Related papers: Global attractivity in almost periodic single spec…
We develop a theory which allows making qualitative conclusions about the dynamics of both monotone and non-monotone Moreau sweeping processes. Specifically, we first prove that any sweeping processes with almost periodic monotone…
In this article, we study the global dynamics of a discrete two dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this…
We study the existence of non-trivial, non-negative periodic solutions for systems of singular-degenerate parabolic equations with nonlocal terms and satisfying Dirichlet boundary conditions. The method employed in this paper is based on…
Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and…
We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept…
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response…
For a family of $n$-dimensional periodic delay differential equations which encompasses a broad set of models used in structured population dynamics, the existence of a positive periodic solution is obtained under very mild conditions. The…
This paper is devoted to the quantitative study of the attractive velocity of generalized attractors for infinite-dimensional dynamical systems. We introduce the notion of~$\varphi$-attractor whose attractive speed is characterized by a…
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
We investigate fractional Cauchy type problem. By using Schauder fixed point theorem we obtain sufficient conditions for the global attractivity of solutions for nonlinear fractional differential equations in weighted spaces.
Mean field modeling is a popular approach to assess the performance of large scale computer systems. The evolution of many mean field models is characterized by a set of ordinary differential equations that have a unique fixed point. In…
This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class…
In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with…
We consider the Maxwell-Bloch system which is a finite-dimensional approximation of the coupled nonlinear Maxwell-Schr\"odinger equations. The approximation consists of one-mode Maxwell field coupled to two-level molecule. We construct…
The aim of this paper is to study the remotely almost periodic motions of dynamical systems and solutions of nonlinear differential equations. We establish some properties of remotely almost periodic motions and generalize the well known…
For a class of quasilinear parabolic systems with nonlinear Robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity. We further show that a priori estimates in lower norms are…
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 establish and prove a fixed point theorem from which some sufficient conditions on the existence of positive almost periodic solutions for a model of hematopoiesis with oscillatory circulation loss rate are deduced. Some particular…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…