Related papers: Rate-induced Tipping in Discrete-time Dynamical Sy…
A function with finite asymptotic limits gives rise to a transition equation between a "past system" and a "future system". This question is analyzed in the case of nonautonomous coercive nonlinear scalar ordinary differential equations…
This paper investigates recursive feasibility, recursive robust stability and near-optimality properties of policy iteration (PI). For this purpose, we consider deterministic nonlinear discrete-time systems whose inputs are generated by PI…
This work provides a geometric approach to the study of bifurcation and rate induced transitions in a class of non-autonomous systems referred to herein as $\textit{asymptotically slow-fast systems}$, which may be viewed as 'intermediate'…
The integrability of two symplectic maps, that can be considered as discrete-time analogs of the Garnier and Neumann systems is established in the framework of the $r$-matrix approach, starting from their Lax representation. In contrast…
An application of optimal control theory results in a lower bound on the speed $|\dot{\lambda}(t)|$ that must be attained at least once by any external forcing function that induces tipping in the asymptotically autonomous scalar ODE…
Slow-fast dynamics and resonant phenomena can be found in a wide range of physical systems, including problems of celestial mechanics, fluid mechanics, and charged particle dynamics. Important resonant effects that control transport in the…
We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined…
Test-time adaptation (TTA) has emerged as a promising solution to tackle the continual domain shift in machine learning by allowing model parameters to change at test time, via self-supervised learning on unlabeled testing data. At the same…
Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…
Given a discounted cost, we study deterministic discrete-time systems whose inputs are generated by policy iteration (PI). We provide novel near-optimality and stability properties, while allowing for non stabilizing initial policies. That…
Computing the rate of evolution in spatially structured populations is difficult. A key quantity is the fixation time of a single mutant with relative reproduction rate $r$ which invades a population of residents. We say that the fixation…
The discrete-time robust repetitive control (RC, or repetitive controller, also designated RC) problem for nonlinear systems is both challenging and practical. This paper proposes a discrete-time output-feedback RC design for a class of…
We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…
This paper studies performance preserving event design in nonlinear event-based control systems based on a local L2-type performance criterion. Considering a finite gain local L2-stable disturbance driven continuous-time system, we propose…
The propagation path of topologically protected states is bound to the interface between regions with different topology, and as such, the functionality of linear photonic devices leveraging these states is fixed during fabrication. Here,…
Tipping behavior can occur when an equilibrium of a dynamical system loses stability in response to a slowly varying parameter crossing a bifurcation threshold, or where noise drives a system from one attractor to another, or some…
For autonomous vehicles to operate persistently in a typical urban environment, it is essential to have high accuracy position information. This requires a mapping and localisation system that can adapt to changes over time. A localisation…
In the context of network dynamics, the complexity of systems increases possible evolutionary paths that often are not deterministic. Occasionally, some map routs form over the course of time which guide systems towards some particular…