Class Of Dynamical Networks Research Articles

Bounded confidence opinion dynamics: A survey

At the beginning of this century, Hegselmann and Krause proposed a dynamical model for opinion formation that is referred to as the Bounded Confidence Opinion Dynamics (BCOD) model and that has since attracted a wide interest from different research communities. The model can be viewed as a dynamic network, in which each agent is endowed with a state variable representing an opinion and two agents interact if the distance between their opinions does not exceed a constant confidence bound. This relation of instantaneous proximity between the opinions naturally induces a dynamic interaction graph. At each stage of the opinion iteration, all agents synchronously update their opinion to the average of all opinions that belong to the neighbors in the interaction graph.BCOD models exhibit a broad variety of phenomena that cannot be studied by traditional methods, and their analysis has enriched the systems and control field with a number of novel mathematical tools. This fact, together with the existence of an extensive literature on the topic scattered across different fields, calls for a systematic presentation of the existing results on this class of dynamic networks. The aim of this survey is to provide an overview of BCOD models with time-synchronous interactions, with possibly asymmetric and heterogeneous confidence bounds. Conditions on the different classes of BCOD which ensure the convergence (in finite time or asymptotically) of the opinions are discussed, and the possible structures of the terminal opinions are described. The numerous phenomena highlighted in the literature from numerical studies, e.g., the characterization of steady state behaviors and the sensitivity to confidence thresholds, are also reviewed. Finally, some recent modifications and applications of BCOD models are discussed, and suggestions of directions for future research are provided.

Pinning Synchronization Control for a Class of Dynamical Networks with Coupled Time-Varying Delays: An Interval-Observer-Based Approach

This paper is concerned with the pinning synchronization control issue for a class of discrete-time complex dynamical networks. By resorting to the interval observer approach, a novel pinning synchronization control strategy is adopted to control a small fraction of the network nodes with hope to reduce the implementation cost. By using the Lyapunov stability theorem, some synchronization criteria have been derived to ensure the desired synchronization performance. Finally, a numerical simulation is presented to illustrate the effectiveness and usefulness of the theoretical results.

Cluster Motion in a Two-Contour System with Priority Rule for Conflict Resolution

A deterministic dynamical system representing the contour network is considered. The number of contours is two. At each contour there is a segment moving with a constant velocity which is called the cluster, because in the discrete variant of the system it corresponds to the cluster of particles, that is, to the group of particles occupying the adjacent cells and moving simultaneously. The lengths of contours and the lengths of clusters are prescribed. There is a common point named a node. Clusters cannot pass a node simultaneously. A cluster stops and waits for the node to empty if this cluster comes to the node at the instance when another cluster passes through the node. If clusters come to a node simultaneously, then precedence is given to the cluster considered the priority cluster (the priority rule of conflict resolution). The theorems on the average speed of cluster motion are proved taking delays in different types of the system’s behavior into account. It is established that the average speed of motion of each cluster in the system is independent of the cluster position at the initial time instance in contrast to the analogous system with another rule of conflict resolution considered previously, where such dependence appears in the general case. The possible practical interpretation of the studied system is given. The presented system is referred to as the class of dynamical networks introduced and investigated by A.P. Buslaev. The results may be applied to solve questions on the automatization of motion of a continuous mass, simulate the motion of transport, and other areas.

The universally quickest transshipment problem in a certain class of dynamic networks with uniform path-lengths

In the universally quickest transshipment problem, we are given a network with a transit time function on its arc set. The goal is to minimize the time when the last supply reaches the sink and to maximize the amount of supplies which have reached the sink at every time step. In this paper, we consider this problem in a class of dynamic networks which is a generalization of grid networks with uniform capacity and uniform transit time, and present a polynomial-time algorithm for this case.

Modeling complex systems with adaptive networks

Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and biological networks. In this paper, we introduce fundamental concepts and unique properties of adaptive networks through a brief, non-comprehensive review of recent literature on mathematical/computational modeling and analysis of such networks. We also report our recent work on several applications of computational adaptive network modeling and analysis to real-world problems, including temporal development of search and rescue operational networks, automated rule discovery from empirical network evolution data, and cultural integration in corporate merger.

Pinning Cluster Synchronization for Delayed Dynamical Networks via Kronecker Product

In this paper, the cluster synchronization is investigated for a class of dynamical networks composed of N delayed Lur’e systems by using pinning control strategy. Through combining the Kronecker product with reciprocal convex technique, some sufficient conditions are derived to ensure the cluster synchronization for the addressed networks such that the designed linear feedback controller can be employed to every cluster. Especially, the inner coupling matrices are not restricted to be diagonal and the problems of the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which extend the application area and reduce the computational complexity. Finally, three numerical examples are provided to demonstrate the effectiveness of the derived results.

