Stability and bifurcation in a discrete system of two neurons with delays

In this paper, we consider a simple discrete two-neuron network model with three delays. The characteristic equation of the linearized system at the zero solution is a polynomial equation involving very high order terms. We derive some sufficient and necessary conditions on the asymptotic stability of the zero solution. Regarding the eigenvalues of connection matrix as the bifurcation parameters, we also consider the existence of three types of bifurcations: Fold bifurcations, Flip bifurcations, and Neimark–Sacker bifurcations. The stability and direction of these three kinds of bifurcations are studied by applying the normal form theory and the center manifold theorem. Our results are a very important generalization to the previous works in this field.     

Finding a feasible flow in a strongly connected network

We give a linear-time algorithm to find a feasible flow in a strongly connected network with fixed supplies and demands, each summing to a common value that is at most the minimum arc capacity. This algorithm speeds up the Goldberg-Rao maximum flow method by a constant factor.     

Synchronization of neural networks based on parameter identification and via output or state coupling

For neural networks with all the parameters unknown, we focus on the global robust synchronization between two coupled neural networks with time-varying delay that are linearly and unidirectionally coupled. First, we use Lyapunov functionals to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global robust synchronization regardless of their initial states. Second, by employing the invariance principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time-varying delay based on the parameter identification of uncertain delayed neural networks. Finally, numerical simulations validate the effectiveness and feasibility of the proposed technique.     

Combined neural network and reduced FRF techniques for slight damage detection using measured response data

Summary  This paper deals with structural damage detection using measured frequency response functions (FRF) as input data to artificial neural networks (ANN). A major obstacle, the impracticality of using full-size FRF data with ANNs, was circumvented by applying a data-reduction technique based on principal component analysis (PCA). The compressed FRFs, represented by their projection onto the most significant principal components, were used as the ANN input variables instead of the raw FRF data. The output is a prediction of the actual state of the specimen, i.e. healthy or damaged. A further advantage of this particular approach is its ability to deal with relatively high measurement noise, which is a common occurrence when dealing with industrial structures. The methodology was applied to detect three different states of a space antenna: reference, slight mass damage and slight stiffness damage. About 600 FRF measurements, each with 1024 spectral points, were included in the analysis. Six 2-hidden layer networks, each with an individually-optimised architecture for a specific FRF reduction level, were used for damage detection. The results showed that it was possible to distinguish between the three states of the antenna with good accuracy, subject to using an adequate number of principal components together with a suitable neural network configuration. It was also found that the quality of the raw FRF data remained a major consideration, though the method was able to filter out some of the measurement noise. The convergence and detection properties of the networks were improved significantly by removing those FRFs associated with measurement errors. Received 9 March 2000; accepted for publication 12 December 2000     

Opinion dynamics in networked command and control organizations

An opinion dynamics model for a Command and Control (C2) organization is essential for simulating combat system effectiveness. However, few studies have addressed opinion evolution in C2 simulation. With the goal of overcoming this research gap, this paper proposes an opinion exchange model, which is illustrated through a practical example of an Armored Division network. The model is divided into homogeneous and heterogeneous aspects: the former is mainly characterized by communication rules and types, while the latter is extended with the influence of multi-level opinion leaders. After carrying out the simulation of the two main models, the results show that the opinion evolution of the hierarchical leveled C2 organization with descending influence is much more complex and unpredictable than that of social networks.     

Aircraft and crew scheduling for fractional ownership programs

Fractional aircraft ownership programs, where individuals or corporations own a fraction of an aircraft, have revolutionized the corporate aviation industry. Fractional management companies (FMC) manage all aspects of aircraft operations enabling the owners to enjoy the benefits of private aviation without the associated responsibilities. We describe here the development of a scheduling decision support tool for a leading FMC. We present mathematical models, exact and heuristic solution methods. Our computational results using real and randomly generated data indicate that these models are quite effective in finding optimal or near-optimal solutions. The first phase of the implementation of one of these models at the FMC led to a significant improvement in effective utilization of the aircraft, reduction of costs due to reduced empty moves, and hence increased profits.     

A preferential attachment model with Poisson growth for scale-free networks

We propose a scale-free network model with a tunable power-law exponent. The Poisson growth model, as we call it, is an offshoot of the celebrated model of Barabási and Albert where a network is generated iteratively from a small seed network; at each step a node is added together with a number of incident edges preferentially attached to nodes already in the network. A key feature of our model is that the number of edges added at each step is a random variable with Poisson distribution, and, unlike the Barabási–Albert model where this quantity is fixed, it can generate any network. Our model is motivated by an application in Bayesian inference implemented as Markov chain Monte Carlo to estimate a network; for this purpose, we also give a formula for the probability of a network under our model.     

Analysis on global exponential robust stability of reaction-diffusion neural networks with S-type distributed delays

To avoid the unstable phenomena caused by time delays and perturbations, we investigate the sufficient conditions to ensure the global exponential robust stability with a convergence rate for the reaction-diffusion neural networks with S-type distributed delays. Because S-type distributed delays lead to some difficulty, we also introduce a new generalized Halanay inequality and a novel method-system-approximation method into the qualitative research of neural networks. Moreover, the sufficient criteria provided here, which are rather accessible and feasible, have wider adaptive range.     

Redundant paths and reliability bounds in gamma networks

Multistage Interconnection Networks (MINs) are network systems providing fast and efficient communications at a reasonable cost. A gamma network is a specific class of MINs, which provides redundant paths in the system. In a gamma network, information from source nodes is transmitted through a specific set of routes to destination nodes. Reliability of an MIN is used as a measure of system’s ability to transform information from input to output devices. Due to the complexity of network configuration and availability of redundant paths, reliability bounds to estimate the exact reliability of a gamma network is proposed. A numerical example of an 8 × 8 gamma network is presented to demonstrate the accuracy of the reliability bounds. When the lower bound reliability provides sufficient assurance that the system will be operational at some specified time and closely approximates the exact reliability, then no further effort for obtaining the exact reliability expression is necessary.     

Stability analysis for neural networks with inverse Lipschitzian neuron activations and impulses

In this paper, a new concept called α-inverse Lipschitz function is introduced. Based on the topological degree theory and Lyapunov functional method, we investigate global convergence for a novel class of neural networks with impulses where the neuron activations belong to the class of α-inverse Lipschitz functions. Some sufficient conditions are derived which ensure the existence, and global exponential stability of the equilibrium point of neural networks. Furthermore, we give two results which are used to check the stability of uncertain neural networks. Finally, two numerical examples are given to demonstrate the effectiveness of results obtained in this paper.