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Recent/current projects of my work include:

- Multiple Time-Scales (mixed-mode oscillations, singular bifurcation diagrams, canards, critical transitions)

- Bifurcation Theory (global and multi-parameter bifurcations, desingularization, generalized models, chaos)

- Stochastic Dynamical Systems (SDEs, SPDEs, stochastic bifurcations, large deviations, UQ, warning signs)

- Computational Dynamics (continuation, invariant manifolds, boundary value problems, stochastics, software)

- Applications (neuroscience, ecology, epidemiology, chemical oscillations, socio-/econo-physics, climate)

- Evolution Equations (reaction-diffusion systems, travelling waves, anomalous diffusion, pattern formation)

- Elliptic PDE (singular perturbations, spike layers, steady states and bifurcations, non-local operators)

- Networks (adaptive networks, agent-based models, self-organized criticality, moment closure)

- Other Interestes (Conley index, scaling laws, non-smooth systems, data analysis, visualization)

             Remarks on reviews (for editors)

   

Preprints & Work in Progress:

 

*
"Stochastic mixed-mode oscillations in a three-species predator-prey model"



S. Sadhu and C. Kuehn





*
"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






*
"Early warning signs for bifurcations with bounded noise"



C. Kuehn, G. Malavolta and M. Rasmussen





*
"Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem"



A. Iuorio, C. Kuehn and P. Szmolyan





*
"Tracking particles in flows near invariant manifolds via balance functions"


C. Kuehn, H. Kuhlmann and F. Romano






    Journal Publications (refereed):  

J40



C. Kuehn and C. Münch


SIAM Journal on Applied Dynamical Systems, accepted / to appear






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  
       
  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 (refereed):  
  B2 "PDE Dynamics: An Introduction", C. Kuehn, SIAM (under contract), manuscript in preparation
 
       
  B1 "Multiple Time Scale Dynamics", C. Kuehn, Springer, 2015  
   
Multiple Time Scale Dynamics
Christian Kuehn
Springer Verlag, 2015

I maintain documents for the book with

 
     Reviews: DSWeb / MathSciNet / Zentralblatt
 





    Book Chapters & Reviews (refereed):  
  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:

 

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