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Localized synchronous patterns in weakly coupled bistable oscillator systems

https://doi.org/10.1016/j.physd.2025.134537

Bergland, Erik; Bramburger, Jason J; Sandstede, Björn (February 2025, Physica D: Nonlinear Phenomena)

Free, publicly-accessible full text available February 1, 2026
The Speed of Traveling Waves in a FKPP-Burgers System

https://doi.org/10.1007/s00205-021-01660-5

Bramburger, Jason J.; Henderson, Christopher (August 2021, Archive for Rational Mechanics and Analysis)

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Snaking bifurcations of localized patterns on ring lattices

https://doi.org/10.1093/imamat/hxab023

Tian, Moyi; Bramburger, Jason J; Sandstede, Björn (June 2021, IMA Journal of Applied Mathematics)
null (Ed.)
Abstract 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 show that sparse coupling (for instance, nearest-neighbour or next-nearest-neighbour coupling) and all-to-all coupling lead to significantly different solution branches. In particular, sparse coupling leads to snaking branches with many saddle-node bifurcations, while all-to-all coupling leads to branches with six saddle nodes, regardless of the size of the number of nodes in the graph.
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Localized patterns in planar bistable weakly coupled lattice systems

https://doi.org/10.1088/1361-6544/ab7d1e

Bramburger, Jason J; Sandstede, Björn (July 2020, Nonlinearity)

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Spatially Localized Structures in Lattice Dynamical Systems

https://doi.org/10.1007/s00332-019-09584-x

Bramburger, Jason J.; Sandstede, Björn (April 2020, Journal of Nonlinear Science)

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Localized Radial Roll Patterns in Higher Space Dimensions

https://doi.org/10.1137/18M1218728

Bramburger, Jason J.; Altschuler, Dylan; Avery, Chloe I.; Sangsawang, Tharathep; Beck, Margaret; Carter, Paul; Sandstede, Björn (January 2019, SIAM Journal on Applied Dynamical Systems)

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