Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Game theoretic modeling of AIMD network equilibrium

This paper deals with modeling of network’s dynamic using game theory approach. The process of interaction among players (network users), trying to maximize their payoffs (e.g. throughput) could be analyzed using game-based concepts (Nash equilibrium, Pareto efficiency, evolution stability etc.). In this work we presented the model of TCP network’s dynamic and proved existence and uniqueness of solution, formulated payoff matrix for a network game and found conditions of equilibrium existence depending of loss sensitivity parameter. We consider influence if denial of service attacks on the equilibrium characteristics and illustrate results by simulations.В данной работе исследуется моделирования динамики сети на основе теоретико-игрового подхода. Процесс взаимодействия между пользоватлями, которые пытаются максимизировать свои выигрыши (например, долю сети) допускает представление в форме игры и применение методов анализа равновесия. В работе предлагается модель TCP сети и доказано существование и единственность точки устойчивого распределения ресурсов, построена матрица сетевой игры и найдены условия существования равновесия в зависимости от чувствительности пользователей к наличию ошибок. Рассмотрены также влияние атак на характеристики равновесия и проведено имитационное моделирование.В даній роботі досліджується моделювання динаміки мережі на основі теоретико-ігрового підходу. Процес взаємодії між користувачами, що намагаються максимізувати свої виграші (наприклад, частку мережі) допускає представлення у формі гри та застосування методів аналізу рівноваги. В роботі пропонується модель TCP мережі та доведено існування і єдність точки стійкого розподілу ресурсів, побудована матриця мережевої гри та знайдені умови існування рівноваги в залежності від чутливості користувачів до наявності помилок. Розглянуто також вплив атак на характеристики рівноваги та проведене імітаційне моделювання

Mean-Field-Type Games in Engineering

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201

Data based reconstruction of complex geospatial networks, nodal positioning, and detection of hidden node

Funding This work was supported by ARO under grant no. W911NF-14-1-0504.Peer reviewedPublisher PD

Modeling and analysis of market share dynamics in a duopoly subject to affine feedback advertising policies and delays

Presents extensions of the Vidale-Wolfe and Lanchester models for market share duopoly dynamics. The novelties in the proposed extensions are the explicit introduction of a set of undecided clients into existing models, which consider only the sets of clients of the two competing firms, as well as the use of decentralized affine feedback advertising policies. It is shown that, under the proposed class of advertising policies, the extended Vidale-Wolfe and Lanchester models, despite having different dynamics, have equilibria in identical locations, with the same stability properties. The introduction of a third set of undecided clients also motivates the introduction of a more elaborate model of market share dynamics based on the replicator-mutator model from evolutionary game theory. This is done by identifying strategies with the entries of a preference matrix consisting of the choice preferences of firms by clients and the mutation matrix representing transition probabilities from one set of clients to another. The proposed model is analysed with respect to equilibria and their stability properties, as well as parametric sensitivity, under the proposed advertising policies. All proposed models are analysed for stability, the presence of oscillations, existence of Hopf bifurcations when implementation or adoption delays are introduced. The extended models of Vidale-Wolfe and Lanchester are robust to implementation delays, while for adoption delays, bifurcations can occur. The proposed replicator-mutator model is robust for both types of delays.Apresenta extensões aos modelos de Vidale-Wolfe e Lanchester para a dinâmica de duopólios. As novidades nas extensões propostas são a introdução explícita de um conjunto de clientes indecisos nos modelos existentes, os quais consideram apenas os conjuntos de clientes das duas empresas concorrentes, e o uso de políticas de publicidade afins com realimentação. Demonstra-se que sob a classe proposta de políticas de publicidade, os modelos estendidos de Vidale-Wolfe e Lanchester, apesar de terem dinâmicas diferentes, apresentam pontos de equilíbrio idênticos com as mesmas propriedades de estabilidade. A introdução de um terceiro conjunto de clientes indecisos também motiva a introdução de um modelo mais elaborado da dinâmica de mercado baseado no modelo Replicador-Mutador da teoria dos jogos evolucionários. A proposta do modelo é realizada identificando estratégias com elementos de uma matriz de preferência consistindo nas preferências de escolha das empresas pelos clientes e a matriz de mutação representa probabilidades de transição de um conjunto de clientes para outro. O modelo proposto é analisado em relação aos pontos de equilíbrios e suas propriedades de estabilidade, bem como a sensibilidade paramétrica sob as políticas de publicidade propostas. Todos os modelos propostos são analisados quanto à estabilidade, a presença de oscilações, a existência de bifurcações de Hopf quando atrasos de implementação ou de adoção são introduzidos. Os modelos estendidos de Vidale-Wolfe e Lanchester são robustos para atrasos em implementação enquanto que para o atraso de adoção apresentam a existência de bifurcações. O modelo Replicador-Mutador proposto é robusto para ambos tipos de atrasos

Engineering Emergence: A Survey on Control in the World of Complex Networks

Complex networks make an enticing research topic that has been increasingly attracting researchers from control systems and various other domains over the last two decades. The aim of this paper was to survey the interest in control related to complex networks research over time since 2000 and to identify recent trends that may generate new research directions. The survey was performed for Web of Science, Scopus, and IEEEXplore publications related to complex networks. Based on our findings, we raised several questions and highlighted ongoing interests in the control of complex networks.publishedVersio

The lower convergence tendency of imitators compared to best responders

Imitation is widely observed in nature and often used to model populations of decision-making agents, but it is not yet known under what conditions a network of imitators will reach a state where they are satisfied with their decisions. We show that every network in which agents imitate the best performing strategy in their neighborhood will reach an equilibrium in finite time, provided that all agents are opponent coordinating, i.e., earn a higher payoff if their opponent plays the same strategy as they do. It follows that any non-convergence observed in imitative networks is not necessarily a result of population heterogeneity nor special network topology, but rather must be caused by other factors such as the presence of non-opponent-coordinating agents. To strengthen this result, we show that large classes of imitative networks containing non-opponent-coordinating agents never equilibrate even when the population is homogeneous. Comparing to best-response dynamics where equilibration is guaranteed for every network of homogeneous agents playing 2 × 2 matrix games, our results imply that networks of imitators have a lower equilibration tendency