Integrability and zero-Hopf bifurcation in the Sprott A system

被引：7

作者：

Barreira, Luis ^{[1
]}

Llibre, Jaume ^{[2
]}

Valls, Claudia ^{[1
]}

机构：

[1] Univ Tecn Lisboa, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon, Portugal

[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2020年 / 162卷

基金：

欧盟地平线“2020”;

关键词：

Darboux integrability; Sprott A system; Zero-Hopf bifurcation; Averaging theory; CANONICAL DYNAMICS; CURVES;

D O I：

10.1016/j.bulsci.2020.102874

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The first objective of this paper is to study the Darboux integrability of the polynomial differential system (x) over dot = y, (y)over dot = -x - yz, (z)over dot = y(2) - 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. (C) 2020 Elsevier Masson SAS. All rights reserved.

引用

页数：16

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