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The cost of stochastic resetting is considered within the context of a discrete random walk model. In addition to standard stochastic resetting, for which a reset occurs with a certain probability after \emph{each} step, we introduce a…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…
Although resetting has widespread applicability, applying it to the dynamics in the presence of spatial quenched disorder, which is essential in many physical problems, is challenging. In this study, we consider a well-known one-dimensional…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We…
One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped…
Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially…
A dynamical process that takes a random time to complete, e.g., a chemical reaction, may either be accelerated or hindered due to resetting. Tuning system parameters such as temperature, viscosity or concentration, can invert the effect of…
First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here we study the interplay…
We consider the problem of the first passage time to the origin of a spatially non-homogeneous random walk with a position-dependent drift, known as the Gillis random walk, in the presence of resetting. The walk starts from an initial site…
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.…
Renewal processes are zero-dimensional processes defined by independent intervals of time between zero crossings of a random walker. We subject renewal processes them to stochastic resetting by setting the position of the random walker to…
In this work we consider a stochastic movement process with random resets to the origin followed by a random residence time there before the walker restarts its motion. First, we study the transport properties of the walker, we derive an…
Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling…
In studying the time evolution of isolated many-body quantum systems, a key focus is determining whether the system undergoes relaxation and reaches a steady state at a given point in time. Traditional approaches often rely on specific…
In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…