Periodic orbits and their stability in the Rössler prototype-4 system

Isaac A. García; Jaume Llibre; Susanna Maza

doi:https://doi.org/10.1016/j.physleta.2012.05.035

Periodic orbits and their stability in the Rössler prototype-4 system

Isaac A. García, Jaume Llibre, Susanna Maza

Department of Mathematics

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

7 Citations (Scopus)

Abstract

For the Rössler prototype-4 system ẋ=-y-z, ẏ=x, ż=αy(1-y)-βz we prove the existence of periodic orbits and study their stability or instability. The main tool for proving these results is the averaging theory. Recently the existence of some of these periodic orbits were detected numerically. © 2012 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	2234-2237
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	376
Issue number	33
DOIs	https://doi.org/10.1016/j.physleta.2012.05.035
Publication status	Published - 2 Jul 2012

Keywords

Averaging theory
Periodic orbit
Rössler system

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https://ddd.uab.cat/record/150501

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title = "Periodic orbits and their stability in the R{\"o}ssler prototype-4 system",

abstract = "For the R{\"o}ssler prototype-4 system ẋ=-y-z, ẏ=x, {\.z}=αy(1-y)-βz we prove the existence of periodic orbits and study their stability or instability. The main tool for proving these results is the averaging theory. Recently the existence of some of these periodic orbits were detected numerically. {\textcopyright} 2012 Elsevier B.V. All rights reserved.",

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T1 - Periodic orbits and their stability in the Rössler prototype-4 system

AU - García, Isaac A.

AU - Llibre, Jaume

AU - Maza, Susanna

PY - 2012/7/2

Y1 - 2012/7/2

N2 - For the Rössler prototype-4 system ẋ=-y-z, ẏ=x, ż=αy(1-y)-βz we prove the existence of periodic orbits and study their stability or instability. The main tool for proving these results is the averaging theory. Recently the existence of some of these periodic orbits were detected numerically. © 2012 Elsevier B.V. All rights reserved.

AB - For the Rössler prototype-4 system ẋ=-y-z, ẏ=x, ż=αy(1-y)-βz we prove the existence of periodic orbits and study their stability or instability. The main tool for proving these results is the averaging theory. Recently the existence of some of these periodic orbits were detected numerically. © 2012 Elsevier B.V. All rights reserved.

KW - Averaging theory

KW - Periodic orbit

KW - Rössler system

U2 - https://doi.org/10.1016/j.physleta.2012.05.035

DO - https://doi.org/10.1016/j.physleta.2012.05.035

M3 - Article

VL - 376

SP - 2234

EP - 2237

IS - 33

ER -

Periodic orbits and their stability in the Rössler prototype-4 system

Abstract

Keywords

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