On the global dynamics of the Newell–Whitehead system
- 10.1080/14029251.2019.1640466How to use a DOI?
- Global dynamics; Poincaré compactification; Newell–Whitehead system; invariant algebraic curve; invariant
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.
- © 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 -