Christian Bick

Associate Professor
Department of Mathematics
Vrije Universiteit Amsterdam

OCIAM Visiting Research Fellow
Mathematical Institute
University of Oxford

Honorary Associate Professor
Department of Mathematics
University of Exeter

Visiting Fellow
Institute for Advanced Study
Technische Universität München

e-mail

research profiles

ORCiD Google Scholar arXiv Twitter/X


picture courtesy of A. Goriely

mail
Department of Mathematics
Vrije Universiteit Amsterdam
De Boelelaan 1111
1081 HV Amsterdam
The Netherlands
office
NU-9A35

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.

Open Positions

BeyondTheEdge PhD Position in Network Dynamical Systems (deadline June 15, 2024)

Projects

2024–2027 BeyondTheEdge: Higher-Order Networks and Dynamics
Marie SkÅ‚odowska–Curie Doctoral Network
2020–2023 Higher-order interactions and heteroclinic network dynamics
EPSRC New Investigator Award
2019–2023 Network Dynamical Systems with State-Dependent Interactions
Hans Fischer Fellowship
2015–2017 GECO: Dynamics of Phase Oscillator Networks with Generalized Coupling
Marie Curie Intra European Fellowship (IEF)

Books

C. Bick, P. Mulas, R. Mulas. Bear Networks. Zenodo, 2024 [ Zenodo ].

Publications

Preprints

  1. 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 ].
  2. 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 ].
  3. 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 ].
  4. C. Bick, T. Böhle, O. E. Omel'chenko. Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions. Submitted, 2023 [ arXiv ].
  5. C. Bick, T. Böhle, C. Kuehn. Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude. Submitted, 2023 [ arXiv ].

Journal Articles

  1. 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 ].
  2. 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 ].
  3. C. Bick, D. Sclosa. Dynamical Systems on Graph Limits and Their Symmetries. Journal of Dynamics and Differential Equations 2, 2024 [ article (open access), arXiv ].
  4. 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 ].
  5. 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 ].
  6. 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 ].
  7. M. I. Rabinovich, C. Bick, P. Varona. Beyond neurons and spikes: cognon, the hierarchical dynamical unit of thought. Cognitive Neurodynamics, 2023 [ article (open access) ].
  8. 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 ].
  9. 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 ].
  10. 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 ].
  11. 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 ].
  12. 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 ].
  13. 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 ].
  14. 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 ].
  15. P. Ashwin, C. Bick, C. Poignard. Dead zones and phase reduction of coupled oscillators. Chaos, 31(9):093132, 2021 [ article, arXiv ].
  16. 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 ].
  17. 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 ].
  18. C. Kuehn, C. Bick. A Universal Route to Explosive Phenomena. Science Advances, 7(16):eabe3824, 2021 [ article (open access), arXiv ].
  19. 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 ].
  20. 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) ].
  21. 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) ].
  22. 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 ].
  23. 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 ].
  24. 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 ].
  25. 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 ].
  26. 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 ].
  27. 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) ].
  28. 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 ].
  29. 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 ].
  30. C. Bick, M. J. Panaggio, E. A. Martens. Chaos in Kuramoto oscillator networks. Chaos, 28(7):071102, 2018 [ article, arXiv ].
  31. C. Bick. Heteroclinic switching between chimeras. Physical Review E, 97(5):050201(R), 2018 [ article, arXiv ].
  32. 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 ].
  33. 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 ].
  34. C. Bick, M. Field. Asynchronous networks: modularization of dynamics theorem. Nonlinearity, 30(2):595–621, 2017 [ article, arXiv ].
  35. C. Bick, M. Field. Asynchronous networks and event driven dynamics. Nonlinearity, 30(2):558–594, 2017 [ article (open access), arXiv ].
  36. E. A. Martens, C. Bick, M. J. Panaggio. Chimera states in two populations with heterogeneous phase lag. Chaos 26(9):094819, 2016 [ article, arXiv ].
  37. C. Bick, P. Ashwin, A. Rodrigues. Chaos in generically coupled phase oscillator networks with nonpairwise interactions. Chaos, 26(9):094814, 2016 [ article, arXiv ].
  38. 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 ].
  39. C. Bick, P. Ashwin. Chaotic Weak Chimeras and their Persistence in Coupled Populations of Phase Oscillators. Nonlinearity, 29(5):1468-1486, 2016 [ article, arXiv ].
  40. C. Bick, E. A. Martens. Controlling Chimeras. New Journal of Physics, 17(3):033030, 2015 [ article (open access), arXiv ].
  41. C. Bick, C. Kolodziejski, M. Timme. Controlling Chaos Faster. Chaos, 24(3):033138, 2014 [ article, arXiv ].
  42. C. Bick, C. Kolodziejski, M. Timme. Stalling Chaos Control Accelerates Convergence. New Journal of Physics, 15(6):063038, 2013 [ article (open access) ].
  43. 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 ].
  44. 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 ].
  45. 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 ].
  46. C. Bick, M. I. Rabinovich. On the occurrence of stable heteroclinic channels in Lotka–Volterra models. Dynamical Systems, 25(1):97–110, 2010 [ article ].
  47. 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)