Taiwanese Journal of Mathematics

THE PERIOD OF A LOTKA-VOLTERRA SYSTEM1

Shagi-Di Shih

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Abstract

A classical Lotka-Volterra system of two rst-order nonlinear dierential equations modeling predator prey competition in population biology has been known to have an algebraic relation between two dependent variables for its periodic behavior in the phase plane since pioneering works by Lotka [12] on chemical reaction, Lotka [13] on parasitology, and Volterra [24] on shing activity in the upper Adriatic Sea. The techniques of Volterra [24], Hsu [10], Waldvogel [25, 26], Rothe [19], and Shih [22] in obtaining an integral representation of the period of Lotka-Volterra system are surveyed. These integrals are then shown to be equivalent.

Article information

Source
Taiwanese J. Math., Volume 1, Number 4 (1997), 451-470.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406122

Digital Object Identifier
doi:10.11650/twjm/1500406122

Mathematical Reviews number (MathSciNet)
MR1486565

Subjects
Primary: 34-02: Research exposition (monographs, survey articles) 34A34: Nonlinear equations and systems, general 34C25: Periodic solutions 92D25: Population dynamics (general)

Keywords
Lotka-Volterra predator prey system periodic solution period

Citation

Shih, Shagi-Di. THE PERIOD OF A LOTKA-VOLTERRA SYSTEM1. Taiwanese J. Math. 1 (1997), no. 4, 451--470. doi:10.11650/twjm/1500406122. https://projecteuclid.org/euclid.twjm/1500406122


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