Published Journal Articles
Phase Amplitude Reduction Methods
- D. Wilson. Data-driven model identification using forcing-induced limit cycles. Physica D. 459: Art. No. 134013, 2024.
- D. Wilson. Koopman operator inspired nonlinear system identification. SIAM Journal on Applied Dynamical Systems. 22(2):1445-1471, 2023.
- A. Dewanjee, S. Sahyoun, S. Djouadi, and D. Wilson. Data-driven inference of low order representations of observable dynamics
for an airfoil model. Physica D. 457: Art. No. 133941, 2024.
- T. Ahmed and D. Wilson. Phase-amplitude coordinate-based neural networks for inferring oscillatory dynamics. Journal of Nonlinear Science. 34(1): Art. No. 15, 2024.
- D. Wilson. A reduced order modeling framework for strongly perturbed nonlinear dynamical systems near arbitrary trajectory sets. SIAM Journal on Applied Dynamical Systems. 22(2):603-634, 2023.
- D. Wilson. A direct method approach for data-driven inference of high accuracy adaptive phase-isostable reduced order models. Physica D. 446: Art. No. 133675, 2023.
- T. Ahmed, A. Sadovnik, and D. Wilson Data-driven inference of low order isostable-coordinate-based dynamical models using neural networks. Nonlinear Dynamics. 111: 2501-2519, 2023.
- D. Wilson Data-driven identification of dynamical models using adaptive parameter sets. Chaos. 32(2): Art. No. 023118, 2022.
- D. Wilson. An adaptive phase-amplitude reduction framework without order epsilon constraints on inputs. SIAM Journal on Applied Dynamical Systems. 21(1): 204-230, 2022.
- D. Wilson Data-Driven inference of high-accuracy isostable-based dynamical models in response to external inputs. Chaos. 31(6): Art. No. 063137, 2021.
- D. Wilson. Degenerate isostable reduction for fixed-point and limit-cycle attractors with defective linearizations. Physical Review E. 103: Art. No. 022211, 2021.
- D. Wilson and S. Djouadi. Adaptive isostable reduction of nonlinear PDEs with time varying parameters. IEEE Control Systems Letters. 5(1): 187-192, 2021.
- D. Wilson. Phase-amplitude reduction far beyond the weakly perturbed paradigm. Physical Review E. 101: Art. No. 022220, 2020.
- D. Wilson A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems. Chaos. 30(1): Art. No. 013121, 2020.
- D. Wilson and B. Ermentrout Phase models beyond weak coupling. Physical Review Letters. 123(16): Art. No. 164101, 2019.
- B. Ermentrout, Y. Park, and D. Wilson Recent advances in coupled oscillator theory. Philosophical Transactions of the Royal Society A. 377: Art. No. 20190092, 2019.
- D. Wilson and B. Ermentrout. Augmented phase reduction of (not so) weakly perturbed coupled oscillators. SIAM Review. 61(2): 277-315, 2019.
- D. Wilson. Isostable reduction of oscillators with piecewise smooth dynamics and complex Floquet multipliers. Physical Review E. 99(2): Art. No. 022210, 2019.
- B. Monga, D. Wilson, T. Matchen, and J. Moehlis. Phase reduction and phase-based optimal control for biological systems: a tutorial. To Appear in Biological Cybernetics.
- D. Wilson and B. Ermentrout. An operational definition of phase characterizes the transient response of perturbed limit cycle oscillators. SIAM Journal on Applied Dynamical Systems. 17(4): 2516-2543, 2018
- D. Wilson and B. Ermentrout. Greater accuracy and broadened applicability of phase reduction using isostable coordinates. Journal of Mathematical Biology. 76(1-2):37-66, 2018.
- D. Wilson and J. Moehlis. Isostable reduction of periodic orbits. Physical Review E. 94(5): Art. No. 052213, 2016.
- D. Wilson and J. Moehlis. Determining individual phase response curves from aggregate population data. Physical Review E. 92: Art. No. 022902, 2015.
- G. S. Schmidt, D. Wilson, F. Allgower, and J. Moehlis. Selective averaging with application to phase reduction and neural control. Nonlinear Theory and Its Applications. IEICE 5(4): 424-435, 2014.
Stabilization of Periodic Orbits
- T. S. Das and D. Wilson. Data-driven phase-isostable reduction for optimal nonfeedback stabilization of cardiac alternans. Physical Review E. 103: Art. No. 052203, 2021.
- D. Wilson. Optimal open-loop desynchronization of neural oscillator populations. To Appear in Journal of Mathematical Biology.
- D. Wilson. Stabilization of weakly unstable fixed points as a common dynamical mechanism of high-frequency electrical stimulation. Scientific Reports. 10: 5922, 2020.
- D. Wilson. An optimal framework for nonfeedback stability control of chaos. SIAM Journal on Applied Dynamical Systems. 18(4): 1982-1999, 2019.
Control of Excitable Systems
- D. Wilson and J. Moehlis. Isostable reduction with applications to time-dependent partial differential equations. Physical Review E. 94(1): Art. No. 012211, 2016.
- D. Wilson and J. Moehlis. Extending phase reduction to excitable media: theory and applications. SIAM Review. 57(2): 201-222, 2015.
Applications to Cardiology
- T. S. Das and D. Wilson. Optimal Entrainment for Removal of Pinned Spiral Waves.. Physical Review E. 105(6): Art. No. 064213, 2022.
- D. Wilson, B. Ermentrout, J. Nemec, and G. Salama A model of cardiac ryanodine receptor gating predicts experimental Ca2+-dynamics and Ca2+-triggered arrhythmia in the long QT syndrome. Chaos. 27(9): Art. No. 093940, 2017.
- D. Wilson and B. Ermentrout. Stochastic Pacing inhibits Spatially Discordant Alternans. Biophysical Journal. 113(11): 2552-2572, 2017
- D. Wilson and J. Moehlis. Spatiotemporal control to eliminate cardiac alternans using isostable reduction. Physica D. 342: 32-44, 2017.
- D. Wilson and J. Moehlis. Towards a more efficient implementation of low energy antifibrillation pacing. PLoS One. 11(7): e0158239, 2016.
Applications to Neuroscience
- D. Wilson and J. Moehlis. Recent advances in the analysis and control of large populations of neural oscillators. To Appear in Annual Reviews in Control.
- A. B. Holt, D. Wilson, M. Shinn, J. Moehlis, and T. I. Netoff. Closed-loop approach to tuning deep brain stimulation parameters for Parkinson's disease. PLoS Computational Biology. 12(7): e1005011, 2016.
- D. Wilson and J. Moehlis. Clustered desynchronization from high-frequency deep brain stimulation. PLoS Computational Biology. 11(12): e1004673, 2015.
- D. Wilson and J. Moehlis. A Hamilton-Jacobi-Bellman approach for termination of seizure-like bursting. Journal of Computational Neuroscience. 37(2): 345-355, 2014.
- D. Wilson and J. Moehlis. Locally optimal extracellular stimulation for chaotic desynchronization of neural populations. Journal of Computational Neuroscience. 37(2): 243-257, 2014.
- D. Wilson and J. Moehlis. Optimal chaotic desynchronization for neural populations. SIAM Journal on Applied Dynamical Systems. 13(1): 276-305, 2014.
Synchronization and Entrainment
- K. Toth and D. Wilson Control of coupled neural oscillations using near-periodic inputs. Chaos. 32(3): Art. No. 033130, 2022.
- D. Wilson. Optimal control of oscillation timing and entrainment using large magnitude inputs: an adaptive phase-amplitude-coordinate-based approach.. SIAM Journal on Applied Dynamical Systems. 20(4): 1814-1843, 2021.
- Y. Park and D. Wilson. High-order accuracy computation of coupling functions for strongly coupled oscillators. SIAM Journal on Applied Dynamical Systems. 20(3): 1464-1484, 2021.
- T. Ahmed and D. Wilson Exploiting circadian memory to hasten recovery from circadian misalignment. Chaos. 31(7): Art. No. 073130, 2021.
- D. Wilson. Analysis of input-induced oscillations using the isostable coordinate framework. Chaos. 31: Art. No. 023131, 2021.
- D. Wilson, S. Faramarzi, J. Moehlis, M. R. Tinsley, and K. Showalter. Synchronization of heterogeneous oscillator populations in response to weak and strong coupling. Chaos. 28: Art. No. 123114, 2018.
- R. Snari, M. Tinsley, D. Wilson, S. Faramarzi, T. I. Netoff, J. Moehlis, and K. Showalter. Desynchronization of stochastically synchronized chemical oscillators. Chaos. 25(12): Art. No. 123116, 2015.
- D. Wilson, A.B. Holt, T. Netoff, and J. Moehlis. Optimal entrainment of heterogeneous noisy neurons. Frontiers in Neuroscience. 9: Art. No. 192, 2015.
- D. Wilson and J. Moehlis. An energy-optimal approach for entrainment of uncertain circadian oscillators. Biophysical Journal. 107(7): 1744-1755, 2014.
- D. Wilson and J. Moehlis. An energy-optimal methodology for synchronization of excitable media. SIAM Journal on Applied Dynamical Systems. 13(2): 994-957, 2014.
Patents
Refereed Conference Proceedings
News Articles