Related papers: Partially controlling transient chaos in the Loren…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number…
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…
We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of ~12 ns. Our approach is a prescription for how to implement…
We consider Rayleigh particles in a periodically modulated optical trap formed by two counter-propagating Gaussian beams. It is shown that for certain values of parameters the system exhibits transient chaos which manifests itself in…
We describe adaptive control algorithms whereby a chaotic dynamical system can be steered to a target state with desired characteristics. A specific implementation considered has the objective of directing the system to a state which is…
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…
A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…
Autonomous agents are often tasked with operating in an area where feedback is unavailable. Inspired by such applications, this paper develops a novel switched systems-based control method for uncertain nonlinear systems with temporary loss…
Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When…
This paper proposes a finite-time Newton seeking control design for systems described by unknown multivariable static maps. The Newton seeking system has an averaged system that implements a Newton continuous-time algorithm. The averaged…
To characterize local finite-time properties associated with transient chaos in open dynamical systems, we introduce an escape rate and fractal dimensions suitable for this purpose in a coarse-grained description. We numerically illustrate…
We introduce system norms which assess transient behavior of stable Linear Time-Invariant (LTI) systems. This allows us to address undesired responses to initial conditions, finite resource consumption signals, or persistent perturbations.…
Self-adjusting, or adaptive systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these…
Understanding the interplay of order and disorder in chaotic systems is a central challenge in modern quantitative science. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work…
A phenomenon of weak transient chaos is discussed that is caused by sub-exponential divergence of trajectories in the basin of a non-chaotic attractor. Such a regime is not easy to detect, because conventional characteristics, such as the…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties…