Exponential Stability of Pseudo Almost Periodic Solutions for Cellular Neural Networks with Multi-Proportional Delays

This paper concerns with the pseudo almost periodic solutions for a class of cellular neural networks model with multi-proportional delays. By applying contraction mapping fixed point theorem and differential inequality techniques, we establish some sufficient conditions for the existence and exponential stability of pseudo almost periodic solutions for the model, which improve and supplement existing ones. Moreover, an example and its numerical simulation are given to support the theoretical results.     

Pseudo Almost Periodic Solutions for High-Order Hopfield Neural Networks with Time-Varying Leakage Delays

In this paper, high-order Hopfield neural networks with time-varying leakage delays are investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. Some simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies.     

Exponential stability for nonautonomous impulsive neutral partial stochastic evolution equations with delay

In this paper, we give sufficient conditions for the exponential stability of pseudo almost periodic in distribution mild solutions for nonautonomous impulsive neutral partial stochastic evolution equations with delay in a Hilbert space. Our working tools are based on the interpolation theory, the stochastic analysis techniques and fixed point theorem. To illustrate our main result, we study the exponential stability of a pseudo almost periodic in distribution solution for the neutral stochastic model arising in physical systems.     

Pseudo Almost Periodic Solutions for SICNNs with Oscillating Leakage Coefficients and Complex Deviating Arguments

This paper is concerned with the existence of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with oscillating leakage coefficients and complex deviating arguments. Applying the contraction mapping fixed point theorem and inequality techniques, some sufficient conditions are presented to ensure the existence of pseudo almost periodic solutions of this model, which are new and supplement some previously known ones.     

Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Cellular Neural Networks with <Emphasis Type="Italic">D</Emphasis> Operator

This article is concerned with a class of neutral type cellular neural networks with D operator. By using Lyapunov functional method and differential inequality techniques, we establish a novel result to ensure the existence and global exponential stability of pseudo almost periodic solutions for the addressed system. In addition, an example and its numerical simulations are given to illustrate our result.     

Pseudo almost periodic solutions for neutral type SICNNs with D operator

In this paper, neutral type shunting inhibitory cellular neural networks with D operator are considered. Based on Lyapunov functional method and differential inequality technique, some new criteria are derived to guarantee the existence and global exponential stability of pseudo almost periodic solutions of considered systems. In addition, an example and its numerical simulations are provided to show the validity and the advantages of the obtained results.     

Almost periodic cellular neural networks with neutral-type proportional delays

This paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.     

Pseudo Almost Automorphic Solutions of Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays

In this paper, existence, uniqueness and global exponential stability of pseudo almost automorphic solutions for a class of recurrent neural networks with time-varying coefficients and mixed delays are established by employing the fixed point theorem and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.     

Multistability of HNNs with almost periodic stimuli and continuously distributed delays

In this article, we investigate multistability of Hopfield neural networks (HNNs) with almost periodic stimuli and continuously distributed delays. By employing the theory of exponential dichotomy and Schauder's fixed point theorem, sufficient conditions are gained for the existence of 2 ^N almost periodic solutions which lie in invariant regions. Meanwhile, we derive some new criteria for the networks to converge toward these 2 ^N almost periodic solutions and the domain of attraction is also given. The obtained results are new, general and improve corresponding results existing in previous literature.     

Pseudo almost periodic solutions for CNNs with oscillating leakage coefficients and complex deviating arguments

In this paper, cellular neural networks with oscillating leakage coefficients and complex deviating arguments are considered. Some criteria are established for the existence of pseudo almost periodic solutions for these models by using the contraction mapping fixed point theorem and inequality analysis technique. The results of this paper are new and complement the previously known ones.     

Effect of leakage delay on the almost periodic solutions of fuzzy cellular neural networks

ABSTRACT

In this paper, fuzzy cellular neural networks with time-varying delays in leakage terms are investigated. With the help of the differential inequality theory and almost periodic function theory, a set of sufficient criteria that guarantee the existence and exponential stability of almost periodic solutions of fuzzy cellular neural networks with time-varying delays in leakage terms are established. Our results are new and complement some previously known ones. Moreover, numerical simulations are carried out to verify our theoretical results.     

Pseudo Almost Periodic Solution of Recurrent Neural Networks with D Operator on Time Scales

This paper is concerned with a class of neutral type recurrent neural networks with time-varying delays, distributed delay and D operator on time–space scales which unify the continuous-time and the discrete-time recurrent neural networks under the same framework. Some sufficient conditions are given for the existence and the global exponential stability of the pseudo almost periodic solution by using inequality analysis techniques on time scales, fixed point theorem and the theory of calculus on time scales. An example is given to show the effectiveness of the derived results via computer simulations.

     

Almost periodic solutions for Hopfield neural networks with continuously distributed delays

In this paper Hopfield neural networks with continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results.     

Almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term

In this paper, we propose a class of quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term. In order to overcome the difficulty of the non-commutativity of quaternion multiplication, we first decompose the system under consideration into four real-valued systems. Then by using the exponential dichotomy theory of linear differential equations and Banach's fixed point theorem, we establish sufficient conditions to ensure the existence and global exponential stability of almost periodic solutions for this class of neural networks. Finally, a numerical example is given to demonstrate the effectiveness of the obtained result.     

一类分布参数动态系统的周期性分析

通过构造适当的Lyapunov泛函、利用M矩阵性质和不等式技巧, 在不要求神经网络激励函数的有界性、单调性和可微性弱保守条件下, 探讨了一类具有分布参数和分布时滞的Cohen-Grossberg动态神经网络周期解的存在性和指数稳定性问题, 提出了一系列充分性判据来确保这类同时具有分布参数和分布时滞神经网络周期解的存在性和指数稳定性, 并通过几个注解以及与其他文献结果进行比较说明了该方法的优越性. 最后, 给出了数值例子和计算机仿真来验证这一理论的有效性.     

Weighted Pseudo Almost Periodic Shunting Inhibitory Cellular Neural Networks with Multi-proportional Delays

Neural Processing Letters - In this present paper, the dynamics of weighted pseudo almost periodic shunting inhibitory cellular neural networks with multi-proportional delays is concerned. By...     

Dynamic behaviors of memristor-based delayed recurrent networks

This paper investigates the problem of the existence and global exponential stability of the periodic solution of memristor-based delayed network. Based on the knowledge of memristor and recurrent neural network, the model of the memristor-based recurrent networks is established. Several sufficient conditions are obtained, which ensure the existence of periodic solutions and global exponential stability of the memristor-based delayed recurrent networks. These results ensure global exponential stability of memristor-based network in the sense of Filippov solutions. And, it is convenient to estimate the exponential convergence rates of this network by the results. An illustrative example is given to show the effectiveness of the theoretical results.     

Almost Periodic Solutions for SICNNs with Neutral Type Proportional Delays and <Emphasis Type="Italic">D</Emphasis> Operators

This article is concerned with shunting inhibitory cellular neural networks involving neutral type proportional delays and D operators. Applying Lyapunov functional method and differential inequality techniques, we employ a novel argument to establish some new criteria on the existence and generalized exponential stability of almost periodic solutions of the addressed systems. In addition, numerical simulations are carried out to verify our theoretical findings.     

Stability and existence of periodic solutions in inertial BAM neural networks with time delay

In this paper, the global exponential stability and existence of periodic solutions for inertial BAM neural networks are investigated. The system is transformed to first-order differential equation with chosen variable substitution. Then, some new sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov function, using Weierstrass criteria and boundedness of solutions. Finally, an example is given to illustrate the effectiveness of the results.