In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. López-de-la-Cruz and A. Rapaport. A way ...

This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random ...

In this article, the authors investigate the system of Schr odinger and Klein-Gordon equations with Yukawa coupling. They ...

We show the existence of an exponential attractor for non-autono-mous dynamical system with bounded delay. We considered ...

In this work, we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic ...

This work discloses an epidemiological mathematical model to predict an empirical treatment for dogs infected by Pseudomonas ...

This article investigates the three-dimensional globally modified Navier-Stokes equations with unbounded variable delays. ...

We revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on the input flow ...

In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and ...

The paper addresses a kind of non-autonomous nonlocal parabolic equations when the external force contains hereditary ...

In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a ...

In this paper we consider a non-autonomous Navier-Stokes-Voigt model including a variety of delay terms in a unified ...

In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal ...

A non-autonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion ...

In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the ...

On the one hand, the classical heat equation∂tu= ∆udescribes heatpropagation in a homogeneous medium, while the time ...

In this paper, we study a stochastic epidemic model with isolation and nonlinear incidence. In particular, we propose a ...

This thesis applies the great advances of modern dynamical systems theory (DST) to consciousness. Consciousness, or ...

In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model ...

This paper is devoted to analyze the stability of the economy according to an extended version of Kaldor's economic growth ...

The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed ...

In this article we analyze the randomized non-autonomous Bertalanffy model x 0 (t, ω) = a(t, ω)x(t, ω) + b(t, ω)x(t, ω) 2/3, ...

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating ...

In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term ...

In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential ...

This paper considers a new model in search theory to find a randomly located target in the 3-dimensional space. An ...

The main aim of this letter is to use the strong compact strong trajectory attractor to construct the strong trajectory ...

In this work we present results to ensure a weak upper semicontinuity for a family of impulsive cocycle attractors of ...

Some results concerning a stochastic 2D Navier-Stokes system when the external forces contain hereditary characteristics ...

In this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness ...

In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy ...

The long-run aim of this thesis is to solve delay differential equations with infinite delay of the type d dt u(t) = ...

In this paper, we prove some existence, uniqueness and Hyers-Ulam stability results for the coupled random fixed point of ...

We randomize the following class of linear differential equations with delay, x 0 τ (t) = axτ(t) + bxτ(t − τ), t > 0, and ...

In this work the theory of generalized processes is used to describe the dynamics of a nonautonomous multivalued problem ...

In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. ...

This paper is concerned with the well-posedness and dynamics of delay impulsive fractional stochastic evolution equations ...

Focusing on epidemic model in random environments, this paper uses white noise and Lévy noise to model the dynamics of the ...

In this article we consider a model introduced by Ucar in order to simply describe chaotic behaviour with a one dimensional ...

This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive ...

The existence and uniqueness of global solutions for a fractional functional differential equation is established. The ...

We first prove the existence and regularity of the trajectory attractor for a threedimensional system of globally modified ...

In this paper, we consider the environmental defensive expenditures model with delay proposed by Russu in P. Russu, Hopf ...

This paper focuses on a pumped-storage generating system with a reversible Francis turbine and presents an innovative ...

In this paper we prove the existence of mild solutions for a first-order impulsive semilinear stochastic differential ...

In this paper we prove some results on the existence of solutions and the mean square asymptotic stability for a class of ...

Some results related to 2D Navier-Stokes equations when the external force contains hereditary characteristics involving ...

The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The ...

In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced ...

In this paper, the existence and uniqueness of weak and strong solutions for a non-autonomous nonlocal reaction-diffusion ...

Based on the theory of functional diferential equations, theory of semigroup, theory of random dynamical systems and theory ...

In this paper, the existence of regular pullback attractors as well as their upper semicontinuous behaviour in H1-norm are ...

In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for ...

Mathematical modeling, currently, is a very important element in health system, since it allows studying the incidence, ...

This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic ...

