33 citations · 189 across the 26 of their papers we have counts for
26 papers
Detecting random bifurcations via rigorous enclosures of large deviations rate functions
Alexandra Blessing, Alex Blumenthal, Maxime Breden +1
The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time L…
Noise-induced instabilities in a stochastic Brusselator
Maximilian Engel, Guillermo Olicón-Méndez
We consider a stochastic version of the so-called Brusselator - a mathematical model for a two-dimensional chemical reaction network - in which one of its parameters is assumed to…
Continuous-time extensions of discrete-time cocycles
Robin Chemnitz, Maximilian Engel, Péter Koltai
We consider linear cocycles taking values in driven by homeomorphic transformations of a smooth manifold, in discrete and continuous time. We show that…
Canards in modified equations for Euler discretizations
Maximilian Engel, Georg A. Gottwald
Canards are a well-studied phenomenon in fast-slow ordinary differential equations implying the delayed loss of stability after the slow passage through a singularity. Recent studi…
A stochastic variant of replicator dynamics in zero-sum games and its invariant measures
Maximilian Engel, Georgios Piliouras
We study the behavior of a stochastic variant of replicator dynamics in two-agent zero-sum games. We characterize the statistics of such systems by their invariant measures which c…
Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise
Dennis Chemnitz, Maximilian Engel
We prove the positivity of Lyapunov exponents for the normal form of a Hopf bifurcation, perturbed by additive white noise, under sufficiently strong shear strength. This completes…
Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation
Maximilian Engel, Felix Hummel, Christian Kuehn +3
We study a singularly perturbed fast-slow system of two partial differential equations (PDEs) of reaction-diffusion type on a bounded domain via Galerkin discretisation. We assume…
Synchronization and random attractors for reaction jump processes
Maximilian Engel, Guillermo Olicón-Méndez, Nathalie Unger +1
This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random d…
The conditioned Lyapunov spectrum for random dynamical systems
Matheus M. Castro, Dennis Chemnitz, Hugo Chu +3
We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned…
Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors
Akim Viennet, Nikki Vercauteren, Maximilian Engel +1
We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discusse…
A traveling wave bifurcation analysis of turbulent pipe flow
Maximilian Engel, Christian Kuehn, Björn de Rijk
Using various techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al., Nature, 526:550-553, 2015], which describes the ri…
On the pitchfork bifurcation for the Chafee-Infante equation with additive noise
Alex Blumenthal, Maximilian Engel, Alexandra Neamtu
We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor i…
A General View on Double Limits in Differential Equations
Christian Kuehn, Nils Berglund, Christian Bick +4
In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to…
Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions
Maximilian Engel, Felix Hummel, Christian Kuehn
In this paper, we study slow manifolds for infinite-dimensional evolution equations. We compare two approaches: an abstract evolution equation framework and a finite-dimensional sp…
Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
Maxime Breden, Maximilian Engel
We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic prope…
Geometric analysis of a truncated Galerkin discretization of fast-slow PDEs with transcritical singularities
Maximilian Engel, Christian Kuehn
We consider a fast-slow partial differential equation (PDE) with reaction-diffusion dynamics in the fast variable and the slow variable driven by a differential operator on a bound…
Homogenization of Fully-Coupled Chaotic Fast-Slow Systems via Intermediate Stochastic Regularization
Maximilian Engel, Marios-Antonios Gkogkas, Christian Kuehn
In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter such that, for every fixed value of the slow variable…
Extended and symmetric loss of stability for canards in planar fast-slow maps
Maximilian Engel, Hildeberto Jardón-Kojakhmetov
We study fast-slow maps obtained by discretization of planar fast-slow systems in continuous time. We focus on describing the so-called delayed loss of stability induced by the slo…
A Random Dynamical Systems Perspective on Isochronicity for Stochastic Oscillations
Maximilian Engel, Christian Kuehn
For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time…
Discretized Fast-Slow Systems with Canards in Two Dimensions
Maximilian Engel, Christian Kuehn, Matteo Petrera +1
We study the problem of preservation of maximal canards for time discretized fast-slow systems with canard fold points. In order to ensure such preservation, certain favorable stru…
Discretized Fast-Slow Systems near Pitchfork Singularities
Luca Arcidiacono, Maximilian Engel, Christian Kuehn
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an…
A Markov jump process modelling animal group size statistics
Pierre Degond, Maximilian Engel, Jian-Guo Liu +1
We translate a coagulation-framentation model, describing the dynamics of animal group size distributions, into a model for the population distribution and associate the \blue{nonl…
Discretized Fast-Slow Systems near Transcritical Singularities
Maximilian Engel, Christian Kuehn
We extend slow manifolds near a transcritical singularity in a fast-slow system given by the explicit Euler discretization of the corresponding continuous-time normal form. The ana…
Conditioned Lyapunov exponents for random dynamical systems
Maximilian Engel, Jeroen S. W. Lamb, Martin Rasmussen
We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to trajectories that stay within a bounded domain for asymptotically long times. This is mot…