Related papers: Studying the global dynamics of conservative dynam…
This work builds off the manifold-constrained Gaussian process inference (MAGI) method for Bayesian parameter inference and trajectory reconstruction of ODE-based dynamical systems, focusing primarily on sparse and noisy data conditions.…
Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to migration of orbits, resonant…
We investigate the regular or chaotic nature of orbits of stars moving in the meridional plane (R,z) of an axially symmetric galactic model with a dense, massive spherical nucleus and a dark matter halo component. In particular, we study…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
The main features of 1P/Halley chaotic dynamics can be described by a two dimensional symplectic map. Using Mel'nikov integral we semi-analytically determine such a map for 1P/Halley taking into account gravitational interactions from the…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
In this paper we apply the method of Lagrangian descriptors as an indicator to study the chaotic and regular behavior of trajectories in the phase space of the classical double pendulum system. In order to successfully quantify the degree…
Real world systems evolve in continuous-time according to their underlying causal relationships, yet their dynamics are often unknown. Existing approaches to learning such dynamics typically either discretize time -- leading to poor…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their…
Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…
The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
The regular and chaotic character of orbits is investigated in a 3D potential describing motion in the central parts of a barred galaxy. This potential is an extension in the 3D space of a 2D potential based on a family of figure-eight…
A new approach to seismic interpretation is proposed to leverage visual perception and human visual system modeling. Specifically, a saliency detection algorithm based on a novel attention model is proposed for identifying subsurface…
The Galilean satellites' dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation computers it became…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…