Publications

Publications

A collection of books, preprints, publications, refereed conference proceedings, conference reports, outreach and public interest articles and theses

1. J. Bramburger Data-Driven Methods for Dynamic Systems. Society for Industrial and Applied Math (SIAM), 2024
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1. E. Bergland, J. Bramburger, and B. Sandstede. Localized synchronous patterns in weakly coupled bistable oscillators.
2. M. Mignacca, S. Brugiapaglia, and J. Bramburger. Real-time motion detection using dynamic mode decomposition.
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3. J. Bramburger, D. Hill, and D. Lloyd. Localized multi-dimensional patterns.
4. J. Bramburger, M. Holzer, and J. Williams. Persistence of steady-states for dynamical systems on large networks.
5. A.M. Neuman and J. Bramburger. Transferability of graph neural networks using graphon and sampling theories.
6. J.N. Kutz, A. Rahman, M. Ebers, J. Koch, and J. Bramburger. Universal dynamics of damped-driven systems: The logistic map as a normal form for energy balance.
1. J. Bramburger and G. Fantuzzi. Data-driven discovery of invariant measures. Proceedings of the Royal Society A 480, (2024) 20230627
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2. D. Hill, J. Bramburger, and D. Lloyd. Dihedral rings of patterns emerging from a Turing bifurcation. Nonlinearity 37, (2024) 035015
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3. Z. Nicolaou and J. Bramburger. Complex localization mechanisms in networks of coupled oscillators: two case studies. Chaos 34, (2024) 013131
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4. J. Bramburger and G. Fantuzzi. Auxiliary functions as Koopman observables: Data-driven analysis of dynamical systems via polynomial optimization. Journal of Nonlinear Science 34, (2024) 8
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5. K. Kaheman, U. Fasel, J. Bramburger, B. Strom, J.N. Kutz, and S. Brunton. The experimental multi-arm pendulum on a cart: a benchmark system for chaos, learning, and control. HardwareX 15, (2023) e00465
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6. J. Bramburger and M. Holzer. Pattern formation in random networks using graphons. SIAM Journal on Mathematical Analysis 55, (2023) 2150-2185
7. A. Chernyavsky, J. Bramburger, G. Fantuzzi, and D. Goluskin. Convex relaxations of integral variational problems: pointwise dual relaxation and sum-of-squares optimization. SIAM Journal on Optimization 33, (2023) 481-512
8. D. Hill, J. Bramburger, and D. Lloyd. Approximate localised dihedral patterns near a Turing instability. Nonlinearity 36, (2023) 2567-2630
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9. K. Kaheman, J. Bramburger, J.N. Kutz, and S. Brunton. Saddle transport and chaos in the double pendulum. Nonlinear Dynamics 111, (2023) 7199-7233
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10. M. Tian, J. Bramburger, and B. Sandstede. Snaking bifurcations of localized patterns on ring lattices. IMA Journal of Applied Mathematics 86, (2021) 1112-1140
11. J. Bramburger, S. Brunton, and J.N. Kutz. Deep learning of conjugate mappings. Physica D 447, (2021) 133008
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12. J. Bramburger and C. Henderson. The speed of traveling waves in a FKPP-Burgers system. Archive for Rational Mechanics and Analysis 241, (2021) 643-681
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13. J. Bramburger. Isolas of multi-pulse solutions to lattice dynamical systems. Proceedings of the Royal Society of Edinburgh A 151, (2021) 916-952
14. J. Bramburger, J.N. Kutz, and S. Brunton. Data-driven stabilization of periodic orbits. IEEE Access 9, (2021) 43504-43521
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15. J. Bramburger. Exact minimum speed of traveling waves in a Keller-Segel model. Applied Mathematics Letters 111, (2021) 106594
16. J. Bramburger and D. Goluskin. Minimum wave speeds in monostable reaction-diffusion equations: sharp bounds by polynomial optimization. Proceedings of the Royal Society A 476, (2020) 20200450
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17. J. Bramburger, D. Dylewsky, and J.N. Kutz. Sparse identification of slow timescale dynamics. Physical Review E 102, (2020) 022204.
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18. J. Bramburger and B. Sandstede. Localized patterns in planar bistable weakly coupled lattice systems. Nonlinearity 33, (2020) 3500-3525.
19. J. Bramburger and B. Sandstede. Spatially localized structures in lattice dynamical systems. Journal of Nonlinear Science 30, (2020) 603-644.
20. J. Bramburger and J.N. Kutz. Poincaré maps for multiscale physics discovery and nonlinear Floquet theory. Physica D 408, (2020) 132497.
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21. J. Bramburger, J. Cuevas-Maraver, and P.G. Kevrekidis. Vortex pairs in the discrete nonlinear Schrodinger equation. Nonlinearity 33, (2020) 2159-2180.
22. J. Bramburger. Ultracontractive properties for directed graph semigroups with applications to coupled oscillators. Canadian Mathematical Bulletin 63, (2020) 13-30.
23. J. Bramburger. Stable periodic solutions to lambda-omega lattice dynamical systems. Journal of Differential Equations 268, (2020) 3201-3254.
24. S. Alexander, J. Bramburger, and E. McDonough. Dark disk substructure and superfluid dark matter. Physics Letters B 797, (2019) 134871.
25. J. Bramburger, D. Altschuler, C. Avery, T. Sangsawang, M. Beck, P. Carter, and B. Sandstede. Localized radial roll patterns in higher space dimensions. SIAM Journal on Applied Dynamical Systems 18, (2019) 1420-1453.
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26. J. Bramburger and F. Lutscher. Analysis of integrodifference equations with a separable dispersal kernel. Acta Applicandae Mathematicae 161, (2019) 127-151.
27. J. Bramburger. Rotating wave solutions to lattice dynamical systems II: Persistence results. Journal of Dynamics and Differential Equations 31, (2019) 499-536.
28. J. Bramburger. Rotating wave solutions to lattice dynamical systems I: The anti-continuum limit. Journal of Dynamics and Differential Equations 31, (2019) 469-498.
29. J. Bramburger. Stability of infinite systems of coupled oscillators via random walks on weighted graphs. Transactions of the American Mathematical Society 372, (2019) 1159-1192.
30. J. Bramburger, B. Dionne, and V.G. LeBlanc. Zero-Hopf bifurcation in the Van der Pol oscillator with delayed position and velocity feedback. Nonlinear Dynamics 78, (2014) 2959-2973.
1. J. Bramburger, S. Dahdah, and J. Forbes
  Synthesizing control laws from data using sum-of-squares optimization
  2024 IEEE Conference on Control Technology and Applications (CCTA) Newcastle upon Tyne, UK, 2024
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1. J. Bramburger
  Data-driven system analysis using polynomial optimization and the Koopman operator Oberwolfach Reports 35, (2024) 33-34.
2. J. Bramburger, C. Budd, J. Hu, and A. Wan
  Structured machine learning and timestepping for dynamical systems (24w5301) BIRS Report (2024).
3. J. Bramburger
  Localized patterns on graphs: The influence of dimension and topology on pattern formation Oberwolfach Reports 37, (2021) 16-17.
1. J. Bramburger
  The emerging utility of graphons in applied math SIAM News 56 (2023).
2. J. Bramburger
  Patterns and waves in theory, experiment, and application Snapshot of Modern Mathematics from Oberwolfach (2023).
1. J. Bramburger
  On the existence and stability of rotating wave solutions to lattice dynamical systems. Ph.D. Thesis, University of Ottawa 2017.
2. J. Bramburger
  Steady-state/Hopf interactions in the Van der Pol oscillator with delayed feedback. M.Sc. Thesis, University of Ottawa 2013.

Jason Bramburger

Assistant Professor

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