Related papers: Minimality properties of set-valued processes and …
We study the long-term behavior of the distribution of the solution process to the non-autonomous McKean-Vlasov stochastic delay lattice system defined on the integer set $\mathbb{Z}$. Specifically, we first establish the well-posedness of…
We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we…
In this paper, we study the asymptotic behavior of the solutions of a nonautonomous differential inclusion modeling a reaction-diffusion equation with a discontinuous nonlinearity. We obtain first several properties concerning the…
As in our previous paper, the 3D Navier-Stokes equations with a translationally bounded force contain pullback attractors in a weak sense. Moreover, those attractors consist of complete bounded trajectories. In this paper, we present a…
This work establishes the existence and regularity of random pullback attractors for parabolic partial differential equations with rough nonlinear multiplicative noise under natural assumptions on the coefficients. To this aim, we combine…
In this paper, under some appropriate assumptions, we prove the existence of the minimal time-dependent pullback $\mathcal D_{\sigma}^{\mathcal{H}_{t}}$-attractors ${\mathcal{A}}_{\mathcal D_{\sigma}^{\mathcal{H}_{t}}}$ for the…
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…
Compared to ordinary function minimization problems, min-max optimization algorithms encounter far greater challenges because of the existence of periodic cycles and similar phenomena. Even though some of these behaviors can be overcome in…
Reaction systems are discrete dynamical systems that model biochemical processes in living cells using finite sets of reactants, inhibitors, and products. We investigate the computational complexity of a comprehensive set of problems…
In this work we define the generalized $\varphi$-pullback attractors for evolution processes in complete metric spaces, which are compact and positively invariant families, such that they pullback attract bounded sets with a rate determined…
The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…
A method is proposed to deal with some multivalued semiflows with weak continuity properties. An application to the reaction-diffusion problems with nonmonotone multivalued semilinear boundary condition and nonmonotone multivalued…
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of…
The structure of the graph defined by the interactions in a Boolean network can determine properties of the asymptotic dynamics. For instance, considering the asynchronous dynamics, the absence of positive cycles guarantees the existence of…
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…
We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations…
A recent generalization of the Conley index to discrete multivalued dynamical systems without a continuous selector is motivated by applications to data-driven dynamics. In the present paper we continue the program by studying…
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…
This article is devoted to the study of multivalued semigroups and their asymptotic behavior, with particular attention to iterations of set-valued mappings. After developing a general abstract framework, we present an application to a time…