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Complex dynamical behavior in a four-neuron recurrent neural network with discrete delays is investigated in this paper. The dissipativity of the system and stability of equilibrium point are studied by mens of Lyapunov theory. Stable fixed point, periodic and quasi-periodic orbits, and chaotic motion are observed in system via numerical calculation. With the change of the slope and threshold of activation function, as well as time delay and synaptic weight, the system passes from stable to periodic and then to chaotic regimes. Interestingly, the system returns to periodic or stable regimes by further changing these parameter values. Furthermore, some numerical evidences, such as phase portraits, bifurcation diagrams, power spectrum density, are given to confirm chaos. [ABSTRACT FROM AUTHOR]

Based on the linear matrix inequality (LMI), new sufficient conditions on the global exponential stability and asymptotic stability of bidirectional associative memory neural networks with variable delay are presented, and exponential converging velocity index is estimated. Furthermore, the results in this paper are less conservative than the ones reported so far in the literature. One example is given to illustrate the feasibility of our main results. [ABSTRACT FROM AUTHOR]

This paper presents some new results for the absolute stability of Hopfield neural networks with activation functions chosen from sigmoidal functions which have unbounded derivatives. Detailed discussions are also given to the relation and difference of absolute stabilities between neural networks and Lurie systems with multiple nonlinear controls. Although the basic idea of the absolute stability of neural networks comes from that of Lurie control systems, it provides a very useful practical model for the study of Lurie control systems. [ABSTRACT FROM AUTHOR]

In view of the character of saturation linearity of output functions of neurons of the cellular neural networks, the method decomposing the state space to sub-regions is adopted to study almost sure exponential stability on delayed cellular neural networks which are in the noised environment. When perturbed terms in the model of the neural network satisfy Lipschitz condition, some algebraic criteria are obtained. The results obtained in this paper show that if an equilibrium of the neural network is the interior point of a sub-region, and an appropriate matrix related to this equilibrium has some stable degree to stabilize the perturbation, then the equilibrium of the delayed cellular neural network can still remain the property of exponential stability. All results in the paper is only to compute eigenvalues of matrices. [ABSTRACT FROM AUTHOR]

Because of VLSI realization of artificial neural networks and measuring the elements of the circuits, noises coming from the circuits and the errors of the parameters of the network systems are therefore unavoidable. Making use of the stochastic version of Razumikhin theorem of stochastic functional differential equation, Lyapunov direct methods and matrix analysis,almost sure exponential stability on interval neural networks perturbed by white noises with time varying delays is examined, and some sufficient algebraic criteria which only depend on the systems' parameters are given. For well designed deterministic neural networks, the results obtained in the paper also imply that how much tolerance against perturbation they have. [ABSTRACT FROM AUTHOR]

A method is proposed for asymptotic stability analysis of neutral neural networks with delayed state. The delay is assumed unknown, but constant. Sufficient conditions on delay-independent asymptotic stability are given in terms of the existence of symmetric and positive definite solutions of a constant Riccati algebraic matrix equation coupled with a discrete Lyapunov equation. [ABSTRACT FROM AUTHOR]

In this paper, global exponential stability in Lagrange sense is further studied for continuous recurrent neural network with three different activation functions. According to the parameters of the system itself, detailed estimation of global exponential attractive set, and positive invariant set is presented without any hypothesis on existence. It is also verified that outside the global exponential attracting set; i.e., within the global attraction domain, there is no equilibrium point, periodic solution, almost periodic solution, and chaos attractor of the neural network. These theoretical analysis narrowed the search field of optimization computation and associative memories, provided convenience for application. [ABSTRACT FROM AUTHOR]

In this paper, we have obtained some sufficient conditions to guarantee that Cohen-Grossberg neural networks with discrete and distributed delays have a periodic orbit and this periodic orbit are globally attractive. The results presented in this paper are the improvement and extension of the existed ones in some existing works. Finally, the validity and performance of the results are illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

A method is proposed for stability analysis of neural networks with linear and nonlinear time delays. Given a neural network and the corresponding generalized algebraic Riccati equation with two unknown positive matrices, using the Razumikhin-type theory, the problem of insuring the globally asymptotic stability of the neural networks with linear and nonlinear time delays is obtained. [ABSTRACT FROM AUTHOR]

This paper investigate the problems of global exponential stability and exponential convergence rate for delayed impulsive Hopfield type neural networks. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimate of exponential convergence rate is also obtained. A numerical example is worked out to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global exponential stability for a class of Cohen-Grossberg neural networks (CGNN) with time-varying delays and continuously distributed delays. CGNN herein is a general neural networks model which includes some well-known neural networks as its special cases. Firstly, applying the homeomorphism theory, we establish the new sufficient condition of existence and uniqueness of the equilibrium point to CGNN. Then, the sufficient criteria of global exponential stability of CGNN, which are easy to verify, are given by M-matrix. Our results imply and generalize some existed ones in previous literature. Furthermore, it is convenient to estimate the exponential convergence rates of the neural networks by using the criteria. Compared with the previous methods, our method does not resort to any Lyapunov functions or functionals. Finally, a example is given to illustrate the effective of our results. [ABSTRACT FROM AUTHOR]

A new theoretical result on the global exponential stability of recurrent neural networks with delay is presented. It should be noted that the activation functions of recurrent neural network do not require to be bounded. The presented criterion, which has the attractive feature of possessing the structure of linear matrix inequality (LMI), is a generalization and improvement over some previous criteria. A example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper investigates the chaos synchronization problem of a new 4-scroll chaotic system. Three nonlinear control approaches via state variables are studied, namely nonlinear feedback control, adaptive control and adaptive sliding mode type of control. Based on Lyapunov stability theory, control laws are derived such that the two identical 4-scroll systems are to be synchronized. Some sufficient conditions for the synchronization are obtained analytically in three cases. Numerical simulation results are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The rapid growth of the World-Wide Web poses unprecedented scaling challenges for general-purpose crawlers. Topic-specific web crawler is developed to collect relevant web pages of interested topics form the Internet. Based on the analyses of HITS algorithm, a new P-HITS algorithm is proposed for topic-specific web crawler in this paper. Probability is introduced to select the URLs to get more global optimality, and the metadata of hyperlinks is appended in this algorithm to predict the relevance of web pages better. Experimental results indicate that our algorithm has better performance. [ABSTRACT FROM AUTHOR]