Related papers: Classification of Possible Finite-Time Singulariti…
Hyperbolic systems in one dimensional space are frequently used in modeling of many physical systems. In our recent works, we introduced time independent feedbacks leading to the finite stabilization for the optimal time of homogeneous…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
Finite time analysis of the continuous system is investigated through both stability and stabilization based on Sum of squares programming. A systematic approach is proposed to construct Lyapunov function and Control Lyapunov function for…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…
Functional autoregressive (FAR) models provide a fundamental framework for analyzing temporally dependent functional data. However, the infinite-dimensional nature of the underlying Hilbert space introduces intrinsic ill-posedness, as the…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
This paper presents an analysis approach to finite-time attraction in probability concerns with nonlinear systems described by nonlinear random differential equations (RDE). RDE provide meticulous physical interpreted models for some…
The $f(T)$ gravity is one of the extensions of teleparallel equivalent of general relativity, in which more general functions of the torsion scalar $T$ can be described. With the proposed functional form of $f(T) = \alpha T - \beta u^{-n} +…
Using one loop functional RG we study two problems of pinned elastic systems away from their equilibrium or steady states. The critical regime of the depinning transition is investigated starting from a flat initial condition. It exhibits…
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
The paper discusses extensions of the renormalization group (RG) formalism for 3D incompressible Euler equations, which can be used for describing singularities developing in finite (blowup) or infinite time from smooth initial conditions…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
We present a systematic implementation of differential renormalization to all orders in perturbation theory. The method is applied to individual Feynamn graphs written in coordinate space. After isolating every singularity. which appears in…
In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
We discuss the problem of renormalization of dynamical equations which arises in an effective field theory description of nuclear forces. By using a toy model of the separable NN potential leading to logarithmic singularities in the Born…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…