Related papers: Efficient algorithm for detecting unstable periodi…
As originally formulated, the Generalized Alignment Index (GALI) method of chaos detection has so far been applied to distinguish quasiperiodic from chaotic motion in conservative nonlinear dynamical systems. In this paper we extend its…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…
The complexity of arbitrary dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit - in the form of a limit cycle, dividing surface, instanton trajectories or some other related…
In this paper, we consider the application of optimal periodic control sequences to switched dynamical systems. The control sequence is obtained using a finite-horizon optimal method based on dynamic programming. We then consider Euler…
The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with…
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…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work…
Spatio-temporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A…
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
We report on the application of chaos control to the irregular motion of an electron under the combined influence of a Coulomb and a magnetic field, the so-called ``diamagnetic Kepler problem'' (DKP). We show how to stabilize the classical…
A method for exploring unstable structures generated by nonlinear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters by Replica Exchange Monte Carlo (REM), and efficient both for the search of…
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…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
We propose a new unsupervised and non-parametric method to detect change points in intricate quasi-periodic signals. The detection relies on optimal transport theory combined with topological analysis and the bootstrap procedure. The…
Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…
The gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic…