Related papers: Data-Driven Stabilization of Periodic Orbits

A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…

With an increasing interest in the design of long and complex space missions, the search for orbits that require the least amount of fuel is of fundamental interest. This paper develops existing computational models for locating Unstable…

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…

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…

The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered…

Chaotic trajectories in multi-body dynamical systems play a crucial role in designing low-energy trajectories in astrodynamics. However, predicting these trajectories is inherently difficult, as small errors in initial conditions can grow…

In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different…

Using an innovative damped-Newton method, we report the first calculation of many distinct unstable periodic orbits (UPOs) of a large high-dimensional extensively chaotic partial differential equation. A majority of the UPOs turn out to be…

We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to…

In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the…

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…

Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR),…

This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…

We study the forms of the orbits in a symmetric configuration of a realistic model of the H2O molecule with particular emphasis on the periodic orbits. We use an appropriate Poincar\'e surface of section (PSS) and study the distribution of…

This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…

We obtain and investigate theoretically a broad family of stable and unstable time-periodic orbits-oscillating Turing rolls (OTR)-in the Lugiato-Lefever model of optical cavities. Using the dynamical systems tools developed in fluid…

The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…

This paper proposes a sparse identification of nonlinear dynamics (SINDy) with control and exogenous inputs for highly accurate and reliable prediction. Although SINDy is recognized as a remarkable approach for identifying nonlinear…

The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…