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Full Publication List:


       

    Preprints & Work in Progress:

     

    P08
    "Slow manifolds for infinite-dimensional evolution equations"



    F. Hummel and C. Kuehn





    P07c
    "Blow-up analysis of fast-slow PDEs with loss of hyperbolicity"



    M. Engel and C. Kuehn





    P07b
    "Graphop mean-field limits for Kuramoto-type models"



    M.-A. Gkogkas and C. Kuehn





    P06b
    "Random attractors via pathwise mild solutions for stochastic parabolic evolution equations"



    C.Kuehn, A. Neamtu and S. Sonner






    P06a
    "Metastable speeds in the fractional Allen-Cahn equation"



    F. Achleitner, C.Kuehn, M. Melenk and A. Rieder






    P04
    "Traveling wave dynamics for Allen-Cahn equations with strong irreversibility"



    G. Akagi, C.Kuehn and K.-I. Nakamura






    P03b
    "Homogenization of fully-coupled chaotic fast-slow systems via intermediate stochastic regularization"



    M. Engel, M.-A. Gkogkas and C. Kuehn





    P03a
    "Travelling waves for discrete stochastic bistable equations"


    C. Geldhauser and C. Kuehn





    P02d "A universal route to explosive phenomena"


    C. Kuehn and C. Bick





    P02c
    "Multiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations"



    K. Eichinger, M. Gnann and C. Kuehn





    P02b
    "Numerical continuation for fractional PDEs: sharp teeth and bloated snakes"



    N. Ehstand, C. Kuehn and C. Soresina





    P11d
    "Controlling canard cycles"



    H. Jardon Kojakhmetov and C. Kuehn





    P11c
    "A random dynamical systems perspective on isochronicity for stochastic oscillations"



    M. Engel and C. Kuehn





    P11b
    "Predicting sparse circle maps from their dynamics"


    F. Krahmer, C. Kuehn and N. Sissouno






    P10
    "On the influence of cross-diffusion in pattern formation"



    M. Breden, C. Kuehn and C. Soresina






    P07a
    "Discretized fast-slow systems with canard points in two dimensions"



    M. Engel, C. Kuehn, M. Petrera and Y. Suris






    P11a
    "Rough center manifolds"



    C. Kuehn and A. Neamtu





        Journal Publications:  

    J77
    "A geometric analysis of the SIR, SIRS and SIRWS epidemiological models"


    H. Jardon Kojakhmetov, C. Kuehn, A. Pugliese and M. Sensi


    Nonlinear Analysis: Real World Applications, accepted / to appear, 2020






    J76
    "Global martingale solutions for quasilinear SPDEs via the boundedness-by-entropy method"


    G. Dhariwal, F. Huber, A. Jüngel, C. Kuehn and A. Neamtu


    Annals de l'Institut Henri Poincaré (B) Probabilités et Statistiques, accepted / to appear, 2020






    J75
    "Coupled dynamics on hypergraphs: master stability of steady states and synchronization"


    R. Mulas, C. Kuehn and J. Jost


    Physical Review E, Vol. 101, No. 6, 062313, 2020






    J74
    "Random attractors for stochastic partly dissipative systems"


    C. Kuehn, A. Neamtu and A. Pein


    Nonlinear Differential Equations and Applications NoDEA, Vol. 27, No. 35, 2020






    J73
    "On fast-slow consensus networks with a dynamic weight"


    H. Jardon Kojakhmetov and C. Kuehn


    Journal of Nonlinear Science, accepted / to appear, 2020






    J72
    "Network dynamics on graphops"


    C. Kuehn


    New Journal of Physics, Vol. 22, 053030, 2020






    J71
    "Pathwise mild solutions for quasilinear stochastic partial differential equations"


    C. Kuehn and A. Neamtu


    Journal of Differential Equations, Vol. 269, No. 3, pp. 2185-2227, 2020






    J70
    "Computing invariant sets of random differential equations using polynomial chaos"


    M. Breden and C. Kuehn


    SIAM Journal on Applied Dynamical Systems, Vol. 19, No. 1, pp. 577-618, 2020






    J69
    "Combined error estimates for local fluctuations of SPDEs"


    C. Kuehn and P. Kürschner


    Advances in Computational Mathematics, Vol. 46, No. 11, 2020






    J68
    "Numerical continuation for a fast-reaction system and its cross-diffusion limit"


    C. Kuehn and C. Soresina


    SN Partial Differential Equations and Applications, Vol. 1, No. 7, 2020






    J67
    "Adaptive voter model on simplicial complexes"


    L. Horstmeyer and C. Kuehn


    Physical Review E, Vol. 101, No.2, 022305, 2020






    J66
    "Travelling waves in monostable and bistable stochastic partial differential equations"


    C. Kuehn


    Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 122, No. 2, pp. 73-107, 2020





    J65
    "Sample paths estimates for stochastic fast-slow systems driven by fractional Brownian motion"


    K. Eichinger, C. Kuehn and A. Neamtu


    Journal of Statistical Physics, Vol. 179, No. 5, pp. 1222-1266, 2020






    J64
    "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, Vol. 13, No. 4, pp. 1269-1290, 2020





    J63
    "Random switching near bifurcations"


    T. Hurth and C. Kuehn


    Stochastics and Dynamics, Vol. 20, No. 2, 2050008, 2020





    J62
    "Mathematical analysis of nonlocal  PDEs for network generation"


    T. Böhle and C. Kuehn



    Mathematical Modelling of Natural Phenomena, Vol. 14, No. 5, 506, 2019






    J61
    "Discretized fast-slow systems near pitchfork singularities"


