27 citations · 285 across the 42 of their papers we have counts for
6 papers · 2 filters
Dihedral rings of patterns emerging from a Turing bifurcation
Dan J. Hill, Jason J. Bramburger, David J. B. Lloyd
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is kno…
Saddle Transport and Chaos in the Double Pendulum
Kadierdan Kaheman, Jason J. Bramburger, J. Nathan Kutz +1
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a pr…
Localized patterns in planar bistable weakly coupled lattice systems
Jason J. Bramburger, Bjorn Sandstede
Localized planar patterns in spatially extended bistable systems are known to exist along intricate bifurcation diagrams, which are commonly referred to as snaking curves. Their an…
Spatially Localized Structures in Lattice Dynamical Systems
Jason J. Bramburger, Bjorn Sandstede
We investigate stationary, spatially localized patterns in lattice dynamical systems that exhibit bistability. The profiles associated with these patterns have a long plateau where…
Localized radial roll patterns in higher space dimensions
Jason J. Bramburger, Dylan Altschuler, Chloe I. Avery +4
Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the len…
Approximate localised dihedral patterns near a Turing instability
Dan J. Hill, Jason J. Bramburger, David J. B. Lloyd
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathemati…