Christian Bick
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![](pics/chris_m24.jpg)
mail
Department of Mathematics
Vrije Universiteit Amsterdam
De Boelelaan 1111
1081 HV Amsterdam
The Netherlands
office
NU-9A35
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Research Interests
Dynamical systems and applications: Dynamics of coupled oscillator networks.
Network dynamical systems with generalized, higher-order, and adaptive interactions.
Dynamics of asynchronous networks.
Projects
Books
C. Bick, P. Mulas, R. Mulas.
Bear Networks.
Zenodo, 2024
[ Zenodo ].
Publications
Preprints
- C. Bick, B. Rink, B. A. J. de Wolff.
When time delays and phase lags are not the same: higher-order phase reduction unravels delay-induced synchronization in oscillator networks.
Submitted, 2024
[ arXiv ].
- J. L. Ocampo-Espindola, I. Z. Kiss, C. Bick, K. C. A. Wedgwood.
Strong coupling yields abrupt synchronization transitions in coupled oscillators.
Submitted, 2024
[ arXiv ].
- C. G. Alexandersen, L. Douw, M. L. M. Zimmermann, C. Bick, A. Goriely.
Pseudo-craniotomy of a whole-brain model reveals tumor-induced alterations to neuronal dynamics in glioma patients.
Submitted, 2023
[ bioRxiv ].
Journal Articles
- C. Bick, T. Böhle, C. Kuehn.
Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude.
Journal of Nonlinear Science, 34:77, 2024.
[ article (open access),
arXiv ].
- C. Bick, T. Böhle, O. E. Omel'chenko.
Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions.
Journal of Physics: Complexity, 5:025026, 2024.
[ article (open access),
arXiv ].
- C. G. Alexandersen, A. Goriely, C. Bick.
Neuronal activity induces symmetry breaking in neurodegenerative disease spreading.
Journal of Mathematical Biology, 89:3, 2024.
[ article (open access),
bioRxiv ].
- C. Bick, S. von der Gracht.
Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.
Journal of Complex Networks, 12(2):cnae009, 2024
[ article (open access),
arXiv ].
- C. Bick, D. Sclosa.
Dynamical Systems on Graph Limits and Their Symmetries.
Journal of Dynamics and Differential Equations 2, 2024
[ article (open access),
arXiv ].
- B. Duchet, C. Bick, Á. Byrne.
Mean-field approximations with adaptive coupling for networks with spike-timing-dependent plasticity.
Neural Computation 35:1481–1528, 2023
[ article,
bioRxiv ].
- C. Bick, E. Gross, H. A. Harrington, M. T. Schaub.
What are higher-order networks?
SIAM Review 65(3):686–731, 2023
[ article (open access),
arXiv ].
- M. Aguiar, C. Bick, A. Dias.
Network Dynamics with Higher-Order Interactions: Coupled Cell Hypernetworks for Identical Cells and Synchrony.
Nonlinearity 36(9):4641–4673, 2023
[ article (open access),
arXiv ].
- M. I. Rabinovich, C. Bick, P. Varona.
Beyond neurons and spikes: cognon, the hierarchical dynamical unit of thought.
Cognitive Neurodynamics, 2023
[ article (open access) ].
- C. Bick, T. Böhle, C. Kuehn.
Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability and Bifurcations.
SIAM Journal on Applied Dynamical Systems, 22(3):1590–1638, 2023
[ article,
arXiv ].
- C. G. Alexandersen, W. de Haan, C. Bick, A. Goriely.
A multi-scale model explains oscillatory slowing and neuronal hyperactivity in Alzheimer's disease.
Journal of The Royal Society Interface, 20(198):20220607, 2023
[ article (open access),
bioRxiv ].
- O. Burylko, E. A. Martens, C. Bick.
Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators.
Chaos, 32(9):093109, 2022.
[ article (open access),
arXiv ].
- C. Bick, T. Böhle, C. Kuehn.
Multi-Population Phase Oscillator Networks with Higher-Order Interactions.
Nonlinear Differential Equations and Applications NoDEA 29:64, 2022
[ article (open access),
arXiv ].
-
J. Cabral, F. Castaldo, J. Vohryzek, V. Litvak, C. Bick, R. Lambiotte, K. Friston, M. L. Kringelbach, G. Deco.
Synchronization in the connectome: Metastable oscillatory modes emerge from interactions in the brain spacetime network.
Communications Physics 5:184, 2022
[ article (open access),
bioRxiv ].
