Related papers: Controlling unpredictability in the randomly drive…
We are interested in time series of the form $y_{n} = x_{n} + \xi_{n}$ where ${x_{n}}$ is generated by a chaotic dynamical system and where $\xi_{n}$ models observational noise. Using concentration inequalities, we derive fluctuation bounds…
Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most…
An attractor of a dynamical system may represent the system's 'desirable' state. Perturbations to the system may push the system out of the basin of attraction of the desirable attractor and into undesirable states. Hence, it is important…
We demonstrate that final-state uncertainty is ubiquitous in multistable systems of coupled neuronal maps, meaning that predicting whether one such system will eventually be chaotic or nonchaotic is often nearly impossible. We propose a…
The aim of this work is to review and also explore even further the escape properties of orbits in a dynamical system of a two-dimensional perturbed harmonic oscillator, which is a characteristic example of open Hamiltonian systems. In…
The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics.…
We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems'…
Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…
Fluctuational transitions between two co-existing chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the mechanism for such transitions is determined by a hierarchy of…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the drift is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore,…
We show that limit cycle systems in Langevin bath exhibit uncertainty in observables that define the limit-cycle plane, and maintain a positive lower bound. The uncertainty-bound depends on the parameters that determine the shape and…
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers. In order to…
Many systems such as autonomous vehicles and quadrotors are subject to parametric uncertainties and external disturbances. These uncertainties can lead to undesired performance degradation and safety issues. Therefore, it is important to…
We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a _focus_ may occur along the most probable exit path, leading to a…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…