Related papers: Longtime Dynamics of The Oregonator System
This paper reports the 3D planetary geostrophic viscous model has the exponential ergodicity and global attractor if this model is driven by an additive random noise, which results in the support of the integration of invariant measure for…
The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous…
The longtime and global pullback dynamics of stochastic Hindmarsh-Rose equations with multiplicative noise on a three-dimensional bounded domain in neurodynamics is investigated in this work. The existence of a random attractor for this…
In this paper, we present some results for existence of global solutions and attractivity for mulidimensional fractional differential equations involving Riemann-Liouville derivative. First, by using a Bielecki type norm and Banach fixed…
We obtain general analytical solutions of third-order viscous hydrodynamic equations for Bjorken and Gubser flows in systems with vanishing bulk viscosity and chemical potential, and having a constant shear relaxation time. We also…
The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large…
The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…
We prove that the critical surface quasi-geostrophic equation driven by a force $f$ possesses a compact global attractor in $L^2(\mathbb T^2)$ provided $f\in L^p(\mathbb T^2)$ for some $p>2$. First, the De Giorgi method is used to obtain…
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a…
For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some…
We investigate the long-term behavior, as a certain regularization parameter vanishes, of the three-dimensional Navier-Stokes-Voigt model of a viscoelastic incompressible fluid. We prove the existence of global and exponential attractors of…
This article is devoted to a description of the dynamics of the phase flow of monotone contact Hamiltonian systems. Particular attention is paid to locating the maximal attractor (or repeller), which could be seen as the union of compact…
We describe some recent results on the dynamics of singular-hyperbolic (or Lorenz-like) attractors: attractors in this class are expansive and so sensitive with respect to initial data; they admit a unique physical measure whose support is…
In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with…
The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in $\mathbb{R}^4$. In this study, we investigate the behavior of trajectories in the presence of…
This article aims to study the long-time dynamics of the linear viscoelastic plate equation $\displaystyle{u_{tt}+\Delta^2 u-\int_{\tau}^tg(t-s)\Delta^2u(s)ds=0}$ subject to nonlinear and nonlocal boundary conditions. This model, with…
We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solutions satisfy the energy and enstrophy equality. It is shown…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
This paper investigates the global well-posedness of a class of reaction-advection-diffusion models with nonlinear diffusion and Lotka-Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the…
We study the asymptotic long-time behavior of Darcy--Boussinesq convection in layered porous media with narrow transition zones in the material properties. As the transition-layer width tends to zero, we prove the upper semi-continuous…