27 citations · 285 across the 42 of their papers we have counts for
26 papers · 1 filter
Weighted Birkhoff Averages Accelerate Data-Driven Methods
Maria Bou-Sakr-El-Tayar, Jason J. Bramburger, Matthew J. Colbrook
Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages c…
Data-Driven Stabilisation of Unstable Periodic Orbits of the Three-Body Problem
Owen M. Brook, Jason J. Bramburger, Davide Amato +1
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and…
On the lattice property of the Koopman operator spectrum
Jason J. Bramburger
The Koopman operator has become a celebrated tool in modern dynamical systems theory for analyzing and interpreting both models and datasets. The linearity of the Koopman operator…
Capturing the critical coupling of large random Kuramoto networks with graphons
Jason Bramburger, Matt Holzer
Collective oscillations and patterns of synchrony have long fascinated researchers in the applied sciences, particularly due to their far-reaching importance in chemistry, physics,…
Localized synchronous patterns in weakly coupled bistable oscillators
Erik Bergland, Jason J Bramburger, Bjorn Sandstede
Motivated by numerical continuation studies of coupled mechanical oscillators, we investigate branches of localized time-periodic solutions of one-dimensional chains of coupled osc…
Persistence of steady-states for dynamical systems on large networks
Jason J. Bramburger, Matt Holzer, Jackson Williams
The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the a…
Data-driven Discovery of Invariant Measures
Jason J. Bramburger, Giovanni Fantuzzi
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gat…
Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization
Jason J. Bramburger, Giovanni Fantuzzi
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for appro…
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…
Pattern Formation in Random Networks Using Graphons
Jason Bramburger, Matt Holzer
We study Turing bifurcations on one-dimensional random ring networks where the probability of a connection between two nodes depends on the distance between the two nodes. Our appr…
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…
Exact minimum speed of traveling waves in a Keller--Segel model
Jason J. Bramburger
In this paper we present a Keller--Segel model with logistic growth dynamics arising in the study of chemotactic pattern formation. We prove the existence of a minimum wave speed f…
Minimum wave speeds in monostable reaction-diffusion equations: sharp bounds by polynomial optimization
Jason J. Bramburger, David Goluskin
Many monostable reaction-diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are…
Isolas of multi-pulse solutions to lattice dynamical systems
Jason J. Bramburger
This work investigates the existence and bifurcation structure of multi-pulse steady-state solutions to bistable lattice dynamical systems. Such solutions are characterized by mult…
Stable Periodic Solutions to Lambda-Omega Lattice Dynamical Systems
Jason J. Bramburger
In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dy…
Ultracontractive Properties for Directed Graph Semigroups with Applications to Coupled Oscillators
Jason J. Bramburger
It is now well known that ultracontractive properties of semigroups with infinitesimal generator given by an undirected graph Laplacian operator can be obtained through an understa…
Rotating Wave Solutions to Lattice Dynamical Systems II: Persistence Results
Jason J. Bramburger
This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to…