Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non-autonomous Terms

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 attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the existence of a unique pullback attractor for the first-order lattice dynamical systems with both deterministic non-autonomous forcing terms and multiplicative white noise. Our results recover many existing ones on the existences of pullback attractors for lattice dynamical systems with autonomous terms or white noises

Singleton sets random attractor for stochastic FitzHugh-Nagumo lattice equations driven by fractional Brownian motions

The paper is devoted to the study of the dynamical behavior of the solutions of stochastic FitzHugh-Nagumo lattice equations, driven by fractional Brownian motions, with Hurst parameter greater than $1/2$. Under some usual dissipativity conditions, the system considered here features different dynamics from the same one perturbed by Brownian motion. In our case, the random dynamical system has a unique random equilibrium, which constitutes a singleton sets random attractor.Comment: Some details (including the Abstract section) have been improve

Synchronization of Coupled Stochastic Systems Driven by Non-Gaussian L\'evy Noises

We consider the synchronization of the solutions to coupled stochastic systems of $N$-stochastic ordinary differential equations (SODEs) driven by Non-Gaussian L\'evy noises ($N\in \mathbb{N})$. We discuss the synchronization between two solutions and among different components of solutions under certain dissipative and integrability conditions. Our results generalize the present work obtained in Liu et al (2010) and Shen et al (2010).Comment: arXiv admin note: substantial text overlap with arXiv:1402.1790 by other author

A random attractor for stochastic porous media equations on infinite lattices

The paper is devoted to studying the existence of a random attractor for stochastic porous media equations on infinite lattices under some conditions.Comment: 15 pages. Some key details have been adde

Random Attractors of Stochastic Lattice Dynamical Systems Driven by Fractional Brownian Motions and its Erratum

This paper is devoted to considering the stochastic lattice dynamical systems (SLDS) driven by fractional Brownian motions with Hurst parameter bigger than $1/2$. Under usual dissipativity conditions these SLDS are shown to generate a random dynamical system for which the existence and unique of a random attractor is established. Furthermore, the random attractor is in fact a singleton sets random attractor. Next, we give an erratum because of the misused theory.Comment: arXiv admin note: substantial text overlap with arXiv:1310.711

Weak Pullback Mean Random Attractors for Stochastic Evolution Equations and 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 weak pullback mean random attractors for some stochastic models such as stochastic reaction-diffusion equations, the stochastic $p$-Laplace equation and stochastic porous media equations are established.Comment: Few details were improved. Comments are welcom

Regularity of pullback attractors and equilibrium for non-autonomous stochastic FitzHugh-Nagumo system on unbounded domains

A theory on bi-spatial random attractors developed recently by Li \emph{et al.} is extended to study stochastic Fitzhugh-Nagumo system driven by a non-autonomous term as well as a general multiplicative noise. By using the so-called notions of uniform absorption and uniformly pullback asymptotic compactness, it is showed that every generated random cocycle has a pullback attractor in $L^l(\mathbb{R}^N)\times L^2(\mathbb{R}^N)$ with $l\in(2,p]$, and the family of obtained attractors is upper semi-continuous at any intensity of noise. Moreover, if some additional conditions are added, then the system possesses a unique equilibrium and is attracted by a single point

Electromagnetic mass splittings of π,a1,K,K1(1400)\pi, a_1, K, K_1(1400) and K∗(892)K^*(892)

To one-loop order and $O(\alpha_{em})$, the electromagnetic mass splittings of $\pi$, $a_1$, $K$, $K_1(1400)$, and $K^*(892)$ are calculated in the framework of $U(3)_L\times U(3)_R$ chiral field theory. The logarithmic divergences emerging in the Feynman integrations of the mesonic loops are factorized by using an intrinsic parameter $g$ of this theory. No other additional parameters or counterterms are introduced to absorb the mesonic loop divergences. When $f_\pi$,$m_\rho$ and $m_a$ are taken as inputs, the parameter $g$ will be determined and all the physical results are finite and fixed. Dashen's theorem is satisfied in the chiral SU(3) limit of this theory, and a rather large violation of the theorem is revealed at the order of $m_s$ or $m_K^2$. Mass ratios of light quarks have been determined. A relation for electromagnetic corrections to masses of axial-vector mesons is obtained. It could be regarded as a generalization of Dashen's theorem. Comparing with data, it is found that the non-electromagnetic mass difference of $K^*$ is in agreement with the estimation of Schechter, Subbaraman, Weigel.Comment: LateX, 40 pages and five PS files. Final version will appear in Phys. Rev. D5

Random Attractor For Stochastic Lattice FitzHugh-Nagumo System Driven By α\alpha-stable L\'evy Noises

The present paper is devoted to the existence of a random attractor for stochastic lattice FitzHugh-Nagumo system driven by $\alpha$-stable L\'evy noises under some dissipative conditions

Dark matter pair associated with a W boson production at the LHC in next-to-leading order QCD

We investigate the QCD next-to-leading order (NLO) corrections to the production of a pair of fermionic dark matter particles associated with a W boson production through a mediator which couples to standard model particles via either a vector or axial-vector coupling at the LHC. We find that the QCD NLO corrections reduce the dependence of the total cross sections on the factorization and renormalization scales, and the K -factors increase with the increment of the dark matter mass. We also provide the LO and QCD NLO corrected distributions of the transverse momenta p T μ of final muon and transverse mass M T . We find that the LO cross section is significantly changed by the QCD NLO corrections