume 1, Number 3 (1996), 403-423.
The periodic predator-prey Lotka-Volterra model
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.
Adv. Differential Equations, Volume 1, Number 3 (1996), 403-423.
First available in Project Euclid: 25 April 2013
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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