- C. Kuehn, N. Berglund, C. Bick, M. Engel, T. Hurth, A. Iuorio, C. Soresina.
A General View on Double Limits in Differential Equations.
Physica D, 431:133105, 2022
[ article,
arXiv ].
- M. Salman, C. Bick, K. Krischer.
Bifurcations of Clusters and Collective Oscillations in Networks of Bistable Units.
Chaos 31(11):113140, 2021
[ article (open access),
arXiv ].
- P. Ashwin, C. Bick, C. Poignard.
Dead zones and phase reduction of coupled oscillators.
Chaos, 31(9):093132, 2021
[ article,
arXiv ].
- G. Weerasinghe, B. Duchet, C. Bick, R. Bogacz.
Optimal closed-loop deep brain stimulation using multiple independently controlled contacts.
PLOS Computational Biology, 17(8):e1009281, 2021
[ article (open access),
bioRxiv ].
- B. Duchet, F. Ghezzi, G. Weerasinghe, G. Tinkhauser, A. A. Kühn, P. Brown, C. Bick, R. Bogacz.
Average beta burst duration profiles provide a signature of dynamical changes between the ON and OFF medication states in Parkinson's disease.
PLOS Computational Biology, 17(7):e1009116, 2021
[ article (open access),
bioRxiv ].
- C. Kuehn, C. Bick.
A Universal Route to Explosive Phenomena.
Science Advances, 7(16):eabe3824, 2021
[ article (open access),
arXiv ].
- D. García-Selfa, G. Ghoshal, C. Bick, J. Pérez-Mercader, A. P. Muñuzuri.
Chemical oscillators synchronized via an active oscillating medium: dynamics and phase approximation model.
Chaos, Solitons & Fractals, 145:110809, 2021
[ article (open access),
arXiv ].
- B. Duchet, G. Weerasinghe, C. Bick, R. Bogacz.
Optimizing deep brain stimulation based on isostable amplitude in essential tremor patient models.
Journal of Neural Engineering, 18(4):046023, 2021
[ article (open access) ].
- M. Salman, C. Bick, K. Krischer.
Collective oscillations of globally coupled bistable, non-resonant components.
Physical Review Research, 2(4):043125, 2020
[ article (open access) ].
- A. Goriely, E. Kuhl, C. Bick.
Neuronal Oscillations on Evolving Networks: Dynamics, Damage, Degradation, Decline, Dementia, and Death.
Physical Review Letters, 125(12):128102, 2020
[ article,
arXiv ].
- C. Bick, M. Goodfellow, C. R. Laing, E. A. Martens.
Understanding the Dynamics of Biological and Neural Oscillator Networks through Exact Mean-Field Reductions: A Review.
Journal of Mathematical Neuroscience, 10(1):9, 2020
[ article (open access),
arXiv ].
- B. Duchet, G. Weerasinghe, H. Cagnan, P. Brown, C. Bick, R. Bogacz.
Phase-dependence of response curves to deep brain stimulation and their relationship: from essential tremor patient data to a Wilson–Cowan model.
Journal of Mathematical Neuroscience, 10(1):4, 2020
[ article (open access),
bioRxiv ].
- P. Ashwin, C. Bick, C. Poignard.
State-dependent effective interactions in oscillator networks through coupling functions with dead zones.
Philosophical Transactions of the Royal Society A, 377(2160):20190042, 2019
[ article (open access),
arXiv ].
- G. Weerasinghe, B. Duchet, H. Cagnan, P. Brown, C. Bick, R. Bogacz.
Predicting the effects of deep brain stimulation using a reduced coupled oscillator model.
PLOS Computational Biology, 15(8):e1006575, 2019
[ article (open access),
bioRxiv ].
- J. L. Ocampo-Espindola, C. Bick, I. Z. Kiss.
Weak Chimeras in Modular Electrochemical Oscillator Networks.
Frontiers in Applied Mathematics and Statistics, 5:38, 2019
[ article (open access) ].
- C. Bick, A. Lohse.
Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks.
Journal of Nonlinear Science, 29(6):2571–2600, 2019
[ article (open access),
arXiv ].
- C. Bick.
Heteroclinic Dynamics of Localized Frequency Synchrony: Heteroclinic Cycles for Small Populations.
Journal of Nonlinear Science, 29(6):2547–2570, 2019
[ article (open access),
arXiv ].
- C. Bick, M. J. Panaggio, E. A. Martens.