Stability analysis for a special class of dynamical networks

In this article, stability analysis and decentralised control problems are studied for a special class of linear dynamical networks. Necessary and sufficient conditions for stability and stabilisability under a decentralised control strategy are given for this type of linear networks. Especially, two types of linear regular networks, star-shaped networks and globally coupled networks, are studied in detail, respectively. A dynamical network can be viewed as a large-scale system composed of some subsystems with some coupling structures, based on this, the relationship between the stability of a network and the stability of its corresponding subsystems is studied. Different from the discussions that the subsystems in networks vary with different coupling structures (Duan, Z.S., Wang, J.Z., Chen, G.R., and Huang, L. (2008), ‘Stability Analysis and Decentralised Control of a Class of Complex Dynamical Networks’, Automatica, 44, 1028–1035), the subsystems in network discussed in this article remain unchanged with different interconnections which is the same as in general large-scale system. It is also pointed out that some subsystems must be made unstable for the whole network to be stable in some special cases. Moreover, the controller design method based on parameter-dependent Lyapunov function is provided.

Optimisation of reinforcement learning algorithm applied to dynamic network

Mobile ad-hoc network represent a class of dynamic networks where nodes are non-stationary and the topology is changing rapidly. The routing algorithms for these types of networks play an important role. Traditional routing algorithms do not perform optimally under congestion and high-speed situations. Reinforcement learning-based routing algorithm SAMPLE holds a lot of potential to these types of problems but performs worse as compared to AODV and DSR under the Random Waypoint Mobility Model. To overcome the bottleneck of SAMPLE in terms of performance in a pure ad-hoc environment and enable its optimal performance under dynamic scenarios, we propose a mobility model to characterise group mobility under real city like scenario. The proposed model will be tested for its performance using suitable mobility metrics, verified statistically and then applied to a reinforcement learning algorithm SAMPLE to study its impact.

Global asymptotical synchronisation in linearly coupled networks of RCL-shunted Josephson junctions

This article presents the synchronisation criteria for a class of dynamical networks with each node being resistively-capacitively-inductively-shunted (RCL-shunted) Josephson junction, which guarantee the synchronised states to be global asymptotically stable. These conditions are established in terms of linear matrix inequalities (LMIs), readily solvable by available numerical software. In addition, an interesting conclusion is reached that the stability of synchronisation in the coupled whole 3N-dimensional networks can be converted into that of 3-dimensional space.

Stability Analysis and Hadamard Synergic Control for a Class of Dynamical Networks

Hadamard synergic control is a new kind of control problem which is achieved via a composite strategy of the state feedback control and the direct regulation of the part of connection coefficients of system state variables. Such a control is actually used very often in the practical areas. In this paper, we discuss Hadamard synergic stabilization problem for a class of dynamical networks. We analyze three cases: 1) Synergic stabilization problem for the general twonodenetwork. 2) Synergic stabilization problem for a special kind of networks. 3) Synergic stabilization problem for special kind of networks with communication timedelays. The mechanism of the synergic action between two control strategies: feedback control and the connection coefficients regulations are presented.

Decentralized dynamic output feedback for globally asymptotic stabilization of a class of dynamic networks

The objective of this paper is to propose an approach to stabilization of a class of dynamic networks with each node being a non-linear system with multiple equilibria. The proposed algorithms, which are developed within the convex optimization framework, employ a decentralized dynamic output feedback structure. Furthermore, an interesting conclusion is reached, in which the stabilization problem for the whole Nn-dimensional dynamic networks can be converted into the simple n-dimensional space in terms of only three LMIs. An application of output stabilization of mutually coupled phase-locked loop networks is used to verify the effectiveness of the proposed methods.

Dynamical networks for information processing

Coupled evolution of state and topology of dynamical networks is introduced. Due to a well organized tensor structure, the governing equations are presented in a canonical form, and required attractors as well as their basins can be easily placed and controlled. This new class of dynamical networks can represent phenomenological models for self-organization in physics and biology. Applications of these networks to pattern recognition, associative memory, synthesis of models based upon observation data, detection of abnormalities and data compression are discussed. The difference between the proposed dynamical networks and neural networks is emphasized.

COMPUTING SHORTEST, FASTEST, AND FOREMOST JOURNEYS IN DYNAMIC NETWORKS

New technologies and the deployment of mobile and nomadic services are driving the emergence of complex communications networks, that have a highly dynamic behavior. This naturally engenders new route-discovery problems under changing conditions over these networks. Unfortunately, the temporal variations in the network topology are hard to be effectively captured in a classical graph model. In this paper, we use and extend a recently proposed graph theoretic model, which helps capture the evolving characteristic of such networks, in order to propose and formally analyze least cost journey (the analog of paths in usual graphs) in a class of dynamic networks, where the changes in the topology can be predicted in advance. Cost measures investigated here are hop count (shortest journeys), arrival date (foremost journeys), and time span (fastest journeys).