Integrability and zero-Hopf bifurcation in the Sprott A system

Luis Barreira; Jaume Llibre; Claudia Valls

doi:10.1016/j.bulsci.2020.102874

Integrability and zero-Hopf bifurcation in the Sprott A system

Luis Barreira, Jaume Llibre^*, Claudia Valls

^*Corresponding author for this work

Department of Mathematics

University of Lisbon

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

8 Citations (Scopus)

Abstract

The first objective of this paper is to study the Darboux integrability of the polynomial differential system x˙=y,y˙=−x−yz,z˙=y²−a and the second one is to show that for a>0 sufficiently small this model exhibits one small amplitude periodic solution that bifurcates from the origin of coordinates when a=0. This model was introduced by Hoover as the first example of a differential equation with a hidden attractor and it was used by Sprott to illustrate a differential equation having a chaotic behavior without equilibrium points, and now this system is known as the Sprott A system.

Original language	English
Article number	102874
Number of pages	16
Journal	Bulletin des Sciences Mathematiques
Volume	162
DOIs	https://doi.org/10.1016/j.bulsci.2020.102874
Publication status	Published - Sept 2020

Keywords

Averaging theory
Darboux integrability
Sprott A system
Zero-Hopf bifurcation

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title = "Integrability and zero-Hopf bifurcation in the Sprott A system",

abstract = "The first objective of this paper is to study the Darboux integrability of the polynomial differential system x˙=y,y˙=−x−yz,z˙=y2−a and the second one is to show that for a>0 sufficiently small this model exhibits one small amplitude periodic solution that bifurcates from the origin of coordinates when a=0. This model was introduced by Hoover as the first example of a differential equation with a hidden attractor and it was used by Sprott to illustrate a differential equation having a chaotic behavior without equilibrium points, and now this system is known as the Sprott A system.",

keywords = "Averaging theory, Darboux integrability, Sprott A system, Zero-Hopf bifurcation",

author = "Luis Barreira and Jaume Llibre and Claudia Valls",

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year = "2020",

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AU - Barreira, Luis

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2020/9

Y1 - 2020/9

N2 - The first objective of this paper is to study the Darboux integrability of the polynomial differential system x˙=y,y˙=−x−yz,z˙=y2−a and the second one is to show that for a>0 sufficiently small this model exhibits one small amplitude periodic solution that bifurcates from the origin of coordinates when a=0. This model was introduced by Hoover as the first example of a differential equation with a hidden attractor and it was used by Sprott to illustrate a differential equation having a chaotic behavior without equilibrium points, and now this system is known as the Sprott A system.

AB - The first objective of this paper is to study the Darboux integrability of the polynomial differential system x˙=y,y˙=−x−yz,z˙=y2−a and the second one is to show that for a>0 sufficiently small this model exhibits one small amplitude periodic solution that bifurcates from the origin of coordinates when a=0. This model was introduced by Hoover as the first example of a differential equation with a hidden attractor and it was used by Sprott to illustrate a differential equation having a chaotic behavior without equilibrium points, and now this system is known as the Sprott A system.

KW - Averaging theory

KW - Darboux integrability

KW - Sprott A system

KW - Zero-Hopf bifurcation

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DO - 10.1016/j.bulsci.2020.102874

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SN - 0007-4497

VL - 162

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

M1 - 102874

ER -

Integrability and zero-Hopf bifurcation in the Sprott A system

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Keywords

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