Global Robust Exponential Stability of Interval General BAM Neural Network with Delays

In this paper, a class of interval general bidirectional associative memory (BAM) neural networks with delays are introduced and studied, which include many well-known neural networks as special cases. By using fixed point technic, we prove an existence and uniqueness of the equilibrium point for the interval general BAM neural networks with delays. By using a proper Lyapunov functions, we get a sufficient condition to ensure the global robust exponential stability for the interval general BAM neural networks with delays, and we just require that activation function is globally Lipschitz continuous, which is less conservative and less restrictive than the monotonic assumption in previous results. In the last section, we also give an example to demonstrate the validity of our stability result for interval neural networks with delays.     

Periodic Dynamics for Memristor-based Bidirectional Associative Memory Neural Networks with Leakage Delays and Time-varying Delays

This paper deals with a class of memristor-based bidirectional associative memory (BAM) neural networks with leakage delays and time-varying delays. With the aid of the framework of Filippov solutions, Chain rule and some inequality techniques, a sufficient condition which ensures the boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks with leakage delays and time-varying delays is established. Applying a new approach involving Yoshizawa-like theorem, we prove the existence of periodic solution of the memristor-based BAM neural networks. By using the theory of set-valued maps and functional differential inclusions, Lyapunov functional, a set of sufficient conditions which guarantee the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks are derived. An example is given to illustrate the applicability and effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known studies of Li et al. [Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural networks 75 (2016) 97-109.]     

Continuous-time temporal back-propagation with adaptable timedelays

Backpropagation is extended to continuous-time feedforward networks with internal, adaptable time delays. The new technique is suitable for parallel hardware implementation, with continuous multidimensional training signals. The resulting networks can be used for signal prediction, signal production, and spatiotemporal pattern recognition tasks. Unlike conventional backpropagation networks, they can easily adapt while performing true signal prediction. Simulation results are presented for networks trained to predict future values of the Mackey-Glass chaotic signal, using its present value as an input. For this application, networks with adaptable delays had less than half the prediction error of networks with fixed delays, and about one-quarter the error of conventional networks. After training, the network can be operated in a signal production configuration, where it autonomously generates a close approximation to the Mackey-Glass signal.     

Synchronisation of complex dynamical networks with additive stochastic time-varying delays

In this letter, a class of complex dynamical networks with additive stochastic time-varying delays is investigated. Two kinds of delays in complex dynamical networks are taken into consideration, one is called the nodes-induced delay in this paper, and the other is the network-induced delay. Both of the delays are assumed to obey different stochastic distributions. By utilising a novel Lyapunov–Krasovskii functional and stochastic analysis techniques, a sufficient criterion is obtained in the form of linear matrix inequalities to ensure the synchronisation of the complex dynamical networks. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

含时延的联想记忆神经网络的指数吸引域和指数收敛速度

采用不等式技巧和非负矩阵性质, 给出了含时延的联想记忆神经网络平衡点的指数吸引域和指数收敛速度估计以及指数稳定的一些判断条件.     

Consensus networks with time-delays over finite fields

In this paper, we investigate the consensus problem in networks with time-delays over finite fields. The delays are categorised into three cases: single constant delay, multiple constant delays, and time-varying bounded delays. For all cases, some sufficient and necessary conditions for consensus are derived. Furthermore, assuming that the communication graph is strongly connected, some of the obtained necessary conditions reveal that the conditions for consensus with time-delays over finite fields depend not only on the diagonal entries but also on the off-diagonal entries, something that is intrinsically distinct from the case over real numbers (where having at least one nonzero diagonal entry is a sufficient and necessary condition to guarantee consensus). In addition, it is shown that delayed networks cannot achieve consensus when the interaction graph is a tree if the corresponding delay-free networks cannot reach consensus, which is consistent with the result over real numbers. As for average consensus, we show that it can never be achieved for delayed networks over finite fields, although it indeed can be reached under several conditions for delay-free networks over finite fields. Finally, networks with time-varying delays are discussed and one sufficient condition for consensus is presented by graph-theoretic method.     

