Related papers: On DSS Method for a Fast Identification of the Sta…

In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…

We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general $\mathbf{L}^2$ initial data in two space dimensions and…

Temporal variations in biological systems and more generally in natural sciences are typically modelled as a set of Ordinary, Partial, or Stochastic Differential or Difference Equations. Algorithms for learning the structure and the…

We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

This report provides an investigation into solving the Kuramoto-Sivashinsky equation in two spatial dimensions (2DKS) using a pseudo-spectral method on various rectangular periodic domains. The Kuramoto-Sivashinsky equation is a fluid…

We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily…

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…

We present a novel approach to system identification (SI) using deep learning techniques. Focusing on parametric system identification (PSI), we use a supervised learning approach for estimating the parameters of discrete and…

Thermodynamics and dynamics of a classical two-dimensional system with dipole-like isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical…

Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…

Many amorphous materials show spatially heterogenous dynamics, as different regions of the same system relax at different rates. Such a signature, known as Dynamic Heterogeneity, has been crucial to understand the jamming transition in…

Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism…

Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six--dimensional phase space, making simulations of…

We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…

We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…