We study a continuous Hénon system obtained by considering the discrete original model in continuous time. While the ...

The research proposed in this paper focuses on the dynamic evolution of a hydraulic-mechanical-electric system under the ...

A predator prey model with nonlinear harvesting (Holling type-II) with both constant and distributed delay is considered. ...

In this work we prove the existence of solution for a p-Laplacian non-autonomous problem with dynamic boundary and infinite ...

Some diseases such as herpes, bovine and human tuberculosis exhibit relapse in which the recovered individuals do not ...

In this article, a stochastic version of a SIR nonautonomous model previously introduced in Kloeden and Kozyakin (2011) ...

In this talk, some random and stochastic disturbances in the chemostat model will be analyzed by making use of the modern ...

We derive general existence theorems for random pullback exponential attractors and deduce explicit bounds for their fractal dimension. The results are formulated for asymptotically compact random dynamical systems in Banach spaces.

This paper is devoted to the investigation of the practical exponential stability of impulsive stochastic functional ...

The objective of this paper is to study a perturbed linear hyperbolic differential equation. The first part of this work ...

In this paper we investigate the well-posedness and dynamics of a fractional stochastic integro-differential equation ...

The existence and limiting behavior of the solutions of stochastic parabolic problems with thermal memory are investigate ...

This paper is concerned with the existence and continuous dependence of mild solutions to stochastic differential equations ...

In this paper we study two stochastic chemostat models, with and without wall growth, driven by a white noise. Specifically, ...

In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results ...

The long-time behavior of solutions (more precisely, the existence of random pullback attractors) for an integro-differential ...

In this paper, the existence of solution for a p-Laplacian parabolic equation with nonlocal diffusion is established. To ...

We show existence and uniqueness of solutions for a non-classical and non-autonomous diffusion equation with infinite delay ...

In this work we will study the theory of dynamical systems with application to a chemostat. Starting with the autonomous ...

Nowadays, mathematical models are one of the most popular tools to study epidemics due to the fact that they enable to ...

We provide a qualitative description of microstructure formation and coarsening phenomena for the solutions of a singularly ...

In this work, we deal with several different notions of attractors that may appear in the impulsive non-autonomous case ...

In this paper we analyze a model presenting formation of microstructure depending on the parameters and the initial data. ...

The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour ...

In this article, a random and a stochastic version of a SIR nonautonomous model previously introduced in P. E. Kloeden and ...

We first study the well-posedness of a non-autonomous incompressible non-Newtonian fluid with delay. The existence of ...

In this talk, some different ways of modeling stochastic chemostats will be presented in order to obtain much more realistic ...

In this work we study the existence, uniqueness and asymptotic behavior of mild solutions for neutral stochastic partial ...

In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, ...

This work is devoted to the construction of impulsive sets in Rn. In the literature, there are many examples of impulsive ...

In this paper we study a semi-Kolmogorov type of population model, arising from a predator-prey system with indirect ...

In this work we study the existence and uniqueness of mild solutions for stochastic partial integrodifferential equations ...

In this work we study semi-Kolmogorov models for predation with both the carrying capacities and the indirect effects ...

The structure of attractors for differential equations is one of the main topics in the qualitative theory of dynamical ...

En las últimas décadas muchos investigadores han estado interesados en estudiar problemas no locales por su utilidad en ...

In this paper, we prove the existence of mild solutions for the following first-order impulsive semilinear stochastic ...

Some results on the existence and uniqueness of mild solution for a system of semilinear impulsive differential equations ...

In this paper, we prove the local and global existence and attractivity of mild solutions for stochastic impulsive neutral functional differential equations with infinite delay, driven by fractional Brownian motion.

In this paper we study a simple chemostat model influenced by white noise which makes this kind of models more realistic. ...

In this work we study a model for virus dynamics with a random immune response and a random production rate of susceptible ...

In this survey we provide an introduction to the theory of impulsive dynamical systems in both the autonomous and nonautonomous ...

In this paper we investigate the long term behavior of a stochastic lattice dynamical system with a diffusive nearest ...

This paper is the Preface of a special issue devoted to Nonlinear Dynamics and Complexity generated by the contributions ...

We investigate the long term dynamics for a predation model of Plankton community with indirect effects, under fluctuating ...

In this paper, we consider a non-autonomous nonlocal reactiondiffusion equation with a small perturbation in the nonlocal ...

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, ...

In this paper we investigate the almost sure practical stability for a class of stochastic functional evolution equations. ...

Chemostat refers to a laboratory device used for growing microorganisms in a cultured environment, and has been regarded ...

In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C0-semigroup.

We consider the effects of additive and multiplicative noise on the asymptotic behavior of a fourth order parabolic equation ...

In this survey paper we review several aspects related to Navier-Stokes models when some hereditary characteristics ...

This paper is concerned with the existence and asymptotic stability in the \,p-th moment of mild solutions of nonlinear ...

The main aim of this paper is to establish some criteria for the mean square and almost sure practical exponential stability of a nonlinear monotone stochastic partial differential equations.

Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations ...

In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. ...

This paper is devoted to study the asymptotic behavior of a time-dependent parabolic equation with nonlocal diffusion and ...

Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and ...

In this paper, it is analyzed a non-classical non-autonomous di_usion equation with delay. First, the well-posedness and ...

The appearance of delay terms in a chemostat model can be fully justified since the future behavior of a dynamical system ...

In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, ...

In this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative ...

El estudio de los sistemas dinámicos es de gran importancia, ya que están relacionados con fenómenos del mundo real. Los ...

In this paper we establish some sufficient conditions for the exponential stability of the stationary solution to a ...

In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we ...

This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic delay ...

The so called Lorenz-84 model has been used in climatological studies, for example by coupling it with a low-dimensional ...

The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The ...

In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation ...

We prove the existence of a pullback attractor for a non{autonomous fourth order evolution equation arising in the fi eld ...

In this paper we establish some su cient conditions ensuring almost sure practical asymptotic stability with a non-exponential decay rate for solutions to stochastic evolution equations based on Lyapunov techniques.

In this paper, we study the existence and asymptotic stability in the pth-moment of mild solutions of nonlinear impulsive ...

This article presents some results on existence and uniqueness of mild solutions to neutral stochastic functional evolution ...

The main aim of this paper is to analyse the asymptotic behaviour of a non-autonomous integrodifferential parabolic equation ...

We define (time dependent) Morse-decompositions for non-autonomous evolution processes (non-autonomous dynamical systems) ...

We establish the results on the existence of pullback attractors for nonautonomous functional differential equations with ...

This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-di ...

The aim of this paper is to describe the structure of global attractors for infinite-dimensional non-autonomous dynamical ...

The globally modified Navier-Stokes equations (GMNSE) were introduced by Caraballo, Kloeden & Real in 2006 and have been ...

We study the long term dynamics of non-autonomous functional di fferential equations. Namely, we establish existence results ...

A nonclassical nonautonomous diffusion equation with delay is analyzed. First, we prove the existence and uniqueness of ...

We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a ...

This paper is devoted to the investigation of the dynamics of non-autonomous differential equations. The description of ...

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like ...

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there ...

In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous ...

In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an ...

Este trabajo está dividido en cinco capítulos. En los Capítulos 1 y 3, se trata la parte teórica de los sistemas dinámicos ...

In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), ...

The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard ...

Este trabajo está dividido en dos partes. Una primera en la que se trata la parte teórica de los sistemas dinámicos autónomos ...

In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic ...

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) ...

The long-time behaviour of a stochastic 3D LANS-® model on a bounded domain is analysed. First, we reformulate the model ...

In this work we present the existence and uniqueness of pullback and random attractors for stochastic evolution equations ...

This paper aims to an present account of some problems considered in the past years in Dynamical Systems, new research directions and also provide some open problems.

We prove the existence and uniqueness of strong solutions of a three-dimensional system of globally modified Navier–Stokes ...

This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results ...

The long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by ...

We prove some regularity results for the pullback attractor of a reaction-diffusion model. First we establish a general ...

The existence of a pullback attractor for a reaction-diffusion equations in an unbounded domain containing a non-autonomous ...

We analyze the existence of almost periodic (respectively, almost automorphic, recurrent) solutions of a linear non-homogeneous ...

In this paper we continue the research started in a previous paper, where we proved that the linear differential equation (1) ...

The well-known Favard's theorem states that the linear differential equation x′=A(t)x+f(t) Turn MathJax on with Bohr ...

In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + ...

We obtain some results on the existence and uniqueness, and exponential stability of solutions for the three-dimensional ...

We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time ...

We establish some results on the existence of pullback attractors for non-autonomous delay di fferential equations with ...

In this paper, we consider a stochastic lattice di®erential equation with di®usive nearest neighbor interaction, a dissipative ...

We obtain regularity results for solutions of the three dimensional system of globally modified Navier-Stokes equations, ...

The synchronization of Stratonovich stochastic di erential equations (SDE) with a one-sided dissipative Lipschitz drift ...

We study the asymptotic behaviour of a non-autonomous stochastic reaction-diffusion equation with memory. In fact, we prove ...

We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without ...

We first prove the existence and uniqueness of pullback and random attractors for abstract multi-valued non-autonomous and ...

En primer lugar probamos la existencia y unicidad de atractor para sistemas dinámicos multivaluados abstractos, tanto en ...

The upper semi-continuous convergence of approximate attractors for an infinite delay differential equation of logistic ...

We prove the existence of attractors for some types of differential problems containing infinite delays. Applications and ...

The aim of this paper is to prove the existence of Levitan/Bohr almost periodic, almost automorphic, recurrent and Poisson ...

Stability investigation of hereditary systems often is connected with the construction of Lyapunov functionals. The general ...

The existence and uniqueness of solutions for a stochastic reaction-diffusion equation with infinite delay is proved. ...

A system of semilinear parabolic stochastic partial differential equations with additive space-time noise is considered ...

In this paper we analyse the almost sure exponential stability and ultimate boundedness of the solutions to a class of ...

We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution ...

This paper is intended to be a brief review on some recent results on the stabilization effect produced by noise in phenomena ...

In this paper, we point out the different long-time behaviour of stochastic partial differential equations when one considers ...

We prove existence and uniqueness of solutions for a stochastic version of the 3DLagrangian averaged Navier-Stokes (LANS-®) ...

We analyse the asymptotic behaviour of a 3D Lagrangian averaged Navier-Stokes -model (3D LANS) with delays. In fact, we ...

We prove the existence of a stationary random solution to a delay random ordinary differential system which attracts all ...

We investigate the asymptotic behaviour of a general set-valued skew product flow (SVSPF), that is, a set-valued cocycle ...

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the ...

Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations ...

We investigate the existence, uniqueness and exponential stability of non-constant stationary solutions of stochastic ...

Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the ...

First, we introduce the concept of pullback asymptotically compact non-autonomous dynamical system as an extension of the ...

We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, ut−Δu = βu−u3, by noise. ...

The asymptotic behaviour of some types of retarded differential equations, with both variable and distributed delays, is ...

"Como es bien conocido, las ecuaciones de Navier-Stokes gobiernan el movimiento de fluidos comunes como el agua, el aire, ...

We introduce the concept of a monotone multi-valued semi- ow as an order-preserving map. This de nition is motivated by ...

The aim of this note is to clarify a misleading statement which appeared in our fi rst paper dealing with the concept of global random attractor for multivalued random dynamical systems, as well as in the subsequent work

It is shown that the synchronization of dissipative systems persists when they are disturbed by additive noise no matter ...

An abstract system of coupled nonlinear parabolic-hyperbolic partial differential equations subjected to additive white ...

Existence and uniqueness of solutions for a stochastic version of the 3D-Lagrangian averaged Navier-Stokes (LANS-®) equation in a bounded domain and containing some hereditary characteristics are proved.

The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is ...

We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when ...

Some results concerning the stability and stabilisation of stochastic linear partial differential equations in the sense ...

The existence of a pullback (and also a uniform forward) attractor is proved for a damped wave equation containing a delay ...

La memoria está compuesta de dos partes: la primera se enmarca dentro del Análisis Estocástico y la segunda parte en la ...

In this paper we study the existence of pullback global attractors for multivalued processes generated by differential ...

Some results on the relationship of the solutions of a stochastic di erential inclusion and the corresponding random di ...

Some results on the pathwise asymptotic stability of solutions to stochastic partial differential equations are proved. ...

This paper presents a comparison between two abstract frameworks in which one can treat multi-valued semiflows and their ...

Some results on the asymptotic behaviour of solutions to Navier-Stokes equations when the external force contains some ...

Weak pullback attractors are de ned for nonautonomous setvalued processes and their existence and upper semi continuous ...

Some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general ...

The concept of nonautonomous (or cocycle) attractor has become a proper tool for the study of the asymptotic behaviour of ...

Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations ...

Some results on the existence and uniqueness of solutions for stochastic evolution equations containing some hereditary ...

We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...

Some results on the pathwise exponential stability of the weak solutions to a stochastic 2D-Navier-Stokes equation are ...

Using the relatively new concept of a pullback attractor, we present some results on the existence of attractors for differential equations with variable delay. We give a variety of examples to which our result applies.

Some results on the asymptotic behaviour of solutions of diff erential equations concerning general decay rate are proved. ...

The concept of global attractor for stochastic partial differential inclusions has been recently introduced as a joint ...

The main objective of this paper is to investigate the asymptotic stability for diffusion processes driven by a class of ...

Some exponential growth results for the pullback attractor of a reaction-diffusion when time goes to ¡1 are proved in this ...

We study in some detail the structure of the random attractor for the Chafee{Infante reaction{di¬usion equation perturbed ...

Some results on the existence and uniqueness of solutions to Navier-Stokes equations when the external force contains some hereditary characteristics are proved.

Existence and uniqueness of solutions for a class of nonlinear functional differential equations in Hilbert spaces are ...

Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, ...

In this paper we consider a stochastic differential inclusion with multiplicative noise. It is shown that it generates a multivalued random dynamical system for which there also exists a global random attractor.

We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...

Existence and uniqueness of strong solutions for a class of stochastic functional di fferential equations in Hilbert spaces ...

We study the asymptotic behaviour of a reaction-diffusion equation, and prove that the addition of multiplicative white ...

The theory of random attracting sets highlights interesting properties of the asymptotic behaviour of some stochastic ...

A semilinear stochastic partial differential equation with variable delays is considered. Sufficient conditions for the ...

Some criteria for the mean square and almost sure exponential stability of nonlinear stochastic partial differential ...

"En el Capítulo 1, presentamos una síntesis de los resultados básicos sobre atractores globales que pueden encontrarse en ...

The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential ...

Sufficient conditions to get exponential stability for the sample paths (with probability one) of a non-linear monotone ...

We consider a stochastic non–linear Partial Differential Equation with delay which may be regarded as a perturbed equation. ...

We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. ...

The main aim of this paper is to study stochastic PDE's with delay terms. In fact, we prove existence and uniqueness of ...

Sufficient conditions for pathwise asymptotic exponential stability of the solution of the stochastic PDE with delay d x ...

"En esta memoria presentamos una contribución al estudio de la estabilidad en la Ecuaciones en Derivadas Parciales ...

Sufficient conditions for pathwise exponential stability of the zero solution of stochastic PDE with deviating argument ...