Dynamics of a Lotka-Volterra map

Francisco Balibrea; Juan Luis García Guirao; Marek Lampart; Jaume Llibre

doi:https://doi.org/10.4064/fm191-3-5

Dynamics of a Lotka-Volterra map

Francisco Balibrea, Juan Luis García Guirao, Marek Lampart, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

Abstract

Given the plane triangle with vertices (0, 0), (0, 4) and (4, 0) and the transformation F : (x, y) → (x(4 - x - y), xy) introduced by A. N. Sharkovskiǐ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior of the Schrödinger equation.

Original language	English
Pages (from-to)	265-279
Journal	Fundamenta Mathematicae
Volume	191
DOIs	https://doi.org/10.4064/fm191-3-5
Publication status	Published - 13 Nov 2006

Keywords

Periodic trajectory
Resultant
Spiral type curve

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title = "Dynamics of a Lotka-Volterra map",

abstract = "Given the plane triangle with vertices (0, 0), (0, 4) and (4, 0) and the transformation F : (x, y) → (x(4 - x - y), xy) introduced by A. N. Sharkovskiǐ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior of the Schr{\"o}dinger equation.",

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AU - Balibrea, Francisco

AU - Guirao, Juan Luis García

AU - Lampart, Marek

AU - Llibre, Jaume

PY - 2006/11/13

Y1 - 2006/11/13

N2 - Given the plane triangle with vertices (0, 0), (0, 4) and (4, 0) and the transformation F : (x, y) → (x(4 - x - y), xy) introduced by A. N. Sharkovskiǐ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior of the Schrödinger equation.

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KW - Periodic trajectory

KW - Resultant

KW - Spiral type curve

U2 - https://doi.org/10.4064/fm191-3-5

DO - https://doi.org/10.4064/fm191-3-5

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SP - 265

EP - 279

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

SN - 0016-2736

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