Related papers: Differential analysis of nonlinear systems: revisi…
This paper proposes a friction model parameter identification routine that can work with highly nonlinear and chaotic systems. The chosen system for this study is a passively-actuated tilted Furuta pendulum, which is known to have a highly…
A new approach is used to describe the large time behavior of the non-local differential equation initially studied in [3]. Our approach is based upon the existence of infinitely many Lyapunov functionals and allows us to extend the…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
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…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov…
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…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
We propose a novel approach for learning the evolution that employs differentiable neural networks to approximate the full GENERIC structure. Instead of manually choosing the fitted parameters, we learn the whole model together with the…
This review considers methods of nonlinear dynamics to apply for analysis of time series corresponding to information streams on the Internet. In the main, these methods are based on correlation, fractal, multifractal, wavelet, and Fourier…
Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…
In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and…
The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its corresponding spectral theory. The second…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
Recently a method which employs computing of fluctuations in a measure of nonlinear similarity based on local recurrence properties in a univariate time series, was introduced to identify distinct dynamical regimes and transitions between…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
Learning-based optimal control algorithms control unknown systems using past trajectory data and a learned model of the system dynamics. These controllers use either a linear approximation of the learned dynamics, trading performance for…
We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and…
We study dynamics of the inverted pendulum on the wheel on a soft surface and under a proportional-integral-derivative controller. The behaviour of such pendulum is modelled by a system with a differential inclusion. If the the system has a…