Related papers: Data-driven Chaos Indicator for Nonlinear Dynamics…
This paper studies the data-driven control of unknown linear-threshold network dynamics to stabilize the state to a reference value. We consider two types of controllers: (i) a state feedback controller with feed-forward reference input and…
We apply the Smaller ALignment Index (SALI) method to a 4--dimensional mapping of accelerator dynamics in order to distinguish rapidly, reliably and accurately between ordered and chaotic motion. The main advantage of this index is that it…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…
We generalize a method of control of chaos which uses delayed feedback at the period of an unstable orbit to stabilize that orbit. The generalization consists of substituting some portion of the nonlinear dynamical system with a delayed…
This work establishes a crucial step toward advancing data-driven trajectory-based methods for stochastic systems with unknown mathematical dynamics. In contrast to scenario-based approaches that rely on independent and identically…
We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realised in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing wave pulses. Unlike the original optical scheme…
In this paper we demonstrate that the phase space arclength of a trajectory, quantified by the time-averaged Lagrangian descriptor, is a robust and self-contained chaos indicator. By invoking Birkhoff's Ergodic Partition Theorem, we show…
In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the…
It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not…
Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty…
We study an opto-electronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly-stable fixed point, which, when subjected to a finite-amplitude…
Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and…
Some new findings for chaos-based wireless communication systems have been identified recently. First, chaos has proven to be the optimal communication waveform because chaotic signals can achieve the maximum signal to noise ratio at…
Descriptor systems arise naturally in real-world applications governed by algebraic constraints, such as power networks, robotics and chemical processes. When a descriptor model contains a nontrivial nilpotent block, the discrete-time…
Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior…
We demonstrate targeting and control over spatiotemporal chaos in an optical feedback loop experiment. Different stationary target patterns are stabilized in real-time by means of a two dimensional space extended perturbation field driven…
The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of…
We study dissipative transport of spontaneously emitting atoms in a 1D standing-wave laser field in the regimes where the underlying deterministic Hamiltonian dynamics is regular and chaotic. A Monte Carlo stochastic wavefunction method is…
Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator…