Related papers: Rate-induced Tipping in Discrete-time Dynamical Sy…
Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function…
A tiling of $\mathbb{R}^d$ is repulsive if no $r$-patch can repeat arbitrarily close to itself, relative to $r$. This is a characteristic property of aperiodic order, for a non repulsive tiling has arbitrarily large local periodic patterns.…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
We examine the question whether random set attractors for continuous-time random dynamical systems on a connected state space are connected. In the deterministic case, these attractors are known to be connected. In the probabilistic setup,…
There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…
A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stable chaotic dynamics. The starting point is a map on a…
Polyhomeostatic adaption occurs when evolving systems try to achieve a target distribution function for certain dynamical parameters, a generalization of the notion of homeostasis. Here we consider a single rate encoding leaky integrator…
We present a sample-based motion planning algorithm specialised to a class of underactuated systems using path parameterisation. The structure this class presents under a path parameterisation enables the trivial computation of dynamic…
We investigate the statistics of the local time $\mathcal{T} = \int_0^T \delta(x(t)) dt$ that a run and tumble particle (RTP) $x(t)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the…
In this paper we develop novel results on self triggering control of nonlinear systems, subject to perturbations and actuation delays. First, considering an unperturbed nonlinear system with bounded actuation delays, we provide conditions…
When the parameter of a map is chosen, at each iteration step, following a certain rule, is called Parametric Perturbation. If the parameters are drawn from a distribution, then this perturbation is called Random Parametric Perturbation.…
In this paper, new results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps with a time-dependent exciter are presented and discussed in detail. The applicability of the results about…
We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties…
We introduce a residence-time approach (RTA) for determining position-dependent diffusivities from biased molecular dynamics simulations. The method is formulated for trajectory segments in which the effective drift along the transport…
Deep reinforcement learning (RL) has shown immense potential for learning to control systems through data alone. However, one challenge deep RL faces is that the full state of the system is often not observable. When this is the case, the…
We study the evolution of the phase-space of collisionless N-body systems under repeated stirrings or perturbations, which has been shown to lead to a convergence towards a limited group of end states. This so-called attractor was…
One of the hardest challenges to face in the development of a non GPS-based localization system for autonomous vehicles is the changes of the environment. LiDAR-based systems typically try to match the last measurements obtained with a…
In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a…
Analysing stationary point databases to extract phenomenological rate constants can become time-consuming for systems with large potential energy barriers. In the present contribution we analyse several different approaches to this problem.…