Characterizing dynamical stability of stochastic gradient descent in overparameterized learning, Journal of Machine Learning Research, 26: 1-46, 2025, DOI, (with D. Chemnitz).
Random attractors on countable state spaces, Electronic Journal of Probability, 30: 1-25, 2025, DOI, (with R. Chemnitz and G. Olicon-Mendez).
On the pitchfork bifurcation for the Chafee-Infante equation with additive noise, Probability Theory and Related Fields, 187: 603-627, 2023, DOI, (with A. Blumenthal, A. Neamtu).
Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise, Communications in Mathematical Physics, 402: 1807–1843, 2023, DOI, (with D. Chemnitz).
Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems, Annals of Applied Probability, 33(2): 1052-1094, 2023, DOI, (with M. Breden). See also an interview in a podcast series concerning this work.
A random dynamical systems perspective on isochronicity for stochastic oscillations, Communications in Mathematical Physics 386(3): 1603-1641, 2021, DOI, (with C. Kuehn).
Discretized fast-slow systems near transcritical singularities, Nonlinearity 32(7): 2365-2391, 2019, DOI, (with C. Kuehn).
Conditioned Lyapunov exponents for random dynamical systems, Transactions of the American Mathematical Society 372(9): 6343-6370, 2019, DOI, (with J.S.W. Lamb, M. Rasmussen).
Bifurcation analysis of a stochastically driven limit cycle, Communications in Mathematical Physics 365(3): 935-942, 2019, DOI, (with J.S.W. Lamb, M. Rasmussen).
Hopf bifurcation with additive noise, Nonlinearity 31(10): 4567-4601, 2018, DOI, (with T.S. Doan, J.S.W. Lamb, M. Rasmussen).
[PP5]: Unfolding the geometric structure and multiple timescales of the urea-urease pH oscillator, 2025, arXiv, pp. 1-44 (with A.V. Straube, G. Olicon Mendez, S. Winkelmann, F. Höfling)
[PP4]: Dynamic link switching induces stable synchronized states in sparse networks , 2025, arXiv, pp. 1-9 (with M. Cenk Eser, E.S. Medeiros, M. Riza).
[PP3]: Separation of time scales in weakly interacting diffusions, 2025, arxiv, pp. 1-30 (with Z. Adams, R. Gvalani).
[PP2]: Strategic control for a Boltzmann like decision-making model, 2024, arXiv, pp. 1-40 (with L. G. Venegas-Pineda, H. Jardon-Kojakhmetov, J. Heitzig, M. C. Eser, M. Cao)
[PP1]: Nonlinear effects within invariance principles, 2024, arXiv, pp. 1-22 (with P. Friz and Tal Orenshtein).
[32]: A singular perturbation analysis for the Brusselator, to appear in Journal of Differential Equations, pp. 1-39, 2025+, arXiv, (with G. Olicon-Mendez).
[31]: Random attractors on countable state spaces, Electronic Journal of Probability, 30: 1-25, 2025, DOI, (with R. Chemnitz and G. Olicon-Mendez).
[30]: Characterizing dynamical stability of stochastic gradient descent in overparameterized learning, Journal of Machine Learning Research, 26: 1-46, 2025, DOI, (with D. Chemnitz).
[29]: Detecting random bifurcations via rigorous enclosures of large deviations rate functions, Physica D: Nonlinear Phenomena, 476: 134617, 2025, DOI (with Alexandra Blessing, Alex Blumenthal, Maxime Breden).
[28]: Assessing Lagrangian coherence in atmospheric blocking, Nonlinear Processes in Geophysics, 32(1): 51-73, 2025, DOI, (with Henry Schoeller, Robin Chemnitz , Péter Koltai and Stephan Pfahl).
[27]: Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups, Discrete and Continuous Dynamical Systems Series B, 30(6): 1952-1995, 2025, DOI, (with R. Chemnitz and P. Koltai).
[26]: The Lyapunov spectrum for conditioned random dynamical systems, Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 61(3): 1845-1877, 2025, DOI, (with M.M. Castro, D. Chemnitz, H. Chu, J.S.W. Lamb, M. Rasmussen).
[25]: Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation, Nonlinearity, 37:115017, 2024, DOI (with F. Hummel, C. Kuehn, N. Popovic, M. Ptashnyk, T. Zacharis).
[24]: Geometric analysis of a truncated Galerkin discretization of fast-slow PDEs with transcritical singularities, SIAM Journal on Applied Dynamical Systems, 23(4): 2853-2898, 2024, DOI (with C. Kuehn).
[23]: Noise-induced instabilities in a stochastic Brusselator, Contemporary Mathematics, 806: 29-48, 2024, DOI (with G. Olicon-Mendez).
