Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays

In this paper, a class of impulsive Cohen-Grossberg-type bi-directional associative memory (BAM) neural networks with distributed delays is investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing the homeomorphism theory, the M-matrix theory and inequality technique, some new general sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen-Grossberg-type BAM neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulsive disturbed intension. An example is given to show the effectiveness of the results obtained here.     

Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, the global exponential stability and periodicity are investigated for a class of delayed high-order Hopfield neural networks (HHNNs) with impulses, which are new and complement previously known results. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results. The numerical simulation shows that our models can occur in many forms of complexities including periodic oscillation and the Gui chaotic strange attractor.     

Existence of periodic solutions for neutral type cellular neural networks with delays

In this paper, by using the theory of abstract continuation theorem of k contractive operator, we study the existence of periodic solutions for neutral type cellular neural networks with delays.     

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.     

Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays

This paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable Lyapunov function and a new differential inequality. The proposed method can also be applied to study the impulsive Cohen-Grossberg-type BAM neural networks with finite distributed delays. The results in this paper extend and improve the earlier publications. Finally, two examples with numerical simulations are given to demonstrate the obtained results.     

Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays

This paper discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. Some novel global stability criteria of the system is derived by using Lyapunov method, linear matrix inequality (LMI) and analytic technique. The LMI-based criteria obtained here are computationally more flexible and more generic than many other existing criteria. A numerical example is given to illustrate our result.     

Stability and periodicity in high-order neural networks with impulsive effects

In this paper, the global exponential stability and periodicity are investigated for a class generalized high-order neural networks with time delays and impulses; some sufficient conditions are derived for checking the global exponential stability and existence of periodic solutions for this system using the generalized Halanay inequality, mathematical induction and a fixed point theorem. The criteria given are easily verified and possess many adjustable parameters, which provides flexibility for the design and analysis of the system. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results.     

Positive periodic solutions for impulsive predator-prey model with dispersion and time delays

In this paper, we study the existence and global attractivity of positive periodic solutions for impulsive predator-prey systems with dispersion and time delays. By using coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions, and by means of a suitable Lyapunov functional, the uniqueness and global attractivity of positive periodic solution is presented. Some known results subject to the underlying systems without impulses are improved and generalized.     

Exponential stability of periodic neural networks with impulsive effects and time-varying delays

By employing Young inequality and constructing suitable Liapunov functions, we investigate the existence and globally exponential stability of periodic neural networks with impulses and time-varying delays. The results extend and improve some earlier ones [1], [5] and [12]. An illustrative example and simulations are given to show the validity of the main results.     

Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses

In this paper we investigate a class of Hopfield neural networks subject to periodic impulses. First we give sufficient conditions to ensure existence and exponential stability of the anti-periodic solutions, which are new and complementary to previously known results. Then we present an example to demonstrate our results.     

Global exponential stability of Hopfield neural networks with distributed delays

In this paper, dynamical behaviors of Hopfield neural networks system with distributed delays were studied. By using contraction mapping principle and differential inequality technique, a sufficient condition was obtained to ensure the existence uniqueness and global exponential stability of the equilibrium point for the model. Here we point out that our methods, which are different from previous known results, base on the contraction mapping principle and inequality technique. Two remarks were also worked out to demonstrate the advantage of our results.     

Periodic bidirectional associative memory neural networks with distributed delays

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.     

Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays

In this paper, by means of constructing the extended impulsive delayed Halanay inequality and by Lyapunov functional methods, we analyze the global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. Some new sufficient conditions ensuring exponential stability of the unique equilibrium point of impulsive Hopfield neural networks with time delays are obtained. Those conditions are more feasible than that given in the earlier references to some extent. Some numerical examples are also discussed in this work to illustrate the advantage of the results we obtained.     

Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays

In this paper, the global stability and almost periodicity are investigated for Hopfield neural networks with continuously distributed neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and they complement the previously known ones. Finally, an example is given to demonstrate the effectiveness of our results.     

Exponential stability of Hopfield neural networks with time‐varying delays via impulsive control

In this paper, by utilizing the Lyapunov functionals, the analysis method and the impulsive control, we analyze the exponential stability of Hopfield neural networks with time‐varying delays. A new criterion on the exponential stabilization by impulses and the exponential stabilization by periodic impulses is gained. We can see that impulses do contribution to the system's exponential stability. Two examples are given to illustrate the effectiveness of our result. Copyright © 2010 John Wiley & Sons, Ltd.     

A new criterion to global exponential stability for impulsive neural networks with continuously distributed delays

This paper considers the global exponential stability and exponential convergence rate of impulsive neural networks with continuously distributed delays in which the state variables on the impulses are related to the unbounded distributed delays. By establishing a new impulsive delay differential inequality, a new criterion concerning global exponential stability for these networks is derived, and the estimated exponential convergence rate is also obtained. The result extends and improves on earlier publications. In addition, two numerical examples are given to illustrate the applicability of the result. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamical analysis of impulsive neural networks with time‐varying delays

In this work, a new criterion concerning the global exponential stability of impulsive neural networks with time‐varying delays is presented by employing the impulsive delayed differential inequality method. The criterion is independent of the time‐varying delays and does not require the differentiability of delay functions. An example and its simulation showing the effectiveness of the present criterion is given finally. Copyright © 2012 John Wiley & Sons, Ltd.     

Exponential stability and periodicity of impulsive cellular neural networks with time delays

This paper is concerned with the stability and periodicity for a class of impulsive neural networks with delays. By means of the Fixed point theory, Lyapunov functional and analysis technique, some sufficient conditions of exponential stability and periodicity are obtained. We can see that impulses do contribution to the stability and periodicity. An example is given to demonstrate the effectiveness of the obtained results.