Open Access
Translator Disclaimer
1996 The periodic predator-prey Lotka-Volterra model
Julián López-Gómez, Rafael Ortega, Antonio Tineo
Adv. Differential Equations 1(3): 403-423 (1996).

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.

Citation

Download Citation

Julián López-Gómez. Rafael Ortega. Antonio Tineo. "The periodic predator-prey Lotka-Volterra model." Adv. Differential Equations 1 (3) 403 - 423, 1996.

Information

Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0849.34026
MathSciNet: MR1401400

Subjects:
Primary: 34C25
Secondary: 92D25

Rights: Copyright © 1996 Khayyam Publishing, Inc.

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.1 • No. 3 • 1996
Back to Top