Pseudo-almost Periodic Solutions Research Articles

New Results for Impulsive Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays

In this paper, we shall explain a new result concerning piecewise weighted pseudo almost-periodic solution of impulsive recurrent neural networks with time-varying coefficients and mixed delays. Precisely, some sufficient conditions are given to prove the existence and the exponential stability of piecewise weighted pseudo almost-periodic solution by employing fixed point theorem, generalized Gronwall–Bellman inequality and differential inequality techniques. Finally, an illustrative example is given to demonstrate the effectiveness of our results.

Weighted pseudo-almost periodic delayed cellular neural networks

This paper investigates a class of non-autonomous cellular neural networks with mixed delays. Based on the basic theory of the weighted pseudo-almost periodic functions, several sufficient conditions are established to ensure that every solution of the addressed model exponentially tends to a weighted pseudo-almost periodic solution as $$t\rightarrow +\infty$$ , which generalize some existing ones. In particular, some numerical examples are also given.

Pseudo-almost periodic solutions for a discrete Nicholson’s blowflies model with harvesting term

This paper is concerned with a discrete Nicholson’s blowflies model, which involves a linear harvesting term. In the case where the coefficients are pseudo-almost periodic functions, we establish the existence and local exponential stability of pseudo-almost periodic solutions for the addressed Nicholson’s blowflies model by using the contraction mapping theorem and a Lyapunov functional. An example is given to illustrate our results.

Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays

In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays.

In this article, we consider a class of neutral impulsive shunting inhibitory cellular neural networks with time varying coefficients and leakage delays. We study the existence and the exponential stability of the piecewise differentiable pseudo almost-periodic solutions and establish sufficient conditions for the existence and exponential stability of such solutions. An example is provided to illustrate the theory developed in this work.

Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks

In this paper, the existence and the exponential stability of piecewise differentiable pseudo-almost periodic solutions for a class of impulsive neutral high-order Hopfield neural networks with mixed time-varying delays and leakage delays are established by employing the fixed point theorem, Lyapunov functional method and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.

Piecewise Pseudo Almost Periodic Solution for Impulsive Generalised High-Order Hopfield Neural Networks with Leakage Delays

Existence of piecewise differentiable pseudo almost-periodic solutions for a class of impulsive high-order Hopfield neural networks with leakage delays are established by employing the fixed point theorem, differential inequality and Lyapunov functionals. The results of this paper are new and they supplement previously known works. Numerical example with graphical illustration is given to illuminate our main results.

Pseudo-almost periodic solution for impulsive hematopoiesis model with infinite delays and linear harvesting term

In this paper, a generalized impulsive model of hematopoiesis with infinite delays and linear harvesting term is investigated. The main purpose of this paper is to study the existence, uniqueness and exponential stability of the positive pseudo-almost periodic solutions, which improve and extend some known relevant results. Moreover, an example is given to illustrate the main findings.

New results on positive pseudo-almost periodic solutions for a delayed Nicholson’s blowflies model

This paper is concerned with a non-autonomous Nicholson’s blowflies model with an oscillating death rate. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive pseudo-almost periodic solution, which improves and extends some known relevant results. Moreover, an example along with its numerical simulations is presented to demonstrate the validity of the proposed result.

Measure Pseudo-Almost Periodic Solutions in the $${\alpha}$$ α -Norm to Some Neutral Partial Differential Equations with Delay

The aim of this work was to study the existence and uniqueness of \({\mu}\)-pseudo almost periodic solutions in the \({\alpha}\)-norm for some partial differential equation with infinite delay. In the last section we give an application.

Piecewise pseudo-almost periodic solution for impulsive non-autonomous high-order Hopfield neural networks with variable delays

In this paper, we provide a new method to study non-autonomous dynamic systems with variable pseudo-almost periodic coefficients. By using some fixed point theorems in Banach space and inequality technique, some completely new sufficient conditions of the existence and exponential stability of piecewise pseudo-almost periodic solutions are established for impulsive non-autonomous high-order Hopfield neural networks with variable coefficients and delays. Finally, a numerical example and simulations are given to illustrate that the obtained results are feasible and effective. It is the first time that the existence and stability of the pseudo-almost periodic solutions for impulsive nonautonomous neural networks are obtained.

Pseudo-almost Periodic and Pseudo-almost Automorphic Solutions to Evolution Equations in Hilbert Spaces

In this work we prove some existence and uniqueness results for pseudo-almost periodic and pseudo-almost automorphic solutions to a class of semi-linear differential equations in Hilbert spaces using theoretical measure theory. The main technique is based upon some appropriate composition theorems combined with the Banach contraction mapping principle and the method of the invariant subspaces for unbounded linear operators. A few illustrative examples will be discussed at the end of the paper.

Existence and Exponential Stability of Weighted Pseudo Almost Periodic Classical Solutions of Integro-Differential Equations with Analytic Semigroups

In this paper, we investigate a class of integro-differential equations having analytic semigroups given by $$\begin{aligned} x'(t)=Ax(t)+f(t,x(t),Gx(t)). \end{aligned}$$ Our main results concern the existence, uniqueness and globally exponential stability of weighted pseudo-almost periodic classical solutions. An example is given to illustrate our results.

Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions to Some Evolution Equations Involving Theoretical Measure Theory

Toka DiaganaHoward University,2441 6th Street N.W.,Washington, D.C. 20059,USA.tdiagana@howard.eduKhalil EzzinbiUniversit´e Cadi Ayyad,Faculte´ des Sciences Semlalia,D´epartement deMath´ematiques,BP 2390, Marrakesh, MarocMohsen MiraouiInstitut sup´erieur des Etudestechnologiques de Kairouan,Rakkada-3191 Kairouan,Tunisie.ABSTRACTMotivated by the recent works by the first and the second named authors, in this paperwe introduce the notion of doubly-weighted pseudo-almost periodicity (respectively,doubly-weighted pseudo-almost automorphy) using theoretical measure theory. Basicproperties of these new spaces are studied. To illustrate our work,westudy,underAcquistapace–Terreni conditions and exponential dichotomy, the existence of (µ,ν)-pseudo almost periodic (respectively, (µ,ν)-pseudo almost automorphic) solutions tosome nonautonomous partial evolution equations in Banach spaces. A few illustrativeexamples will be discussed at the end of the paper.RESUMENMotivado por los trabajos recientes del primer y segundo autor, en este art´iculo intro-ducimos la noci´on de seudo-casi periodicidad con doble peso (seudo-casi automorf´ia condoble peso respectivamente) usando Teor´ia de la Medida. Se estudian las propiedadesbasicas de estos espacios nuevos. Para ilustrar nuestro trabajo, bajo las condiciones deAcquistapace-Terreni y dicotom´ia exponencial estudiamos la existencia de soluciones(respectivamente, (µ,ν) seudo-casi peri´odicas (µ,ν) seudo-casi automorficas) para al-gunas ecuaciones parciales de evoluci´on autonomas en espacios de Banach. Algunosejemplos ilustrativos se discutiran al final del art´iculo.Keywords and Phrases: Evolution family; exponential dichotomy; Acquistapace–Terreni con-ditions; pseudo-almost periodic; pseudo-almost automorphic; evolution equation; nonautonomousequation; doubly-weighted pseudo-almost periodic; doubly-weighted pseudo-almost automorphy;(µ,ν)-pseudo-almost periodicity; (µ,ν)-pseudo-almost automorphy; neutral systems; positive mea-sure.2010 AMS Mathematics Subject Classification: 34C27; 34K14; 34K30; 35B15; 43A60;47D06; 28Axx; 58D25; 65J08.

Global Exponential Stability of Weighted Pseudo-Almost Periodic Solutions of Neutral Type High-Order Hopfield Neural Networks with Distributed Delays

Some sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of weighted pseudo-almost periodic solutions to a class of neutral type high-order Hopfield neural networks with distributed delays by employing fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results. Moreover, an example is given to show the effectiveness of the proposed method and results.

Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in fading memory spaces

We use a new concept of weighted ergodic function based on the measure theory to investigate the existence and uniqueness of weighted pseudo almost periodic solution for a class of partial functional differential equations with infinite delay in fading memory spaces. We illustrate our theoretical results by studying some Lotka-Voltera reaction-diffusion systems with infinite delay.

The existence of pseudo-almost periodic solutions of third-order neutral differential equations with piecewise constant argument

In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations.

Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays.

This paper is concerned with the existence and uniqueness of pseudo almost-periodic solutions to recurrent delayed neural networks. Several conditions guaranteeing the existence and uniqueness of such solutions are obtained in a suitable convex domain. Furthermore, several methods are applied to establish sufficient criteria for the globally exponential stability of this system. The approaches are based on constructing suitable Lyapunov functionals and the well-known Banach contraction mapping principle. Moreover, the attractivity and exponential stability of the pseudo almost-periodic solution are also considered for the system. A numerical example is given to illustrate the effectiveness of our results.

Weighted Pseudo-almost Periodic Solutions of Neutral Integral and Differential Equations

In this paper, we study weighted pseudo-almost periodic solutions togeneral neutral integral equations. By applying the properties ofweighted pseudo-almost periodic functions and the fixed pointtheorem, we establish the conditions for the existence anduniqueness of weighted pseudo-almost periodic solutions of theequations.

Pseudo-almost periodic viscosity solutions of second-order nonlinear parabolic equations

In this paper we generalize the comparison result of Bostan and Namah (2007) [8] to the second-order parabolic case and prove two properties of pseudo-almost periodic functions; then by using Perron’s method we prove the existence and uniqueness of time pseudo-almost periodic viscosity solutions of second-order parabolic equations under usual hypotheses.