Publications

Research with Links Pfeil

Preprints & Work in Progress

  • "Network topology near criticality in adaptive epidemics"
    L. Horstmeyer, C. Kuehn and S. Thurner
  • "Pattern formation in the doubly-nonlocal Fisher-KPP equation"
    C. Kuehn and P. Tkachov
  • "A gradient flow formulation for the stochastic Amari model"
    C. Kuehn and J. Tölle
  • "Rigorous validation of stochastic transition paths"
    M. Breden and C. Kuehn
  • "Pathwise mild solutions for quasilinear stochastic partial differential equations"
    C. Kuehn and A. Neamtu
  • "Towards sample path estimates for fast-slow stochastic partial differential equations"
    M.V. Gnann, C. Kuehn and A. Pein
  • "A note on kernel methods for multiscale systems with critical transitions"
    B. Hamzi, C. Kuehn and S. Mohamed
  • "Smoluchowski's coagulation equation with forcing"
    C. Kuehn and S. Throm
  • "Scaling laws and warning signs for bifurcations of SPDEs"
    C. Kuehn and F. Romano
  • "Validity of amplitude equations for non-local non-linearities"
    C. Kuehn and S. Throm
  • "Combined error estimates for local fluctuations of SPDEs"
    C. Kuehn and P. Kürschner

