A note on stability of maps which preserve equality of distance

In this note, we show a generalized stability of maps which preserve equality of distance.     

Exponential stability of a network of elastic and thermoelastic materials

In this paper, we study the stability of a network of some elastic and thermoelastic edges. We establish the exponential decay rate of the whole system. Copyright © 2012 John Wiley & Sons, Ltd.     

Hopf bifurcation and stability for a delayed tri-neuron network model

A neural network model with three neurons and a single time delay is considered. Its linear stability is investigated and Hopf bifurcations are demonstrated by analyzing the corresponding characteristic equation. In particular, the explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and the center manifold theorem. In order to illustrate our theoretical analysis, some numerical simulations are also included in the end.     

Resource allocation in a large decentralized enterprise

We present a model of an enterprise comprising several operating units pursuing their production goals with a fair degree of autonomy, but under resource constraints imposed by a headquarters function. Specifically, each operating unit is assumed to seek a maximization of a perceived market value of its product output, subject to constraints on resources such as capital for plants and equipment, headcount, etc. imposed by headquarters. The headquarters function pursues a global optimization problem which takes into account the market values of all the products of the operating units, but also the cost of the resources and their regulation. Under suitable assumptions of linearity, the operation of the enterprise is formulated as a novel hierarchical structure of linear programming problems. An algorithm is presented for the solution of a class of such problems.     

Existence and global stability of a periodic solution for a cellular neural network

Purpose of this study is to investigate the dynamical properties of Chua and Yang cellular neural networks (CNNs). Based on the continuation theorem of coincidence degree theory, a novel sufficient condition with respect to the existence of periodic solution for CNNs is derived. Moreover, a generalized Lyapunov–Krasovskii functional is designed to guarantee the global stability of the existed periodic solution. An illustrative example is given to verify the effectiveness and correctness of the proposed method, furthermore, random disturbance is added in the numerical simulation in order to verify the robustness of the proposed approach.     

Local voting protocol for decentralized load balancing of network with switched topology and noise in measurements

The applicability of local voting protocol for the nonstationary problem of load balancing in a decentralized network with switched topology and measurement noise is investigated. The obtained theoretical results are illustrated by simulation models. The system is considered with and without the redistribution of tasks. It is shown that an adaptive multiagent strategy with the redistribution of tasks among the neighbors is better for handling the distribution of tasks than a strategy in which tasks are sent to random nodes and are not redistributed after arrival.     

Characterization of equality in a generalized Dunkl-Williams inequality

We establish a generalization of the Dunkl-Williams inequality and its inverse in the framework of Hilbert C^?-modules and characterize the equality case. As applications, we get some new results and some known results due to J.E. Pe?ari? and R. Raji? [The Dunkl-Williams equality in pre-Hilbert C^?-modules, Linear Algebra Appl. 425 (1) (2007) 16-25].     

Existence of equilibria in a decentralized two-level supply chain

In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.     

Impact of a varying capacity on the all pairs 2-route network flows

Given an undirected edge-weighted network in which one edge capacity is allowed to vary, we propose in this paper a polynomial algorithm that needs only two 2-cut-trees computations to provide the all pairs maximum 2-route flow values.     

Implicit collusion and individual market power in electricity markets

Wholesale electricity markets may not produce competitive outcomes, either as a result of the exercise of market power, or through problems of implicit collusion. In comparison with the great amount of attention paid to issues of market power, the problems of implicit collusion have not been extensively studied. In this paper, we use a coevolutionary approach to explore the effect of the price elasticity of demand, capacity and forward contracts on implicit collusion in a duopoly. We will demonstrate that implicit collusion has the most importance in market conditions under which there is an intermediate amount of market power. Thus markets which are either highly competitive or in which one or both of the two generators can exercise considerable market power, are also markets in which implicitly collusive outcomes are less likely to arise.     

Organizational strategy and tacit collusion in oligopoly with agency

We study a model that integrates organizational structure and agency withdynamic price competition in oligopoly. Workers in different levels of the organizational structure have asymmetric information and heterogeneous objectives; i.e., there are agency conflicts within the firm. The organizational strategy of the firm is to determinesequentially the decision power relating to price and non-price competition instruments at each level. We examine the equilibrium organizational and competitive strategy of firms in a duopoly, and characterize the extent of noncooperative tacit collusion (with respect to price and non-price competition) that is feasible. We identify two sets of sufficient conditions that guarantee, (i) the monopoly solution is sustainable at any discount factor (rate of impatience of the workers), or (ii) the monopoly solution is not sustainable for any level of the discount factor. Interestingly, tacit collusion may be feasible when either the agency problem is non-existentor very severe; i.e., firm profits in equilibrium may be non-monotone in the extent of the agency conflict. Our analysis indicates that intrafirm learning and agency will have a stronger impact on feasible tacit collusion in markets where non-price competition plays a strong role. Moreover, there is an intimate connection between the firm's organizational strategy and the extent of tacit collusion with the (industry) business cycle.     

Hopf bifurcation and stability for a neural network model with mixed delays

A generalized model of the two-neuron network with mixed delays is studied. The main purpose of this paper is to explore the linear stability of the trivial solution and Hopf bifurcation of a two-neuron network with continuous and discrete delays. The general formula of the direction, the estimation formula of period and stability of bifurcated periodic solutions are also studied. Finally, the numerical simulations are given to illustrate the theoretical analysis.     

Impact of compressor failures on gas transmission network capability

National Grid, the gas operator in the United Kingdom, has experienced challenges in evaluating the capability of its gas transmission network to maintain function in the event of risks particularly to withstand the impact of compressor failures. We propose a mathematical programming model to support the operator in dealing with the problem. Several solution techniques are developed to solve the various versions of the problem efficiently. In the case of little data on compressor failure, an uncertainty theory is applied to solve this problem if the compressor failures are independent; while a robust optimisation technique is developed to solve it when they are not. Otherwise, when there are data on compressor failure, Monte Carlo simulation is applied to find the expected capability of the gas transmission network. Computational experiments, carried out on a case study at National Grid, demonstrate the efficiency of the proposed model and solution techniques. A further analysis is performed to determine the impact of compressor failures and suggest efficient maintenance policies for National Grid.     

A model of feedback control system on network and its stability analysis

A model of feedback control system on network is constructed. Some criterions ensuring the robust stability and global exponential stability for the model are established, by applying Lyapunov method and generalized Kirchhoff’s matrix tree theorem. These criterions have a close relation to the topology property of networks. Finally, two examples and simulations are provided to illustrate the theoretical results.     

On a bound on algebraic connectivity: the case of equality

In a recent paper the authors proposed a lower bound on 1 – _i , where _i 1, is an eigenvalue of a transition matrix T of an ergodic Markov chain. The bound which involved the group inverse of I – T, was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when the graph is a weighted tree. It is shown that the bound is sharp only for certain Type I trees. Our proof involves characterizing the case of equality in an upper estimate for certain inner products due to A. Paz.