6 papers
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…
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…
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…