Improved result on stability analysis of discrete stochastic neural networks with time delay

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.     

Solving linear variational inequalities by projection neural network with time-varying delays

A projection neural network with time-varying delays is proposed for solving linear variational inequalities. By the theory of functional differential equation and the linear matrix inequality technique, the proposed neural network is proved to be globally exponentially stable. The obtained results complement and extend the previously known work.     

Improved delay-dependent stability criterion for neural networks with time-varying delays

In this Letter, the problem of stability analysis for neural networks with time-varying delays is considered. By constructing a new Lyapunov functional, a new delay-dependent stability criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criterion.     

Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays

This Letter studies the exponential stability for a class of neural networks (NNs) with both discrete and distributed time-varying delays. Under weaker assumptions on the activation functions, by defining a more general type of Lyapunov functionals and developing a new convex combination technique, new less conservative and less complex stability criteria are established to guarantee the global exponential stability of the discussed NNs. The obtained conditions are dependent on both discrete and distributed delays, are expressed in terms of linear matrix inequalities (LMIs), and contain fewer decision variables. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed conditions.     

Delay-range-dependent stability for fuzzy BAM neural networks with time-varying delays

This Letter considers the problem of delay-range-dependent stability for fuzzy bi-directional associative memory (BAM) neural networks with time-varying interval delays. Based on Lyapunov-Krasovskii theory, the delay-range-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs). By constructing new Lyapunov-Krasovskii functional, stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using some advanced techniques for achieving delay dependence. A numerical example is given to illustrate the effectiveness of the proposed method.     

Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays

In this Letter, the passivity problem of uncertain neural networks with discrete and distributed time-varying delays is investigated. New delay-dependent conditions for this problem are obtained by using a novel Lyapunov functional together with the linear matrix inequality (LMI) approach. Numerical examples are given to show the effectiveness of our theoretical results.     

Stochastic asymptotic stability of Markovian jumping neural networks with Markov mode estimation and mode-dependent delays

In a previous work [Z.D. Wang, Y.R. Liu, L. Yu, X.H. Liu, Phys. Lett. A 356 (2006) 346] an exponential stability analysis for a class of Markovian jumping neural networks (MJNNs) was presented. In this Letter we employ the same technique to extend the results for MJNNs with time-varying delays and mode estimation, appropriate for active fault-tolerant control systems.     

New asymptotic stability criteria for neural networks with time-varying delay

The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delay is investigated. A new class of Lyapunov functional is constructed to derive some new delay-dependent stability criteria.The obtained criterion are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.     

Novel delay-dependent stability criteria for neural networks with interval time-varying delay

The problem of delay-dependent asymptotic stability for neural networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov-Krasovskii functional is constructed. Several novel delay-dependent stability criteria are presented in terms of linear matrix inequality by using the Jensen integral inequality and a new convex combination technique. Numerical examples are given to demonstrate that the proposed method is effective and less conservative.     

New delay-dependent stability criteria for neural networks with time-varying interval delay

The problem of stability analysis of neural networks with time-varying delay in a given range is investigated in this Letter. By introducing a new Lyapunov functional which uses the information on the lower bound of the delay sufficiently and an augmented Lyapunov functional which contains some triple-integral terms, some improved delay-dependent stability criteria are derived using the free-weighting matrices method. Numerical examples are presented to illustrate the less conservatism of the obtained results and the effectiveness of the proposed method.     

Improved Conditions for Global Asymptotic Stability of Cohen--Grossberg Neural Networks with Time-Varying Delays

The global asymptotic stability of delayed Cohen-Grossberg neural networks with impulses is investigated. Based on the new suitable Lyapunov functions and the Jacobsthal inequality, a set of novel sufficient criteria are derived for the global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays and impulses. An illustrative example with its numerical simulations is given to demonstrate the effectiveness of the obtained results.     

Multistability in bidirectional associative memory neural networks

In this Letter, the multistability issue is studied for Bidirectional Associative Memory (BAM) neural networks. Based on the existence and stability analysis of the neural networks with or without delay, it is found that the 2n-dimensional networks can have n³ equilibria and n² equilibria of them are locally exponentially stable, where each layer of the BAM network has n neurons. Furthermore, the results has been extended to (n+m)-dimensional BAM neural networks, where there are n and m neurons on the two layers respectively. Finally, two numerical examples are presented to illustrate the validity of our results.     

The chaotification of discrete Hopfield neural networks via impulsive control

The chaotification of discrete Hopfield neural networks is studied with impulsive control techniques. No matter whether the original systems are stable or not, chaotilication theorems for discrete Hopfield neural networks are derived, respectively. Finally, the effectiveness of the theoretical results is illustrated by some numerical examples.     

A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances

In this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of ‘delay fractioning’, we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result.     

New results on stability criteria for neural networks with time-varying delays

In this paper,the problem of stability analysis for neural networks with time-varying delays is considered.By constructing a new augmented Lyapunov-Krasovskii’s functional and some novel analysis techniques,improved delaydependent criteria for checking the stability of the neural networks are established.The proposed criteria are presented in terms of linear matrix inequalities(LMIs) which can be easily solved and checked by various convex optimization algorithms.Two numerical examples are included to show the superiority of our results.     

Local excitation-lateral inhibition interaction yields oscillatory instabilities in nonlocally interacting systems involving finite propagation delay

The work studies wave activity in spatial systems, which exhibit nonlocal spatial interactions at the presence of a finite propagation speed. We find analytically propagation delay-induced oscillatory instabilities for various local excitatory and lateral inhibitory spatial interactions. Further, the work shows for general nonlocal interactions analytically that the first kernel Fourier moment defines the stability thresholds. The final numerical simulation confirms the analytical results.     

A note on Burgers' equation with time delay: Instability via finite-time blow-up

Burgers' equation with time delay is considered. Using the Cole-Hopf transformation, the exact solution of this nonlinear partial differential equation (PDE) is determined in the context of a (seemingly) well-posed initial-boundary value problem (IBVP) involving homogeneous Dirichlet data. The solution obtained, however, is shown to exhibit a delay-induced instability, suffering blow-up in finite-time.     

Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays

This Letter investigates the problem of delay-dependent exponential stability analysis for uncertain stochastic neural networks with time-varying delay. Based on the Lyapunov stability theory, improved delay-dependent exponential stability criteria for the networks are established in terms of linear matrix inequalities (LMIs).     

Induction of Hopf bifurcation and oscillation death by delays in coupled networks

This work explores a system of two coupled networks that each has four nodes. Delayed effects of short-cuts in each network and the coupling between the two groups are considered. When the short-cut delay is fixed, the arising and death of oscillations are caused by the variational coupling delay.     

Novel global robust stability criteria for interval neural networks with multiple time-varying delays

This Letter is concerned with the problem of robust stability analysis for interval neural networks with multiple time-varying delays and parameter uncertainties. The parameter uncertainties are assumed to be bounded in given compact sets and the activation functions are supposed to be bounded and globally Lipschitz continuous. A sufficient condition is obtained by means of Lyapunov functionals, which guarantees the existence, uniqueness and global asymptotic stability of the delayed neural network for all admissible uncertainties. This condition is in terms of a linear matrix inequality (LMI), which can be easily checked by using recently developed algorithms in solving LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.