Related papers: On DSS Method for a Fast Identification of the Sta…
We develop method that allows to derive reductions and solutions to hyperbolic systems of partial differential equations. The method is based on using functions that are constant in the direction of characteristics of the system. These…
Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations (DNS) by solving the equations that govern the statistics themselves. DSS…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
If $F:H\to H$ is a map in a Hilbert space $H$, $F\in C^2_{loc}$, and there exists $y$, such that $F(y)=0$, $F'(y)\not= 0$, then equation $F(u)=0$ can be solved by a DSM (dynamical systems method). This method yields also a convergent…
Obtaining a realistic and accurate model of the longitudinal dynamics is key for a good speed control of a self-driving car. It is also useful to simulate the longitudinal behavior of the vehicle with high fidelity. In this paper, a…
In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the…
We offer a metal model suitable for the description of fast electrophysical processes in conductors under influence of powerful electronic and laser radiation of femto- and picosecond duration, and also high-voltage electromagnetic pulses…
A review of the authors's results is given. Several methods are discussed for solving nonlinear equations $F(u)=f$, where $F$ is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy…
Available methods for identification of stochastic dynamical systems from input-output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability…
In the identification of differential equations from data, significant progresses have been made with the weak/integral formulation. In this paper, we explore the direction of finding more efficient and robust test functions adaptively…
In this paper we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third-order and has cubic…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
Fast-slow systems with three slow variables and gradient structure in the fast variables have, generically, hyperbolic umbilic, elliptic umbilic or swallowtail singularities. In this article we provide a detailed local analysis of a…
The aim of this paper is to provide a construction of stationary discrete solitons in an extended one-dimensional Discrete NLS model with non-nearest neighbour interactions. These models, models of the type with long-range interactions were…
Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…
Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
This paper is concerned with identifying the instantaneous modal parameters of forced oscillatory systems with response-dependent generalized inertia (mass, inductance, or equivalent) based on their measured dynamics. An identification…
A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. Quantitative measurements of these rates are crucial for optimizing…
Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…