    L. Arcidiacono, M. Engel and C. Kuehn


    Journal of Difference Equations and Applications, Vol. 25, No. 7, pp. 1024-1051, 2019






    J60
    "A survey on the blow-up method for fast-slow systems"


    H. Jardon Kojakhmetov and C. Kuehn


    Contemporary Mathematics, AMS, accepted / to appear, 2019






    J59
    "A gradient flow formulation for the stochastic Amari model"


    C. Kuehn and J. Tölle


    Journal of Mathematical Biology, Vol. 79, No. 4, pp. 1227-1252, 2019






    J58
    "Power network dynamics on graphons"


    C. Kuehn and S. Throm


    SIAM Journal on Applied Mathematics, Vol. 79, No. 4, pp. 1271-1292, 2019






    J57
    "Smoluchowski's coagulation equation with forcing"


    C. Kuehn and S. Throm


    Nonlinear Differential Equations and Applications (NoDEA), Vol. 26, No. 3, 17, 2019






    J56
    "Discretized fast-slow systems near transcritical singularities"


    M. Engel and C. Kuehn


    Nonlinearity, Vol. 32, No. 7, pp. 2365-2391, 2019






    J55
    "Multiscale dynamics of an adaptive catalytic network"


    C. Kuehn


    Mathematical Modelling of Natural Phenomena, Vol. 14, No. 4, 402, 2019






    J54
    "Rigorous validation of stochastic transition paths"


    M. Breden and C. Kuehn


    Journal de Mathématiques Pures et Appliquées, Vol. 131, pp. 88-129, 2019






    J53
    "Duck traps: two-dimensional critical manifolds in planar systems"


    C. Kuehn and C. Münch


    Dynamical Systems: An International Journal, Vol. 34, No. 4, pp. 584-612, 2019






    J52
    "Pattern formation in the doubly-nonlocal Fisher-KPP equation"


    C. Kuehn and P. Tkachov


    Discrete and Continuous Dynamical Systems A, Vol. 39, No. 4, pp. 2077-2100, 2019





    J51
    "Towards sample path estimates for fast-slow stochastic partial differential equations"


    M.V. Gnann, C. Kuehn and A. Pein


    European Journal of Applied Mathematics, Vol. 30, No. 5, pp. 1004-1024, 2019





    J50
    "Scaling laws and warning signs for bifurcations of SPDEs"


    C. Kuehn and F. Romano


    European Journal of Applied Mathematics, Vol. 30, No. 5, pp. 853-868, 2019





    J49
    "Network topology near criticality in adaptive epidemics"


    L. Horstmeyer, C. Kuehn and S. Thurner


    Physical Review E, Vol 98, 042313, 2018






    J48
    "A note on kernel methods for multiscale systems with critical transitions"


    B. Hamzi, C. Kuehn and S. Mohamed


    Mathematical Methods in the Applied Sciences, Vol. 42, No. 3, pp. 907-917, 2018






    J47
    "Validity of amplitude equations for nonlocal nonlinearities"


    C. Kuehn and S. Throm


    Journal of Mathematical Physics, Vol. 59, 071510, 2018





    J46
    "Analysis and predictability for tipping points with leading-order nonlinear terms"


    F. Romano and C. Kuehn


    International Journal of Bifurcation and Chaos, Vol. 28, No. 8, 1850103, 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
    "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





    J42
    "Quenched noise and nonlinear oscillations in bistable multiscale systems"


    C. Kuehn


    EPL (Europhysics Letters), Vol. 120, 10001, 2017






    J41



    C. Kuehn and C. Münch


    SIAM Journal on Applied Dynamical Systems, Vol. 16, No. 3, pp. 1650-1685, 2017






    J40
    "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






    J39
    "Uncertainty transformation via Hopf bifurcation in fast-slow systems"


    C. Kuehn


    Proceedings of the Royal Society A, Vol. 473, 20160346, 2017






    J38
    "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






    J37
    "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






    J36
    "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






    J35
    "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




      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, 2019
     
       

    PDE Dynamics
    Christian Kuehn
    SIAM, 2019


    See also:
    • addenda
    • corrigenda
    SIAM Book Cover

     




      B1 "Multiple Time Scale Dynamics", C. Kuehn, Springer, 2015  
       
    Multiple Time Scale Dynamics
    Christian Kuehn
    Springer Verlag, 2015

    See also:

     
         Reviews: DSWeb / MathSciNet / SIAM Review / Zentralblatt
     





        Book Chapters:  

    C2
    "Dynamics of stochastic reaction-diffusion equations" arXiv


    C. Kuehn and A. Neamtu


    in: Finite and Infinite Dimensional Stochastic Equations with Applications to Physics (editors: H. Lisei & W. Grecksch), Wiley, pp. 1-55, 2020





      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  
           

       

    Further Writings:

     

    L3
    "Introduction to Adaptive Network Dynamics" (available upon request)



    C. Kuehn


    Lecture Notes for: Case Studies in Mathematical Modelling 2018/2019






    V2
    Book Review of ''Hidden Dynamics'' (by M.R. Jeffrey) preprint


    C. Kuehn


    SIAM Review, Vol. 61, No. 3, within pp. 625–640, 2019.





    L2
    "Dynamical Systems I: ODEs and Introduction to Nonlinear Dynamics"


    C. Kuehn


    AMS Open Math Notes, 66pp., 2018





    L1
    "Dynamical Systems II: A Concise Graduate Course"



    C. Kuehn


    AMS Open Math Notes, 125pp., 2018






    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