Related papers: Correction to: Criteria for Strong and Weak Random…
The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak…
It is well-known that random attractors of a random dynamical system are generally not unique. We show that for general pullback attractors and weak attractors, there is always a minimal (in the sense of smallest) random attractor which…
In this paper, we first establish a criterion based on contractive function for the existence of polynomial attractors. This criterion only involves some rather weak compactness associated with the repeated limit inferior and requires no…
In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave…
This work contains the results from a comprehensive study of a new class of attractors. The attractors in this class are characterized by strong local instability, but they are not uniformly hyperbolic. Rigorous results on their dynamical,…
The article focuses on word (or string) attractors, which are sets of positions related to the text compression efficiency of the underlying word. The article presents two combinatorial algorithms based on Suffix automata or Directed…
We develop a formal theory of the weak values with emphasis on the consistency conditions and a probabilistic interpretation in the counter-factual processes. We present the condition for the choice of the post-selected state to give a…
A recent problem in dynamics is to determinate whether an attractor $\Lambda$ of a $C^r$ flow $X$ is $C^r$ robust transitive or not. By {\em attractor} we mean a transitive set to which all positive orbits close to it converge. An attractor…
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.
The aim of this paper is to gain a better understanding of weak and strong positivity for exterior forms on complex vector spaces. We prove a dimensionality reduction argument for positive forms, which allows us to restrict to the case of…
In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We consider two cases, depending on the values of the parameters…
This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…
We discuss the (twisted) weak positivity theorem. We also treat some applications.
In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of…
Previous studies have shown that rate-induced transitions can occur in pullback attractors of systems subject to "parameter shifts" between two asymptotically steady values of a system parameter. For cases where the attractors limit to…
In this paper, we prove the existence of weak pullback mean random attractors for a non-local stochastic reaction-diffusion equation with a nonlinear multiplicative noise. Also, we establish the existence and uniqueness of solutions and…
In this paper, we first introduce the definitions of random evolutionary system that associate with random evolutionary semigroup and the corresponding global weak or strong random attractor. Then we establish the existence result about…
We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback…
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…