Publications

Selected Publications (see full list below)

• 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, 2023, pp. 1-37, 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).

Preprints

• [PP7]: Random attractors on countable state spaces, 2024, arXiv, pp. 1-44, submitted (with R. Chemnitz and G. Olicon-Mendez).

• [PP6]: Strategic control for a Boltzmann like decision-making model, 2024, arXiv, pp. 1-40, submitted (with L. G. Venegas-Pineda, H. Jardon-Kojakhmetov, J. Heitzig, M. C. Eser, M. Cao)

• [PP5]: Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups, 2024, arXiv, pp. 1-51, submitted (with R. Chemnitz and P. Koltai)

• [PP4]: Nonlinear effects within invariance principles, 2024, arXiv, pp. 1-22, submitted (with P. Friz and Tal Orenshtein).

• [PP3]: A singular perturbation analysis for the Brusselator, 2023, arXiv, pp. 1-39, submitted (with G. Olicon-Mendez).

• [PP2]: Geometric analysis of fast-slow PDEs with fold singularities, 2022, arXiv, pp. 1-41, submitted (with F. Hummel, C. Kuehn, N. Popovic, M. Ptashnyk, T. Zacharis).

• [PP1]: Blow-up analysis of fast-slow PDEs with loss of hyperbolicity,  2021, arXiv, pp. 1-37, submitted (with C. Kuehn).

Peer Reviewed Articles

• [24]: The Lyapunov spectrum for conditioned random dynamical systems, to appear in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2024, arXiv, pp. 1-36 (with M.M. Castro, D. Chemnitz, H. Chu, J.S.W. Lamb, M. Rasmussen).

• [23]: Continuous-time extensions of discrete-time cocycles,  Proceedings of the AMS ,11: 23-35, 2024, DOI, (with R. Chemnitz and P. Koltai).

• [22]: Synchronization and random attractors for reaction jump processes,  Journal of Dynamics and Differential Equations, 2024, DOI, pp. 1-36 (with G. Olicon-Mendez, N. Unger, S. Winkelmann).

• [21]: 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).  

• [20]: 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).

• [19]: Noise-induced instabilities in a stochastic Brusselator, to appear in Contemporary Mathematics, arXiv, pp. 1-17, 2023 (with G. Olicon-Mendez). 

• [18]:  Canards in modified equations for Euler discretizations, to appear in Contemporary Mathematics, arXiv, pp.1-13,  2023 (with G. Gottwald).

• [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).

Other Publications

• 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.