Related papers: Dynamics of Axisymmetric Truncated Dynamo Models
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…
Open quantum Dicke models are paradigmatic systems for the investigation of light-matter interaction in out-of-equilibrium quantum settings. Albeit being structurally simple, these models can show intriguing physics. However, obtaining…
We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the…
We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how non-ergodic dynamics can produce interesting…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
We examine global dynamics and bifurcations occurring in a truncated model of a stellar mean field dynamo. This model has symmetry-forced invariant subspaces for the dynamics and we find examples of transient type I intermittency and…
We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions…
Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic…
We investigate a disordered multi-dimensional linear system in which the interaction parameters vary stochastically in time with defined temporal correlations. We refer to this type of disorder as "annealed", in contrast to quenched…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
The nonperturbative real-time evolution of quantum fields out of equilibrium is often solved using a mean-field or Hartree approximation or by applying effective action methods. In order to investigate the validity of these truncations, we…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
The exploration of mean-field galactic dynamos affected by a galactic spiral pattern, begun in Chamandy et al. (2013, hereafter Paper I) with numerical simulations, is continued here with an asymptotic solution. The mean-field dynamo model…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
Inspired by striking advances in language modeling, there has recently been much interest in developing autogressive sequence models that are amenable to analytical study. In this short note, we consider extensions of simple disordered…
Context. The recently developed test-field method permits to compute dynamo coefficients from global, direct numerical simulations. The subsequent use of these parameters in mean-field models enables us to compare self-consistent dynamo…
It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g. by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a…
We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees.…