Related papers: Admissibility and generalized nonuniform dichotomi…
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…
This paper presents a nonlinear dynamical model which consists the system of differential and operator equations. Here differential equation contains a nonlinear operator acting in Banach space, a nonlinear operator equation with respect to…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
This paper deals with the multivalued non-autonomous random dynamical system generated by the non-autonomous stochastic wave equations on unbounded domains, which has a non-Lipschitz nonlinearity with critical exponent in the three…
The classical global linearization theorem for autonomous system given in [C. Pugh, Amer. J. Math., 91 (1969) 363-367] requires that nonlinear system with hyperbolicity satisfies boundedness and Lipschitz continuity.In this paper, we…
Given a nonautonomous and nonlinear differential equation \begin{equation}\label{DE} x'=A(t)x+f(t,x) \quad t\geq 0, \end{equation} on an arbitrary Banach space $X$, we formulate very general conditions for the associated linear equation…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…
We propose a notion of random horseshoe and prove density of random horseshoes for non uniformly expanding random dynamical systems with additive noise
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
In this manuscript, we have considered the system governed by a noninstantaneous impulsive dynamical system of integer order with classical and nonlocal conditions and derived sufficient conditions for the trajectory controllability of the…
We introduce a Banach space-valued extension of random feature learning, a data-driven supervised machine learning technique for large-scale kernel approximation. By randomly initializing the feature maps, only the linear readout needs to…
We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In particular, we consider stochastic parabolic evolution…
In this paper some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias…
We present a framework to calculate large deviations for nonlinear functions of independent random variables supported on compact sets in Banach spaces, by extending the result in Chatterjee and Dembo [6]. Previous research on nonlinear…
We obtain a local stable manifold theorem for perturbations of nonautonomous linear difference equations possessing a very general type of nonuniform dichotomy, possibly with different growth rates in the uniform and nonuniform parts. We…
We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of meta-materials we focus our effort on two recent nonstandard relaxed…
We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the…
We study the properties of "generic", in the sense of the Haar measure on the corresponding Grassmann manifold, subspaces of l^N_infinity of given dimension. We prove that every "well bounded" operator on such a subspace, say E, is a…