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Research Areas:

  • Applied Mathematics & Applied Analysis
  • Differential Equations & Dynamical Systems
  • Probability & Stochastic Analysis
  • Scientific Computing & Numerical Analysis
  • Networks & Complex Systems
  • Applications in the Sciences & Engineering
  • ... and particularly the interfaces between the above fields!

   

Preprints & Work in Progress:

 

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


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





*
"An adaptive voter model on simplicial complexes"



L. Horstmeyer and C. Kuehn





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



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






*
"Random attractors for stochastic partly dissipative systems"



C. Kuehn, A. Neamtu and A. Pein





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



K. Eichinger, C. Kuehn and A. Neamtu





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



H. Jardon Kojakhmetov and C. Kuehn





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



M. Breden and C. Kuehn





* "Rough center manifolds"



C. Kuehn and A. Neamtu





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



C. Kuehn and A. Neamtu






*
"Combined error estimates for local fluctuations of SPDEs"


C. Kuehn and P. Kürschner






    Journal Publications:  

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. 2, 2020





J63
"Travelling waves in monostable and bistable stochastic partial differential equations"


C. Kuehn


Jahresbericht der Deutschen Mathematiker-Vereinigung, accepted / to appear, 2019






J62
"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






J61
"A survey on the blow-up method for fast-slow systems"


H. Jardon Kojakhmetov and C. Kuehn


Contemporary Mathematics, AMS, accepted / to appear, 2019






J60
"A gradient flow formulation for the stochastic Amari model"


C. Kuehn and J. Tölle


Journal of Mathematical Biology, accepted / to appear, 2019






J59
"Power network dynamics on graphons"


C. Kuehn and S. Throm


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






J58
"Random switching near bifurcations"


T. Hurth and C. Kuehn


Stochastics and Dynamics, accepted / to appear, 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, 2365, 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, accepted / to appear, 2019






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


C. Kuehn and C. Münch


Dynamical Systems: An International Journal, accepted / to appear, 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  
       

Remarks on Reviews (for editors)