3 papers
nlin.PS2026
Global bifurcation of localised 2D patterns emerging from spatial heterogeneity
Dan J. Hill, David J. B. Lloyd, Matthew R. Turner
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations contai…
nlin.PS2025
Localized Patterns
Jason J. Bramburger, Dan J. Hill, David J. B. Lloyd
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-under…
math.DS2024
The role of spatial dimension in the emergence of localised radial patterns from a Turing instability
Dan J. Hill
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We pro…