Synchronization of complex networks with coupling delays via adaptive pinning intermittent control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.     

Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays

In this paper, the exponential periodicity and stability of neural networks with Lipschitz continuous activation functions are investigated, without assuming the boundedness of the activation functions and the differentiability of time-varying delays, as needed in most other papers. The neural networks contain reaction-diffusion terms and both variable and unbounded delays. Some sufficient conditions ensuring the existence and uniqueness of periodic solution and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays are obtained by analytic methods and inequality technique. Furthermore, the exponential converging index is also estimated. The methods, which does not make use of Lyapunov functional, is simple and valid for the periodicity and stability analysis of neural networks with variable and/or unbounded delays. The results extend some previous results. Two examples are given to show the effectiveness of the obtained results.     

Exponential synchronization of a class of neural networks with time-varying delays.

This paper aims to present a synchronization scheme for a class of delayed neural networks, which covers the Hopfield neural networks and cellular neural networks with time-varying delays. A feedback control gain matrix is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory, and its exponential synchronization condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. This condition can avoid solving an algebraic Riccati equation. Both the cellular neural networks and Hopfield neural networks with time-varying delays are given as examples for illustration.     

Towards an end-to-end delay analysis of LEO satellite networks for seamless ubiquitous access

LEO satellite networks, with moderate propagation delay and low terminal power requirement, are considered as a promising solution to providing global seamless access services for ubiquitous computing. In order to satisfy the requirement of accessing computing resource for users, end-to-end delays should be bounded for a continual and reliable connectivity. But given dynamic topology and non-uniform distribution of terrestrial users, end-to-end delays within LEO satellite networks are liable to fluctuate. Hence, to examine the delay constraint, an analytical model based on a tandem queue is established under a hot-spot traffic pattern, which is unfavorable for bounded delays. The departure interval moments of a target flow are calculated and fitted for the next link as input parameters, from which queuing delays under cross flows are iteratively obtained. The analytical results show that this model is able to depict the influence by the traffic pattern with satisfying accuracy, which is valuable for the design of routing schemes in satellite networks.     

New criteria for globally exponential stability of delayed Cohen–Grossberg neural network

This paper is concerned with analysis problem for the global exponential stability of the Cohen–Grossberg neural networks with discrete delays and with distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, we employ Lyapunov functions to establish some sufficient conditions ensuring global exponential stability of equilibria for the Cohen–Grossberg neural networks with discrete delays and with distributed delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks.     

A note on stability of analog neural networks with time delays

This note presents a generalized sufficient condition which guarantees stability of analog neural networks with time delays. The condition is derived using a Lyapunov functional and the stability criterion is stated as: the equilibrium of analog neural networks with delays is globally asymptotically stable if the product of the norm of connection matrix and the maximum neuronal gain is less than one.     

Globally asymptotic stability of a class of neutral-type neural networks with delays.

Several stability conditions for a class of systems with retarded-type delays are presented in the literature. However, no results have yet been presented for neural networks with neutral-type delays. Accordingly, this correspondence investigates the globally asymptotic stability of a class of neutral-type neural networks with delays. This class of systems includes Hopfield neural networks, cellular neural networks, and Cohen-Grossberg neural networks. Based on the Lyapunov stability method, two delay-independent sufficient stability conditions are derived. These stability conditions are easily checked and can be derived from the connection matrix and the network parameters without the requirement for any assumptions regarding the symmetry of the interconnections. Two illustrative examples are presented to demonstrate the validity of the proposed stability criteria.     

