Journal of Nonlinear Mathematical Physics

Volume 26, Issue 4, July 2019, Pages 569 - 578

On the global dynamics of the Newell–Whitehead system

Authors
Claudia Valls
Departamento de Matematica, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais 1049–001, Lisboa, Portugal,cvalls@math.ist.utl.pt
Received 18 November 2018, Accepted 22 May 2019, Available Online 9 July 2019.
DOI
10.1080/14029251.2019.1640466How to use a DOI?
Keywords
Global dynamics; Poincaré compactification; Newell–Whitehead system; invariant algebraic curve; invariant
Abstract

In this paper by using the Poincaré compactification in ℝ3 we make a global analysis of the model x′ = z, y′ = b(xdy), z′ = x(x2 −1)+y+cz with b ∈ ℝ and c, d ∈ ℝ+, here known as the three-dimensional Newell–Whitehead system. We give the complete description of its dynamics on the sphere at infinity. For some values of the parameters this system has invariant algebraic surfaces and for these values we provide the dynamics of the system restricted to these surfaces and its global phase portrait in the Poincaré ball. We also include the description of the α-limit and ω-limit set of its orbits in the Poincaré ball including its boundary, that is, in the compactification of ℝ3 with the sphere at the infinity. We recall that the restricted systems are not analytic and so in this paper we overcome this difficulty by using the blow-up technique.

Copyright
© 2019 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)
View full text (HTML)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
26 - 4
Pages
569 - 578
Publication Date
2019/07/09
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2019.1640466How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Claudia Valls
PY  - 2019
DA  - 2019/07/09
TI  - On the global dynamics of the Newell–Whitehead system
JO  - Journal of Nonlinear Mathematical Physics
SP  - 569
EP  - 578
VL  - 26
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1640466
DO  - 10.1080/14029251.2019.1640466
ID  - Valls2019
ER  -