Solutions For Cellular Neural Networks Research Articles

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.

Effect of Proportional Delays and Continuously Distributed Leakage Delays on Global Exponential Convergence of CNNS

AbstractThis paper is concerned with a class of cellular neural networks (CNNs) with proportional delays and continuously distributed leakage delays. Using the differential inequality theory, a set of sufficient conditions which guarantee the exponential convergence of all solutions of CNNs with proportional delays and continuously distributed leakage delays are derived. Computer simulations are carried out to verify our theoretical findings. The obtained results of this paper are new and complement some previous studies.

Weighted Pseudo Almost Periodic Solutions for Cellular Neural Networks with Multi-proportional Delays

This paper is concerned with the dynamics of weighted pseudo almost periodic cellular neural networks with multi-proportional delays. Applying fixed point theorem and differential inequality techniques, several sufficient conditions are derived to ensure the existence and exponential stability of weighted pseudo almost periodic solutions for the addressed model, which are more general and complicated than periodic and pseudo almost periodic results in some existing literatures. Moreover, an example with graphical illustration is given to demonstrate the effectiveness of the theoretical results.

Almost periodic cellular neural networks with neutral-type proportional delays

ABSTRACTThis 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.

Weighted Pseudo Anti‐Periodic Solutions for Cellular Neural Networks with Mixed Delays

AbstractA model of cellular neural networks with mixed delays is proposed. Applying contraction mapping fixed point theorem and differential inequality technique, several sufficient conditions are derived to ensure the existence and exponential stability of weighted pseudo anti‐periodic solutions for the proposed neural networks. Finally, a numerical simulation example is given to illustrate the effectiveness of the obtained results.

Anti-periodic solutions for cellular neural networks with oscillating coefficients in leakage terms

This paper is concerned with the anti-periodic solutions for a class of cellular neural network model with oscillating coefficients in leakage terms. By applying contraction mapping fixed point theorem and differential inequality techniques, we establish some sufficient conditions to guarantee the existence and exponential stability of anti-periodic solutions for this model, which improve and supplement existing ones. Moreover, an example and its numerical simulations are given to support the theoretical results.

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.

On almost automorphic solutions for cellular neural networks with time-varying delays in leakage terms on time scales1

On almost automorphic solutions for cellular neural networks with time-varying delays in leakage terms on time scales1

Existence and stability of almost-periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales

This paper is concerned with cellular neural networks with time-varying delays in leakage terms on time scales. Some sufficient conditions on the existence, uniqueness, and global exponential stability of almost-periodic solutions are established. An example is presented to illustrate the feasibility and effectiveness of the obtained results.

Existence and global stability of a periodic solution for a cellular neural network

Purpose of this study is to investigate the dynamical properties of Chua and Yang cellular neural networks (CNNs). Based on the continuation theorem of coincidence degree theory, a novel sufficient condition with respect to the existence of periodic solution for CNNs is derived. Moreover, a generalized Lyapunov–Krasovskii functional is designed to guarantee the global stability of the existed periodic solution. An illustrative example is given to verify the effectiveness and correctness of the proposed method, furthermore, random disturbance is added in the numerical simulation in order to verify the robustness of the proposed approach.

Existence of Anti-Periodic Solution for Delayed Cellular Neural Networks with Impulsive Effects

As an important tool to study practical problems of biology, engineering and image processing, the cellular neural networks (CNNs) has caused more and more attention. Some interesting results about the existence of solution for cellular neural networks have been obtained. In this paper, by means of iterative analysis, the existence and uniqueness of anti-periodic solution of delayed cellular neural networks with impulsive effects are considered. Some new results are obtained.

Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms

This paper concerns with cellular neural networks with time-varying delays in leakage (or forgetting) terms. Without assuming boundedness on activation functions, we establish sufficient conditions on existence and global exponential stability of almost periodic solutions by using Lyapunov functional method and differential inequality techniques. Our results complement with some recent ones.

Existence and Global Uniform Asymptotic Stability of Almost Periodic Solutions for Cellular Neural Networks with Discrete and Distributed Delays

This paper discusses the existence and global uniform asymptotic stability of almost periodic solutions for cellular neural networks (CNNS). By utilizing the theory of the almost periodic differential equation and the Lyapunov functionals method, some sufficient conditions are obtained to ensure the existence and global uniform asymptotic stability. An example is given to illustrate the effectiveness of the main results.

Existence and Stability of Periodic Solution for Impulsive Hopfield Cellular Neural Networks with Distributed Delays

As an important tool to study practical problems of biology, engineering and image processing, the cellular neural networks (CNNs) has caused more and more attention. Some interesting results about the existence of solution for cellular neural networks have been obtained. In this paper, by means of iterative analysis, the existence of periodic solution and the uniform stability of the equilibrium point of impulsive Hopfield cellular neural networks with distributed delays are considered. Some new results are obtained.

Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales

We study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale 𝕋 = ℝ or ℤ and improve some of the previously known results.

Existence and Global Exponential Stability of Periodic Solutions of Cellular Neural Networks with Distributed Delays and Impulses on Time Scales

In this paper, by using Mawhin’s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results. Keywords—periodic solutions, global exponential stability, coincidence degree, M -matrix

Existence and Global Exponential Stability of Periodic Solution of Cellular Neural Networks with Delay and Impulses

This paper investigates the global periodicity of cellular neural network with impulses and constant delay. Several conditions guaranteeing the existence, uniqueness, and global exponential stability of periodic solution are derived by using the continuation theorem of coincidence degree theory and suitable degenerate Lyapuniv–Krasvovskii functional.

New results on exponential attractivity of multiple almost periodic solutions of cellular neural networks with time-varying delays

We present new results on multi-almost periodicity and attractivity of delayed cellular neural networks (DCNNs). Some criteria are derived for ensuring locally or globally exponential attractivity of multiple almost periodic solutions in designated regions. It is shown that N -dimensional DCNNs can have a coexistence of 2 N locally attractive almost periodic solutions. Furthermore, the obtained conclusions have a wider applicable range, improve and complement the existing ones. Finally, computer simulations are given to show the effectiveness of the theoretical results.

New results of almost periodic solutions for cellular neural networks with mixed delays

In this paper, for cellular neural networks with mixed delays, we prove some new results on the existence of almost periodic solutions by contraction principle. The global exponential stability of almost periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.

On the Almost Periodic Solution of Cellular Neural Networks With Distributed Delays

By exponential dichotomy about differential equations, a formal almost periodic solution (APS) of a class of cellular neural networks (CNNs) with distributed delays is obtained. Then, within different normed spaces, several sufficient conditions guaranteeing the existence and uniqueness of an APS are proposed using two fixed-point theorems. Based on the continuity property and some inequality techniques, two theorems insuring the global stability of the unique APS are given. Comparing with known literatures, all conclusions are drawn with slacker restrictions, e.g., do not require the integral of the kernel function determining the distributed delays from zero to positive infinity to be one, and the activation functions to be bounded, etc.; besides, all criteria are obtained by different ways. Finally, two illustrative examples show the validity and that all criteria are easy to check and apply.