Related papers: AI-Driven Control of Chaos: A Transformer-Based Ap…
Discrete fractional order chaotic systems extends the memory capability to capture the discrete nature of physical systems. In this research, the memristive discrete fractional order chaotic system is introduced. The dynamics of the system…
We demonstrate that chaos can be controlled using a multiplicative exponential feedback control. All three types of unstable orbits - unstable fixed points, limit cycles and chaotic trajectories can be stabilized using this control. The…
Transient chaos is a characteristic behavior in nonlinear dynamics where trajectories in a certain region of phase space behave chaotically for a while, before escaping to an external attractor. In some situations the escapes are highly…
Coarse-grained models of chaotic systems neglect unresolved degrees of freedom, inducing structured model error that limits predictability and distorts long-term statistics. Typical data-driven closures are trained to minimize error over a…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
By modeling quantum chaotic dynamics with ensembles of random operators, we explore howmachine learning learning algorithms can be used to detect pseudorandom behavior in qubit systems.We analyze samples consisting of pieces of correlation…
In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
In this work, we demonstrate the open-loop control of chaotic systems by means of optimized periodic signals. The use of such signals enables us to reduce control power significantly in comparison to simple harmonic perturbations. It is…
We experimentally demonstrate coherent control of a quantum system, whose dynamics is chaotic in the classical limit. Interaction of diatomic molecules with a periodic sequence of ultrashort laser pulses leads to the dynamical localization…
This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design…
In present paper we discuss the control of complex spatio-temporal dynamics in a {spatially extended} non-linear system (fluid model of Pierce diode) based on the concepts of controlling chaos in the systems with few degrees of freedom. A…
We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control.…
A numerical and experimental study of a control method aimed at channeling chaos by building barriers in phase space is performed on a paradigm for wave-particle interaction, i.e., a traveling wave tube. Control of chaotic diffusion is…
Irregular, especially chaotic, behavior is often undesirable for economic processes because it presents challenges for predicting their dynamics. In this situation, control of such a process by its mathematical model can be used to suppress…
This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed…