In this paper, two problems related to FitzHugh–Nagumo lattice systems are analyzed. The first one is concerned with the asymptotic behavior of random delayed driven by nonlinear Wong–Zakai noise. We obtain a new result ensuring that such system approximates corresponding deterministic when correlation time noise goes infinity rather than zero. prove existence tempered attractors for drift func...

at present paper, we establish the existence of pullback $mathcal{d}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $l^2(mathbb{r}^n)times l^2(mathbb{r}^n)$. in order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{d}$-absorbing set, is pullback $widehat{d}_0$-asymptotically compact.

We consider a nonautonomous stochastic $ p $-Laplacian lattice equation with multiplicative noise and nonlinearity that is not locally Lipschitz. For each q\geq1 $, pullback (\ell^2, \ell^q) $-attractor obtained, the measurability of attractor in both spaces by more complicated estimates. Then, time-dependent invariant sample Borel probability measures are constructed carried random attractor. ...

The goal of this work is to study in some detail the asymptotic behaviour of a nonautonomous Lotka–Volterra model, both in the conventional sense (as t-N) and in the ‘‘pullback’’ sense (starting a fixed initial condition further and further back in time). The nonautonomous terms in our model are chosen such that one species will eventually die out, ruling out any conventional type of permanence...

The impact of the El Ni\~no-Southern Oscillation (ENSO) on extratropics is investigated in an idealized, reduced-order model that has a tropical and extratropical module. Unidirectional ENSO forcing used to mimick atmospheric bridge between tropics extratropics. variability coupled ocean-atmosphere module then through analysis its pullback attractors (PBAs). This focuses two types generated by ...

<p style='text-indent:20px;'>In this paper, we prove the existence and uniqueness of tempered pullback random attractors supercritical stochastic wave equations driven by an infinite-dimensional additive white noise on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula> with id="M3">\begin{document}$ n\le ...

where ε ∈ [0, 1], the nonlinearity f and the external force g satisfy some certain conditions specified later. This equation is known as the nonclassical diffusion equation when ε > 0, and the reaction-diffusion equation when ε = 0. Nonclassical diffusion equation arises as a model to describe physical phenomena, such as non-Newtonian flows, soil mechanic, and heat conduction (see, e.g., [1, 7,...