Journal Publications

  • J46
    "Analysis and predictability for tipping points with leading-order nonlinear terms"
    F. Romano and C. Kuehn
    International Journal of Bifurcation and Chaos, accepted / to appear, 2018
  • J45
    "Early-warning signals for bifurcations in random dynamical systems with bounded noise"
    C. Kuehn, G. Malavolta and M. Rasmussen
    Journal of Mathematical Analysis and Applications, Vol. 464, pp. 58–77, 2018
  • J44
    "Tracking particles in flows near invariant manifolds via balance functions"
    C. Kuehn, F. Romano and H. Kuhlmann
    Nonlinear Dynamics, Vol. 92, No. 3, pp. 983-1000, 2018
  • J43
    "Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem"
    A. Iuorio, C. Kuehn and P. Szmolyan
    Discrete and Continuous Dynamical Systems S, accepted / to appear, 2018
  • J42
    "Stochastic mixed-mode oscillations in a three-species predator-prey model"
    S. Sadhu and C. Kuehn
    Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 28, No. 3, 033606, 2018
  • J41
    "Quenched noise and nonlinear oscillations in bistable multiscale systems"
    C. Kuehn
    EPL (Europhysics Letters), Vol. 120, 10001, 2017
  • J40
    "Generalized play hysteresis operators as limits of fast-slow systems"
    C. Kuehn and C. Münch
    SIAM Journal on Applied Dynamical Systems, Vol. 16, No. 3, pp. 1650-1685, 2017
  • J39
    "Model spaces of regularity structures for space-fractional SPDEs"
    N. Berglund and C. Kuehn
    Journal of Statistical Physics, Vol. 168, No. 2, pp. 331-368, 2017
  • J38
    "Uncertainty transformation via Hopf bifurcation in fast-slow systems"
    C. Kuehn
    Proceedings of the Royal Society A, Vol. 473, 20160346, 2017
  • J37
    "Continuation of probability density functions using a generalized Lyapunov approach"
    S. Baars, J.P. Viebahn, T.E. Mulder, C. Kuehn, F.W. Wubs and H.A. Dijkstra
    Journal of Computational Physics, Vol. 336, No. 1, pp. 627–643, 2017
  • J36
    "A meeting point of entropy and bifurcations in cross-diffusion herding"
    A. Jüngel, C. Kuehn and L. Trussardi
    European Journal of Applied Mathematics, Vol. 28, No. 2, pp. 317-356, 2017
  • J35
    "A dynamical systems approach for the contact-line singularity in thin-film flows"
    F.B. Belgacem, M.V. Gnann and C. Kuehn
    Nonlinear Analysis A: Theory, Methods & Applications, Vol. 144, pp. 204-235, 2016
  • J34
    "Heterogeneous population dynamics and scaling laws near epidemic outbreaks"
    A. Widder and C. Kuehn
    Mathematical Biosciences and Engineering, Vol. 13, No. 5, pp. 1093-1118, 2016
  • J33
    "Regularity structures and renormalisation of Fitzhugh-Nagumo SPDEs in three space dimensions"
    N. Berglund and C. Kuehn
    Electronic Journal of Probability, Vol. 21, No. 18, pp. 1-48, 2016 [erratum]
  • J32
    "A remark on geometric desingularization of a non-hyperbolic point using hyperbolic space"
    C. Kuehn
    Journal of Physics: Conference Series, Vol. 727, 012008, 2016
  • J31
    "Numerical continuation and SPDE stability for the 2D cubic-quintic Allen-Cahn equation"
    C. Kuehn
    SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, No. 1, pp. 762-789, 2015
  • J30
    "Predictability of critical transitions"
    X. Zhang, C. Kuehn and S. Hallerberg
    Physical Review E, Vol. 92, 052905, 2015
  • J29
    "Traveling waves for bistable evolution equations with nonlocal-diffusion"
    F. Achleitner and C. Kuehn
    Advances in Differential Equations, Vol. 20, No. 9-10, pp. 887-936, 2015
  • J28
    "Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs" C. Kuehn Applied Mathematics and Computation, Vol. 266, pp. 656-674, 2015
  • J27
    "Multiscale geometry of the Olsen model and non-classical relaxation oscillations"
    C. Kuehn and P. Szmolyan
    Journal of Nonlinear Science, Vol. 25, No. 3, pp. 583-629, 2015
  • J26
    "Early-warning signs for saddle-escape transitions in complex networks"
    C. Kuehn, G. Zschaler and T. Gross
    Scientific Reports, Vol. 5, 13190, 2015 [download paper + correctly-formatted SI here]
  • J25
    "From random Poincaré maps to stochastic mixed-mode-oscillation patterns"
    N. Berglund, B. Gentz and C. Kuehn
    Journal of Dynamics and Differential Equations, Vol. 27, No. 1, pp. 83-136, 2015
  • J24
    "Critical slowing down governs the transition to neuron spiking"
    C. Meisel, A. Klaus, C. Kuehn and D. Plenz
    Plos Computational Biology, Vol. 11, No. 2, e1004097, 2015
  • J23
    "Analysis and numerics of travelling waves for asymmetric fractional reaction-diffusion equations"
    F. Achleitner and C. Kuehn
    Communications in Applied and Industrial Mathematics, Vol. 6, No. 2, 2015
  • J22
    "On bounded positive stationary solutions for a nonlocal Fisher-KPP equation"
    F. Achleitner and C. Kuehn
    Nonlinear Analysis A: Theory, Methods & Applications, Vol. 112, pp. 15-29, 2015
  • J21
    "Early-warning signs for pattern formation in stochastic partial differential equations"
    K. Gowda and C. Kuehn
    Communications in Nonlinear Science and Numerical Simulation, Vol. 22, No. 1, pp. 55-69, 2015
  • J20
    "Normal hyperbolicity and unbounded critical manifolds"
    C. Kuehn
    Nonlinearity, Vol. 27, No. 6, pp. 1351-1366, 2014
  • J19
    "Critical transitions in social network activity"
    C. Kuehn, E. Martens and D. Romero
    Journal of Complex Networks, Vol. 2, No. 2, pp. 141-152, 2014 [see also: OUP Blog]
  • J18
    "Large deviations for nonlocal stochastic neural fields"
    C. Kuehn and M. Riedler
    Journal of Mathematical Neuroscience, Vol. 4, No. 1, pp. 1-33, 2014
  • J17
    "A mathematical framework for critical transitions: normal forms, variance and applications"
    C. Kuehn
    Journal of Nonlinear Science, Vol. 23, No. 3, pp. 457-510, 2013
  • J16
    "Nonlocal generalized models of predator-prey systems"
    C. Kuehn and T. Gross
    Discrete and Continuous Dynamical Systems B, Vol. 18, No. 3, pp. 693-720, 2013
  • J15
    "Warning signs for wave speed transitions of noisy Fisher-KPP invasion fronts"
    C. Kuehn
    Theoretical Ecology, Vol. 6, No. 3, pp. 295-308, 2013
  • J14
    "Dynamical analysis of evolution equations in generalized models"
    C. Kuehn, S. Siegmund and T. Gross
    IMA Journal of Applied Mathematics, Vol. 78, No. 5, pp. 1051-1077, 2013
  • J13
    "Deterministic continuation of stochastic metastable equilibria via Lyapunov equations and ellipsoids"
    C. Kuehn
    SIAM Journal on Scientific Computing, Vol. 34, No. 3, pp. A1635-A1658, 2012
  • J12
    "Mixed-mode oscillations with multiple time scales"
    M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. Osinga and M. Wechselberger
    SIAM Review, Vol. 54, No. 2, pp. 211-288, 2012
  • J11
    "Time-scale and noise optimality in self-organized critical adaptive networks"
    C. Kuehn
    Physical Review E, Vol. 85, No. 2, 026103, 2012
  • J10
    "Hunting French ducks in a noisy environment"
    N. Berglund, B. Gentz and C. Kuehn
    Journal of Differential Equations, Vol. 252, No. 9, pp. 4786-4841, 2012
  • J9
    "Scaling effects and spatio-temporal multilevel dynamics in epileptic seizures"
    C. Meisel and C. Kuehn
    Plos ONE, Vol. 7, No. 2, e30371, 2012
  • J8
    "On decomposing mixed-mode oscillations and their return maps"
    C. Kuehn
    Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 21, No. 3, 033107, 2011
  • J7
    "A mathematical framework for critical transitions: bifurcations, fast-slow systems and stochastic dynamics"
    C. Kuehn
    Physica D: Nonlinear Phenomena, Vol. 240, No. 12, pp. 1020-1035, 2011
  • J6
    "Connecting fast-slow systems and Conley index theory via transversality"
    C. Kuehn
    Electronic Journal of Differential Equations, Vol. 2010, No. 106, pp. 1-20, 2010
  • J5
    "Homoclinic orbits of the Fitzhugh-Nagumo equation: bifurcations in the full system''
    J. Guckenheimer and C. Kuehn
    SIAM Journal on Applied Dynamical Systems, Vol. 9, No. 1, pp. 138-153, 2010
  • J4
    "From first Lyapunov coefficients to maximal canards"
    C. Kuehn
    International Journal of Bifurcation and Chaos, Vol. 20, No. 5, pp. 1467-1475, 2010
  • J3
    "Computing slow manifolds of saddle-type"
    J. Guckenheimer and C. Kuehn
    SIAM Journal on Applied Dynamical Systems, Vol. 4, No. 3, pp. 854-879, 2009
  • J2
    "Homoclinic orbits of the Fitzhugh-Nagumo equation: the singular limit''
    J. Guckenheimer and C. Kuehn
    Discrete and Continuous Dynamical Systems S, Vol. 2, No. 4, pp. 851-872, 2009
  • J1
    "Scaling of saddle-node bifurcations: degeneracies and rapid quantitative changes"
    C. Kuehn
    Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 4, 045101, 2009

Books

  • B2
    "PDE Dynamics: An Introduction", C. Kuehn, SIAM, to appear 2019
  • B1
    "Multiple Time Scale Dynamics", C. Kuehn, Springer, 2015

    Reviews: DSWeb / Mathscinet / SIAM Review / Zentralblatt

Book Chapters & Reviews

  • C1
    "Moment closure - A brief review"
    C. Kuehn
    in: Control of Self-Organizing Complex Systems (editors: E. Schöll, S. Klapp & P. Hövel), Springer, pp. 253-271, 2016
  • R1
    "A numerical framework to understand transitions in high-dimensional stochastic dynamical systems"
    H.A. Dijkstra, A. Tantet, J. Viebahn, E. Mulder, M. Hebbink, D. Castellane, H. van der Pol, J. Frank, S. Baars, F. Wubs, M. Chekroun and C. Kuehn
    Dynamics and Statistics of the Climate System, Vol. 1, No. 1, dzw003 (review paper), 2016

Other Publications

  • L1
    "Dynamical Systems II: A Concise Graduate Course"
    C. Kuehn
    AMS Open Math Notes, 101pp., 2017
  • V1
    Book Review of "Network Science" (by A.-L. Barabasi)preprint
    C. Kuehn
    SIAM Activity Group, DSWeb Magazine, April 2017
  • AC
    "Addenda and Corrigenda to Journal Publications"
    C. Kuehn

  • T4
    "Multiscale dynamical systems: analysis and numerics"
    C. Kuehn
    Habilitation: Vienna University of Technology, 2016
  • E1
    "The curse of instability"
    C. Kuehn
    Complexity, (section: 'Simply Complex'), Vol. 20, No. 6, pp. 9-14, 2015
  • T3
    "Multiple time scale dynamics with two fast variables and one slow variable"
    C. Kuehn
    Ph.D. thesis: Cornell University, 2010
  • T2
    "Introduction to potential theory via applications"
    C. Kuehn
    Part III essay: University of Cambridge, 2006
  • T1
    "Stability analysis of nonlinear subdivision schemes"
    C. Kuehn
    B.Sc. thesis: Jacobs University, 2005
 
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