Chaos in Kuramoto oscillator networks.
Chaos, 28(7):071102, 2018
[ article,
arXiv ].
- C. Bick.
Heteroclinic switching between chimeras.
Physical Review E, 97(5):050201(R), 2018
[ article,
arXiv ].
- C. Bick, M. Sebek, I. Z. Kiss.
Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions.
Physical Review Letters, 119(16):168301, 2017
[ article,
arXiv ].
- C. Bick.
Isotropy of Angular Frequencies and Weak Chimeras With Broken Symmetry.
Journal of Nonlinear Science, 27(2):605–626, 2017
[ article (open access),
arXiv ].
- C. Bick, M. Field.
Asynchronous networks: modularization of dynamics theorem.
Nonlinearity, 30(2):595–621, 2017
[ article,
arXiv ].
- C. Bick, M. Field.
Asynchronous networks and event driven dynamics.
Nonlinearity, 30(2):558–594, 2017
[ article (open access),
arXiv ].
- E. A. Martens, C. Bick, M. J. Panaggio.
Chimera states in two populations with heterogeneous phase lag.
Chaos 26(9):094819, 2016
[ article,
arXiv ].
- C. Bick, P. Ashwin, A. Rodrigues.
Chaos in generically coupled phase oscillator networks with nonpairwise interactions.
Chaos, 26(9):094814, 2016
[ article,
arXiv ].
- P. Ashwin, C. Bick, O. Burylko.
Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling.
Frontiers in Applied Mathematics and Statistics, 2:7, 2016
[ article (open access),
arXiv ].
- C. Bick, P. Ashwin.
Chaotic Weak Chimeras and their Persistence in Coupled Populations of Phase Oscillators.
Nonlinearity, 29(5):1468-1486, 2016
[ article,
arXiv ].
- C. Bick, E. A. Martens.
Controlling Chimeras.
New Journal of Physics, 17(3):033030, 2015
[ article (open access),
arXiv ].
- C. Bick, C. Kolodziejski, M. Timme.
Controlling Chaos Faster.
Chaos, 24(3):033138, 2014
[ article,
arXiv ].
- C. Bick, C. Kolodziejski, M. Timme.
Stalling Chaos Control Accelerates Convergence.
New Journal of Physics, 15(6):063038, 2013
[ article (open access) ].
- C. Bick, M. Timme, C. Kolodziejski.
Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed.
SIAM Journal on Applied Dynamical Systems, 11(4):1310–1324, 2012
[ article,
arXiv ].
- M. I. Rabinovich, V. S. Afraimovich, C. Bick, P. Varona.
Information flow dynamics in the brain.
Physics of Life Reviews, 9(1):51–73, 2012
[ article ].
- C. Bick, M. Timme, D. Paulikat, D. Rathlev, P. Ashwin.
Chaos in Symmetric Phase Oscillator Networks.
Physical Review Letters, 107(24):244101, 2011
[ article,
arXiv ].
- C. Bick, M. I. Rabinovich.
On the occurrence of stable heteroclinic channels in Lotka–Volterra models.
Dynamical Systems, 25(1):97–110, 2010
[ article ].
- C. Bick, M. I. Rabinovich.
Dynamical Origin of the Effective Storage Capacity in the Brain's Working Memory.
Physical Review Letters, 103(21):218101, 2009.
[ article ].
Teaching
Vrije Universiteit Amsterdam
Dynamical Systems (Spring 2021/22, 2022/23, 2023/24) |
MNW Mathematical Methods (Winter 2020/21, 2021/22, 2022/23, 2023/24) |
University of Exeter
MTH3024/ECM3724/ECMM450: Stochastic Processes (Winter 2017/18, 2018/19, 2019/20) |
ECMM718: Dynamical Systems and Chaos (Winter 2014/15, 2015/16) |
ECM3736: Research in the Mathematical Sciences, Geometry substream (Winter 2011/12) |
University of Oxford
InFoMM Core 4: Modelling, analysis and computation of discrete real world problems (Fall 2016/17, 2017/18) |
InFoMM ModCase: Modelling Case Studies (Winter 2016/17) |
Rice University
MATH 211: Ordinary Differential Equations and Linear Algebra (Fall 2014/15) |
MATH 435: Dynamical Systems (Spring 2013/14) |
Georg–August–Universität Göttingen
Seminar: Machine Learning (Fall 2012/13) |
Seminar: Information Theory and Dynamical Systems (Fall 2011/12) |
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