21 citations · 156 across the 29 of their papers we have counts for
6 papers · 1 filter
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…
The speed of traveling waves in a FKPP-Burgers system
Jason J. Bramburger, Christopher Henderson
We consider a coupled reaction-advection-diffusion system based on the Fisher-KPP and Burgers equations. These equations serve as a one-dimensional version of a model for a reactin…
Sparse Identification of Slow Timescale Dynamics
Jason J. Bramburger, Daniel Dylewsky, J. Nathan Kutz
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and appr…
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…