异质性和时滞作用下神经元网络的共振动力学

利用参数互异的Fitzhugh-Nagumo神经元构建了含耦合时滞的无标度神经元网络模型,通过数值模拟的方法,提出研究参数异质性和耦合时滞影响下神经元网络的共振动力学.结果发现,当耦合项中不含时滞时,适中的参数异质性能够使得神经元网络对外界弱周期信号的响应达到最优,即适中的参数异质性能够诱导神经元网络的共振响应,而且异质性诱导共振对耦合强度具有鲁棒性.更重要的是,耦合时滞对参数异质性作用下神经元网络的共振特性也有着显著性影响.当时滞约为信号周期的整数倍时,神经元网络能够周期性地出现共振现象,即适当的耦合时滞能够诱导神经元网络的多重共振,而且这种现象在异质性参数的适当范围内都能明显出现.     

Attracting and invariant sets of non-autonomous reaction-diffusion neural networks with time-varying delays

In this paper, a class of non-autonomous reaction-diffusion neural networks with time-varying delays is investigated. By establishing a new differential inequality and employing the properties of spectral radius of nonnegative matrix and diffusion operator, the global attracting and positive invariant sets and exponential stability of non-autonomous reaction-diffusion neural networks with time-varying delays are obtained. Our results do not require the conditions of boundedness of the coefficient of neural networks. One example is given to illustrate the effectiveness of our conclusion.     

Consensus of Multi-Agent Systems in Directed Networks With Nonuniform Time-Varying Delays

In this note, we study consensus problems for continuous-time multi-agent systems in directed networks with dynamically changing topologies and nonuniform time-varying delays. We have analyzed consensus problems in the following three cases: 1) directed networks with dynamically changing topologies and nonuniform time-varying delays; 2) directed networks with intermittent communication and data packet dropout; and 3) finite-time consensus in directed networks with dynamically changing topologies and nonuniform time-varying delays. We propose a new approach based on a tree-type transformation to investigate consensus problems in all three cases. Some necessary and/ or sufficient conditions are established. Simulation results are also given to demonstrate the theoretical results.      

Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results     

How delays affect neural dynamics and learning

We investigate the effects of delays on the dynamics and, in particular, on the oscillatory properties of simple neural network models. We extend previously known results regarding the effects of delays on stability and convergence properties. We treat in detail the case of ring networks for which we derive simple conditions for oscillating behavior and several formulas to predict the regions of bifurcation, the periods of the limit cycles and the phases of the different neurons. These results in turn can readily be applied to more complex and more biologically motivated architectures, such as layered networks. In general, the main result is that delays tend to increase the period of oscillations and broaden the spectrum of possible frequencies, in a quantifiable way. Simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. Adaptable delays are then proposed as one additional mechanism through which neural systems could tailor their own dynamics. Accordingly, we derive recurrent backpropagation learning formulas for the adjustment of delays and other parameters in networks with delayed interactions and discuss some possible applications.     

Robust stability of stochastic genetic regulatory networks with discrete and distributed delays

In this paper, the problem on asymptotical and robust stability of genetic regulatory networks with time-varying delays and stochastic disturbance is considered. The time-varying delays include not only discrete delays but also distributed delays. The parameter uncertainties are time-varying and norm-bounded. Based on the Lyapunov stability theory and Lur’s system approach, sufficient conditions are given to ensure the stability of genetic regulatory networks. All the stability conditions are given in terms of linear matrix inequalities, which are easy to be verified. Illustrative example is presented to show the effectiveness of the obtained results.     

Global Robust Exponential Stability of Interval BAM Neural Network with Mixed Delays under Uncertainty

In this paper, a class of interval bidirectional associative memory (BAM) neural networks with mixed delays under uncertainty are introduced and studied, which include many well-known neural networks as special cases. The mixed delays mean the simultaneous presence of both the discrete delay, and the distributive delay. Furthermore, the parameter of matrix is taken values in a interval and controlled by a unknown, but bounded function. By using a suitable Lyapunov–Krasovskii function with the linear matrix inequality (LMI) technique, we obtain a sufficient condition to ensure the global robust exponential stability for the interval BAM neural networks with mixed delays under uncertainty, which is more generalized and less conservative, restrictive than previous results. In the last section, the validity of our stability result is demonstrated by a numerical example.