On the global dynamics of the Newell–Whitehead system

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(x−dy), 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/).

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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  -