21 citations · 94 across the 6 of their papers we have counts for
15 papers
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…
Snaking bifurcations of localized patterns on ring lattices
Moyi Tian, Jason J. Bramburger, Bjorn Sandstede
We study the structure of stationary patterns in bistable lattice dynamical systems posed on rings with a symmetric coupling structure in the regime of small coupling strength. We…
Deep Learning of Conjugate Mappings
Jason J. Bramburger, Steven L. Brunton, J. Nathan Kutz
Despite many of the most common chaotic dynamical systems being continuous in time, it is through discrete time mappings that much of the understanding of chaos is formed. Henri Po…
Data-Driven Stabilization of Periodic Orbits
Jason J. Bramburger, J. Nathan Kutz, Steven L. Brunton
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed…