Delays In Leakage Terms Research Articles

The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control.

In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.

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

ABSTRACTIn 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.

Mean-square exponential stability of fuzzy stochastic BAM networks with hybrid delays

We study fuzzy stochastic bidirectional associative memory cellular neural networks with discrete delays in leakage terms and with continuous and infinitely distributed delays in the transmission terms. Under certain structural assumptions, we prove that the networks in question are mean-square exponentially stable. Our main ingredient is the classical direct Lyapunov approach, in which we construct an elaborate Lyapunov–Krasovskii function. The arguments in the paper can be readily adapted to study stability problems for other cellular neural networks.

Adaptive synchronisation of memristor-based neural networks with leakage delays and applications in chaotic masking secure communication

ABSTRACTChaotic synchronisation has caused extensive attention due to its potential application in secure communication. This paper is concerned with the problem of adaptive synchronisation for two different kinds of memristor-based neural networks with time delays in leakage terms. By applying set-valued maps and differential inclusions theories, synchronisation criteria are obtained via linear matrix inequalities technique, which guarantee drive system being synchronised with response system under adaptive control laws. Finally, a numerical example is given to illustrate the feasibility of our theoretical results, and two schemes for secure communication are introduced based on chaotic masking method.

EXISTENCE AND GLOBAL STABILITY OF ALMOST AUTOMORPHIC SOLUTIONS FOR SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS IN LEAKAGE TERMS ON TIME SCALES

In this paper, shunting inhibitory cellular neural networks(SICNNs) with time-varying delays in leakage terms on time scales are investigated. With the aid of the existence of the exponential dichotomy of linear dynamic equations on time scales, fixed point theorem and the theory of calculus on time scales, we establish some sufficient conditions to ensure the existence and exponential stability of almost automorphic solutions for the model. An example with its numerical simulations is given to illustrate the feasibility and effectiveness of the theoretical findings.

Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms

In this paper, bidirectional associative memory (BAM) neural networks with time-varying delays in leakage terms are investigated. A set of sufficient conditions are obtained for the existence and the exponential stability of pseudo almost periodic solutions for this class of neural networks by applying Banach’s fixed point theorems, and differential inequality techniques. Finally, we present a numerical example and simulation to illustrate the effectiveness of the theoretical results. We extend and improve previously know results.

Stability and Hopf Bifurcation of Time Fractional Cohen–Grossberg Neural Networks with Diffusion and Time Delays in Leakage Terms

In this paper, a class of time fractional Cohen---Grossberg neural networks with time delays in leakage terms and diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation are established. By using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.

LMI-based global exponential stability of equilibrium point for neutral delayed BAM neural networks with delays in leakage terms via new inequality technique

The paper is concerned with a class of neutral BAM neural networks with delays in leakage terms. The existence of equilibrium point dependent on time delays of system (1.1) is obtained by establishing and applying two new inequalities. Sufficient condition is established to ensure the global exponential stability of the above neutral networks by establishing and employing above two new inequalities and new LMI methods. The results of this paper are new and complementary to the previously known results.

Global exponential stability of high-order bidirectional associative memory (BAM) neural networks with time delays in leakage terms

High-order bidirectional associative memory (BAM) neural networks with time delays in leakage terms play an increasingly important role in the design and implementation of neural network systems. Based on Lyapunov–Krasovskii functional and linear matrix inequality technique, issues of global exponential stability for high-order BAM neural networks with time delays in leakage terms are investigated. The proposed results, which do not require the boundedness, differentiability and monotonicity of the activation functions. In addition, the stability criteria that depend on the leakage time delays and our results are presented in terms of LMIs, which can be efficiently solved via a standard numerical package. Three numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Existence and Stability of Pseudo Almost Periodic Solution for Neutral Type High-Order Hopfield Neural Networks with Delays in Leakage Terms on Time Scales

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 some sufficient conditions for the existence and global exponential stability of pseudo almost periodic solutions for a class of neutral type high-order Hopfield neural networks with delays in leakage terms on time scales. Our results show that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors. Finally, we give a numerical example and simulation to illustrate the feasibility of our results. Results of this paper are completely new even if the time scale $$\mathbb {T}=\mathbb {R}$$T=R or $$\mathbb {Z}$$Z.

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 exponential stability of almost-periodic solutions for neutral BAM neural networks with time-varying delays in leakage terms on time scales

This paper is concerned with neutral bidirectional associative memory 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. Copyright © 2015 John Wiley & Sons, Ltd.

Almost automorphic solution for neutral type high-order Hopfield neural networks with delays in leakage terms on time scales

In this paper, using the existence of the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, some sufficient conditions for the existence and global exponential stability of almost automorphic solutions for a class of neutral type high-order Hopfield neural networks (HHNNs) with delays in leakage terms on time scales are obtained. Finally, a numerical example is provided to illustrate the feasibility of our results and our results also show that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors. The results of this paper are completely new even when the time scale T=R or Z and show that the delays in the leakage term do harm to the existence and global exponential stability of almost automorphic solutions.

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.

Exponential Stability of BAM Fuzzy Cellular Neural Networks with Time-Varying Delays in Leakage Terms and Impulses

BAM fuzzy cellular neural networks with time-varying delays in leakage terms and impulses are considered. Some sufficient conditions for the exponential stability of the networks are established by using differential inequality techniques. The results of this paper are completely new and complementary to the previously known results. Finally, an example is given to demonstrate the effectiveness and conservativeness of our theoretical results.

Existence and exponential stability of an equilibrium point for fuzzy BAM neural networks with time-varying delays in leakage terms on time scales

In this paper, by using a fixed point theorem and differential inequality techniques, we consider the existence and global exponential stability of an equilibrium point for a class of fuzzy bidirectional associative memory neural networks with time-varying delays in leakage terms on time scales. We also present a numerical example to show the feasibility of obtained results. The results of this paper are completely new and complementary to the previously known results.MSC:34B37, 34N05.

Existence and exponential stability of almost periodic solution for neutral delay BAM neural networks with time-varying delays in leakage terms

This paper is concerned with a class of neutral delay BAM neural networks with time-varying delays in leakage terms. Some sufficient conditions are established to ensure the existence and exponential stability for such class of neural networks by employing the exponential dichotomy of linear differential equations, fixed point theorems and differential inequality techniques. An example is provided to show the effectiveness of the theoretical results. The results of this paper are completely new and complementary to the previously known results.

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.

Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms

This paper is concerned with the existence and exponential stability of anti-periodic solutions for shunting inhibitory cellular neural networks (SICNNs) with time-varying delays in the leakage terms. Some sufficient conditions are established to ensure that all solutions of the networks converge exponentially to the anti-periodic solution, which are new and complement of previously known results.

Periodic Solution for Impulsive Cellar Neural Networks with Time-Varying Delays in the Leakage Terms

This paper is concerned with impulsive cellular neural networks with time-varying delays in leakage terms. Without assuming bounded and monotone conditions on activation functions, we establish sufficient conditions on existence and exponential stability of periodic solutions by using Lyapunov functional method and differential inequality techniques. Our results are complement to some recent ones.