Related papers: Stabilizing chaotic vortex trajectories: an exampl…
Toward scalable quantum computing, the control of quantum systems needs to be robust against both coherent errors induced by parametric uncertainties and incoherent errors induced by environmental decoherence. This poses significant…
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…
Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly any chaotic systems without any prior analytical…
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
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…
A method of controlling Shil'nikov's type chaos using windows that appear in the 1 dimensional bifurcation diagram when perturbations are applied, and using existence of stable homoclinic orbits near the unstable one is presented and…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…
In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the…
The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…
In this paper, we investigate the controllability of the point vortex system by means of a single vortex. The point vortex system is a well-known simplied model for the incompressible Euler equation, where the vorticity is concentrated in a…
This work is focused to study the development and control of the laminar vortex breakdown of a flow enclosed in a cylinder. We show that vortex breakdown can be controlled by the introduction of a small fixed rod in the axis of the…
A simple method to perform chaos control without the need of complex numerical and analytical calculations is proposed. The method works for dynamical systems with bounded solutions and in the trivial case of constant Jacobians.
To stabilize the periodic operation of a chemical reactor the oscillation period should be determined precisely in real time. The method discussed in the paper is based on adaptive sampling of the state variable with the use of chaotic…
Vortex-dominated flows are ubiquitous in engineering, and the ability to efficiently manipulate the dynamics of these vortices has broad applications, from wake shaping to mixing enhancement. However, the strongly nonlinear behavior of the…
Recently, it was shown that giant vortices with arbitrarily large quantum numbers can possibly be created in dilute Bose-Einstein condensates by cyclically pumping vorticity into the condensate. However, multiply quantized vortices are…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are…
In this letter we present a method of constructing dynamical systems with any preassigned number of equilibria by adding symmetry to another system with at least one equilibrium point. If the resulting system is chaotic, we call this…
Unstable periodic orbits (UPOs) are the non-chaotic, dynamical building blocks of spatio-temporal chaos, motivating a first-principles based theory for turbulence ever since the discovery of deterministic chaos. Despite their key role in…