Related papers: Chaos Control with Ion Propulsion
We consider the unsteady regimes of an acoustically-driven jet that forces a recirculating flow through successive reflections on the walls of a square cavity. The specific question being addressed is to know whether the system can sustain…
The dissolution process of star clusters is rather intricate for theory. We investigate it in the context of chaotic dynamics. We use the simple Plummer model for the gravitational field of a star cluster and treat the tidal field of the…
Celestial bodies approximated with rigid triaxial ellipsoids in a two-body system can rotate chaotically due to the time-varying gravitational torque from the central mass. At small orbital eccentricity values, rotation is short-term…
Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we show how the partial control method can be applied in this kind of…
The escape mechanism of the four hill potential is explored. A thorough numerical investigation takes place in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional phase space in…
In this paper, closed-loop entry guidance in a randomly perturbed atmosphere, using bank angle control, is posed as a stochastic optimal control problem. The entry trajectory, as well as the closed-loop controls, are both modeled as random…
We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular,…
Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is…
A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared 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…
A new type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)]. It is characterized by nearly constant laminar phases, which are…
We continue our study of chaotic mixing and transport of passive particles in a simple model of a meandering jet flow [Prants, et al, Chaos {\bf 16}, 033117 (2006)]. In the present paper we study and explain phenomenologically a connection…
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into pairs of coherent sets, which are sets of…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are…
This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation, some astrophysical simulations…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
Due to the deterministic nature of chaotic systems, fluctuations in their trajectories arise solely from the choice of initial conditions. Some of these dynamical fluctuations may lead to extremely unlikely scenarios. Understanding the…