[22]: Canards in modified equations for Euler discretizations, Contemporary Mathematics, 806: 15-28, 2024, DOI (with G. Gottwald).
[21]: Continuous-time extensions of discrete-time cocycles, Proceedings of the AMS ,11: 23-35, 2024, DOI, (with R. Chemnitz and P. Koltai).
[20]: Synchronization and random attractors for reaction jump processes, Journal of Dynamics and Differential Equations, 37: 1207–1242, 2025, DOI, (with G. Olicon-Mendez, N. Unger, S. Winkelmann).
[19]: A stochastic variant of replicator dynamics in zero-sum games and its invariant measures, Physica D: Nonlinear Phenomena, 456: 133940, 2023, DOI (with G. Piliouras).
[18]: On the pitchfork bifurcation for the Chafee-Infante equation with additive noise, Probability Theory and Related Fields, 187: 603-627, 2023, DOI, (with A. Blumenthal, A. Neamtu). (with A. Blumenthal, A. Neamtu).
[17]: Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise, 2023, Communications in Mathematical Physics, 402: 1807–1843, 2023, DOI (with D. Chemnitz).
[16]: Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems, Annals of Applied Probability, 33(2): 1052-1094, 2023, DOI, (with M. Breden).
[15]: Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors, Chaos 32(11): 113145, 2022, DOI, (with A. Viennet, N. Vercauteren, D. Faranda).
[14]: A traveling wave bifurcation analysis of turbulent pipe flow, Nonlinearity 35(11): 5903-5937, 2022, DOI, ( with C. Kuehn, B. de Rijk).
[13]: Discretized fast-slow systems with canards in two dimensions, Journal of Nonlinear Science 32:19. pp. 1-41, 2022, DOI, (with C.Kuehn, M.Petrera, Y. Suris).
[12]: A general view on double limits in differential equations, Physica D: Nonlinear Phenomena 431: 133105, 2022, DOI, (with C.Kuehn, N. Berglund, C. Bick, T. Hurth, A. Iuorio, C. Soresina).
[11]: Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions, Proceedings of the AMS, Series B 8: 252-266, 2021, DOI, (with F. Hummel, C. Kuehn).
[10]: Homogenization of Fully-Coupled Chaotic Fast-Slow Systems via Intermediate Stochastic Regularization, Journal of Statistical Physics 183: 25, pp. 1-34, 2021, DOI, (with M. Gkogkas, C. Kuehn).
[9]: A random dynamical systems perspective on isochronicity for stochastic oscillations, Communications in Mathematical Physics 386(3): 1603-1641, 2021, DOI, (with C. Kuehn).
[8]: Extended and symmetric loss of stability for canards in planar fast-slow maps, SIAM Journal on Applied Dynamical Systems 19(4): 2530-2566, 2020, DOI, (with H.Jardon-Kojakhmetov).
[7]: A Markov jump process modelling animal group size statistics, Communications in Mathematical Sciences 18(1): 55-89, 2020, DOI, (with P. Degond, J. Liu, R. Pego).
[6]: Discretized fast-slow systems near pitchfork singularities, Journal of Difference Equations and Applications 25(7): 1024-1051, 2019, DOI, ( L.Arcidiacono, C.Kuehn).
[5]: Discretized fast-slow systems near transcritical singularities, Nonlinearity 32(7): 2365-2391, 2019, DOI, (with C. Kuehn).
[4]: Conditioned Lyapunov exponents for random dynamical systems, Transactions of the American Mathematical Society 372(9): 6343-6370, 2019, DOI, (with J.S.W. Lamb, M. Rasmussen)
[3]: Bifurcation analysis of a stochastically driven limit cycle, Communications in Mathematical Physics 365(3): 935-942, 2019, DOI, (with J.S.W. Lamb, M. Rasmussen).
[2]: Hopf bifurcation with additive noise, Nonlinearity 31(10): 4567-4601, 2018, DOI, (with T.S. Doan, J.S.W. Lamb, M. Rasmussen)
[1]: Numerical approximation of a coagulation-fragmentation model for animal group size statistics, Networks and Heterogeneous Media 12(2): 217-243, 2017, DOI, (with P. Degond).
A dynamical systems perspective on the analysis of neural networks, arXiv, pp. 1-37, to appear as book chapter in Theoretical Foundations of Deep Learning, Springer, 2025+ (with D. Chemnitz, C. Kuehn, S.-V. Kuntz).
Local phenomena in random dynamical systems: bifurcations, synchronisation, and quasi-stationary dynamics, M.Engel, Ph.D. thesis, Imperial College London, 2018, Engel-M-2018-PhD-Thesis.