Pseudo-almost Periodic Solutions Research Articles

Pseudo-Almost Periodic Solutions in the Alpha-Norm and in Stepanov’s Sense for some Evolution Equations

Pseudo-Almost Periodic Solutions in the Alpha-Norm and in Stepanov’s Sense for some Evolution Equations

On the Weighted Pseudo Almost-Periodic Solutions of Static DMAM Neural Network

On the Weighted Pseudo Almost-Periodic Solutions of Static DMAM Neural Network

Mu-pseudo almost periodic solutions in Lebesgue spaces with variable exponents

The idea to consider the concept of measure pseudo almost periodic oscillation corresponds better to the physical reality since the periodicity is utopic. So, in this research paper, we inform a notion of mu-pseudo-almost periodicity using theoretical measure. Then we study the existence and uniqueness of measure pseudo-almost periodic solutions to some first-order differential equations in Lebesgue spaces with variable exponents.

Dynamics of fuzzy genetic regulatory networks with leakage and mixed delays in doubly-measure pseudo-almost periodic environment

The study of dynamics behaviors of genetic regulatory networks (GRNs) is essential for the understanding of living organisms at both molecular and cellular levels. This paper deals with a class of fuzzy genetic regulatory networks (FGRNs) with time varying-delays in leakage terms, time-varying discrete delays, unbounded distributed delays, and doubly-measure pseudo-almost periodic parameters. Based on the doubly-measure pseudo-almost periodic theory, exponential dichotomy, differential inequality, and the Banach fixed point theorem, we establish some sufficient conditions to support the existence and global exponential stability of doubly-measure pseudo-almost periodic solutions for the considered model. A numerical example along with a graphical illustration are presented to support our main results. The results of this paper are new and extend existing GRNs models using almost periodic and weighted pseudo-almost periodic functions to support a wider range of regulatory processes.

Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays

Cellular neural networks with D operator and time-varying delays are found to be effective in demonstrating complex dynamic behaviors. The stability analysis of the pseudo-almost periodic solution for a novel neural network of this kind is considered in this work. A generalized class neural networks model, combining cellular neural networks and the shunting inhibitory neural networks with D operator and time-varying delays is constructed. Based on the fixed-point theory and the exponential dichotomy of linear equations, the existence and uniqueness of pseudo-almost periodic solutions are investigated. Through a suitable variable transformation, the globally exponentially stable sufficient condition of the cellular neural network is examined. Compared with previous studies on the stability of periodic solutions, the global exponential stability analysis for this work avoids constructing the complex Lyapunov functional. Therefore, the stability criteria of the pseudo-almost periodic solution for cellular neural networks in this paper are more precise and less conservative. Finally, an example is presented to illustrate the feasibility and effectiveness of our obtained theoretical results.

Measure pseudo almost periodic solution for a class of nonlinear delayed stochastic evolution equations driven by Brownian motion

In this work, we present a new concept of measure-ergodic process to define the space of measure pseudo almost periodic process in the p-th mean sense. We show some results regarding the completeness, the composition theorems and the invariance of the space consisting in measure pseudo almost periodic process. Motivated by above mentioned results, the Banach fixed point theorem and the stochastic analysis techniques, we prove the existence, uniqueness and the global exponential stability of doubly measure pseudo almost periodic mild solution for a class of nonlinear delayed stochastic evolution equations driven by Brownian motion in a separable real Hilbert space. We provide an example to illustrate the effectiveness of our results.

Existence and exponential stability of weighted pseudo-almost periodic solutions for genetic regulatory networks with time-varying delays

The importance of prediction for genetic regulatory network (GRNs) makes mathematical modeling a prominent tool. In this paper, we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying delays. We establish the existence, uniqueness, and global exponential stability by employing the theory of dichotomy, the fixed point theorem, and differential inequality. A numerical example along with a graphical illustration are presented to support our main results. Our results extend existing GRNs models using almost periodic functions to support a wider range of regulatory processes.

Piecewise Pseudo Almost-Periodic Solutions of Impulsive Fuzzy Cellular Neural Networks with Mixed Delays

This article examines the existence of the unique piecewise pseudo almost periodic for impulsive fuzzy cellular neural networks by using the contraction mapping principle and piecewise pseudo almost periodic function theory. Further, sufficient certain conditions for their global exponential stability are produced through the use of differential inequality and generalized Gronwall–Bellman inequality. Our results are new and complement some previously known ones. Two examples and their numerical simulations are performed to ensure our theoretical results.

Weighted pseudo-almost periodic solutions and global exponential synchronization for delayed QVCNNs

In this paper, we study the existence of weighted pseudo-almost periodic solutions and the global exponential synchronization of delayed quaternion-valued cellular neural networks (QVCNNs). Firstly, we use the Banach fixed point theorem to establish the existence of weighted pseudo-almost periodic solutions for this class of QVCNNs. Then, under the condition that the drive system has a unique weighted pseudo-almost periodic solution, by designing a state-feedback controller and constructing suitable Lyapunov functions, we see that the drive–response structure of delayed QVCNNs with weighted pseudo-almost periodic coefficients achieve global exponential synchronization. Finally, a numerical example is given to illustrate the feasibility of our results.

Influence of time delay on weighted pseudo-almost periodic dynamics in SICNNs

PurposeThe purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and distributed delays.Design/methodology/approachThe principle of weighted pseudo-almost periodic functions and some new mathematical analysis skills are applied.FindingsA set of sufficient criteria which guarantee the existence and exponential stability of the weighted pseudo-almost periodic solutions of the considered SICNNs are established.Originality/valueThe derived results of this paper are new and complement some earlier works. The innovation of this paper concludes two points: a new sufficient criteria guaranteeing the existence and exponential stability of the weighted pseudo-almost periodic solutions of SICNNs are established; and the ideas of this paper can be applied to investigate some other similar neural networks.

Oscillation and stability of multidirectional associative memory neural network with mixed delays

This paper deals with a generalized multidirectional associative memory neural network with time-varying coefficients and mixed delays. Some criteria are established for the existence and the global exponential stability of weighted pseudo almost-periodic solutions for the studied model. To do so, the exponential dichotomy theory, the contraction mapping fixed point theorem and the differential inequality techniques are used. Moreover, an example and its numerical simulation are employed to illustrate the main results.

Existence and Global Exponential Stability of Pseudo Almost Periodic Solution for Clifford- Valued Neutral High-Order Hopfield Neural Networks With Leakage Delays

In this paper, we are concerned with a class of Clifford-valued neutral high-order Hopfield neural networks with leakage delays. Although the multiplication of Clifford numbers does not satisfy the commutativity, which brings great difficulties to the study of Clifford-valued systems, we have found a method that does not decompose Clifford-valued systems into real-valued systems to study the existence and global exponential stability of pseudo-almost periodic solutions of this class of neural networks. Our results are completely new. Finally, two examples are given to illustrate the effectiveness and feasibility of our main results.

Pseudo-almost periodic solutions for first-order neutral differential equations

In this paper, we study a class of first-order neutral differential equations with time-varying delays and coefficients. Employing the fixed point method and differential inequality techniques, easily verifiable delay-independent criteria are established to ensure the existence and global exponential stability of pseudo-almost periodic solutions for the addressed equations. These theoretical results are also supported with numerical simulations.

The Generalization of the Classical Weighted Pseudo-Almost Periodic Solutions Under the Measure Theory to some Classes of Nonautonomous Partial Evolution Equations

The Generalization of the Classical Weighted Pseudo-Almost Periodic Solutions Under the Measure Theory to some Classes of Nonautonomous Partial Evolution Equations

Weighted Pseudo-Almost Periodic Solutions for Shunting Inhibitory Cellular Neural Networks on Time Scales

In this paper, by using the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, we obtain sufficient conditions for the existence, uniqueness and global exponential stability of weighted pseudo-almost periodic solutions of a class of shunting inhibitory cellular neural networks with mixed delays on time scales. A numerical example is also presented to illustrate the feasibility of our results.

Impulsive generalized high-order recurrent neural networks with mixed delays: Stability and periodicity

Abstract In this paper, by employing fixed point theorem, generalized Gronwall–Bellman inequality and differential inequality techniques, some sufficient conditions are given for the existence and the exponential stability of the unique piecewise weighted pseudo almost-periodic solution of impulsive high-order recurrent neural networks with time-varying coefficients and mixed delays. An illustrative example is also given in the end of this paper to show the effectiveness of our results.

On the Weighted Pseudo-Almost Periodic Solution for BAM Networks with Delays

In this paper, a class of Bidirectional Associative Memory neural networks with time-varying weights and continuously distributed delays is discussed. Sufficient conditions are obtained for the existence and uniqueness of weighted pseudo-almost periodic solution of the considered model and numerical examples are given to show the effectiveness of the obtained results.

Review and Study of Some Doubly-Weighted Pseudo-almost Periodic Solutions of Some Partial Evolution Equations

Review and Study of Some Doubly-Weighted Pseudo-almost Periodic Solutions of Some Partial Evolution Equations

Positive piecewise pseudo-almost periodic solutions of first-order singular differential equations with impulses

This paper is concerned with a kind of first-order singular differential equations with impulses. The main purpose of this paper is to study the existence, uniqueness, and globally exponential stability of the positive piecewise pseudo-almost periodic solutions. The main tools utilized to establish our results consist of the contraction mapping principle and generalized Gronwall–Bellmain inequality. Two examples are given at the end of the paper to illustrate the main results.

Pseudo-Almost Periodic Solution on Time-Space Scales for a Novel Class of Competitive Neutral-Type Neural Networks with Mixed Time-Varying Delays and Leakage Delays

A competitive neural network model was proposed to describe the dynamics of cortical maps in which, there exist two memories: long-term and short-term. In this paper, we investigate the existence and the exponential stability of the pseudo-almost periodic solution of a system of equations modeling the dynamics of neutral-type competitive neural networks with mixed delays in the time-space scales for the first time. The mixed delays include time-varying delays and continuously distributed ones. Based on contraction principle and the theory of calculus on time-space scales, some new criteria proving the convergence of all solutions of the networks toward the unique pseudo-almost periodic solution are derived by using the ad-hoc Lyapunov–Krasovskii functional. Finally, numerical example with graphical illustration is given to confirm our main results.