scholarly journals Combined Synchronization among Three Inconsistent Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Yuan Chai ◽  
Xiaojing Zhu ◽  
Jingjing Cai
Keyword(s):  
Small World ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Community Network ◽  
Partial Control ◽  
Scale Free ◽  
System Combination ◽  
Combination Synchronization ◽  
New Type ◽  
Universal Controller

A new type of network-combination synchronization is proposed between two drive networks, small-world and scale-free, and one response community network based on the model of multiple system combination. According to Lyapunov Stability Theorem, combined controllers are designed to control three disparate networks with different topological structures. A realistic combination model of multiple inhomogeneous networks and a universal controller are devised in the combination design. The paper is characterized by two parts of one response community network loaded from the combined signals of two drive networks. Numerical simulations are presented to show the full and partial control of the proposed method.

scholarly journals A New Type of Combination Synchronization among Multiple Chaotic Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Xingxu Wang ◽  
Lin Sun ◽  
Bingji Wang ◽  
Tousheng Huang
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Representative Case ◽  
Combination Synchronization ◽  
Response System ◽  
New Type ◽  
Drive Systems ◽  
Multiple Chaotic Systems

Based on former combination synchronization studies, a new type of combination synchronization approach is developed in this research, with the consideration of parallel combination of drive systems. This new synchronization approach is referred to as combination synchronization-II. As a representative case, the combination synchronization-II between three drive systems and one response system is studied. Applying Lyapunov stability theorem and active backstepping design, sufficient conditions for the proposed combination synchronization approach are derived. Numerical simulations are performed to show the feasibility and effectiveness of the proposed approach. Based on the investigation in this research, the proposed approach provides an applicable method for designing universal combination synchronization among multiple chaotic systems.

scholarly journals W-Stability of Multistable Nonlinear Discrete-Time Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Zhishuai Ding ◽  
Guifang Cheng ◽  
Xiaowu Mu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Discrete Dynamical Systems ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Converse Theorem ◽  
Discrete Time Systems ◽  
New Type ◽  
Time Systems

Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion ofW-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.

CLUSTER-DENSE NETWORKS

2008 ◽  
Vol 19 (06) ◽  
pp. 939-946 ◽  
Author(s):  
MOSHE SIPPER
Keyword(s):  
Local Density ◽  
Small World ◽  
Node Degree ◽  
Small World Networks ◽  
Scale Free ◽  
Dense Networks ◽  
Graph Theoretic ◽  
Network Cluster ◽  
New Type ◽  
Multiple Clusters

Small-world networks, exhibiting short nodal distances and high clustering, and scale-free networks, typified by a scale-free, power-law node-degree distribution, have been shown to be widespread both in natural and artificial systems. We propose a new type of network — cluster-dense network — characterized by multiple clusters that are highly intra-connected and sparsely inter-connected. Employing two graph-theoretic measures — local density and relative density — we demonstrate that such networks are prevalent in the world of networks.

Top Museums on Instagram

2019 ◽  
Vol 3 (2) ◽  
pp. 18-42 ◽  
Author(s):  
Vasiliki G. Vrana ◽  
Dimitrios A. Kydros ◽  
Evangelos C. Kehris ◽  
Anastasios-Ioannis T. Theocharidis ◽  
George I. Kavavasilis
Keyword(s):  
Social Network ◽  
Network Analysis ◽  
Small World ◽  
Marketing Strategies ◽  
The Other ◽  
Small World Network ◽  
Scale Free ◽  
Centrality Metrics ◽  
Photo Sharing ◽  
Visualization Algorithms

Pictures speak louder than words. In this fast-moving world where people hardly have time to read anything, photo-sharing sites become more and more popular. Instagram is being used by millions of people and has created a “sharing ecosystem” that also encourages curation, expression, and produces feedback. Museums are moving quickly to integrate Instagram into their marketing strategies, provide information, engage with audience and connect to other museums Instagram accounts. Taking into consideration that people may not see museum accounts in the same way that the other museum accounts do, the article first describes accounts' performance of the top, most visited museums worldwide and next investigates their interconnection. The analysis uses techniques from social network analysis, including visualization algorithms and calculations of well-established metrics. The research reveals the most important modes of the network by calculating the appropriate centrality metrics and shows that the network formed by the museum Instagram accounts is a scale–free small world network.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

A Path-Planning Strategy for Overhead Cranes With High Hoisting Speed

2002 ◽  
Author(s):  
Ho-Hoon Lee
Keyword(s):  
Path Planning ◽  
High Performance ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Control Laws ◽  
Planning Strategy ◽  
Overhead Cranes ◽  
Time Control ◽  
Small Load ◽  
Load Swing

This paper proposes a path planning strategy for high-performance anti-swing control of overhead cranes, where the anti-swing control problem is solved as a kinematic problem. First, two anti-swing control laws, one for hoisting up and the other for hoisting down, are proposed based on the Lyapunov stability theorem. Then a new path-planning strategy is proposed based on the concept of minimum-time control and the proposed anti-swing control laws. The proposed path planning is free from the usual constraints of small load swing, slow hoisting speed, and small hoisting distance. The effectiveness of the proposed path planning is shown by computer simulation with high hoisting speed and hoisting ratio.

Independence polynomial and matching polynomial of the Koch network

2015 ◽  
Vol 29 (32) ◽  
pp. 1550234
Author(s):  
Yunhua Liao ◽  
Xiaoliang Xie
Keyword(s):  
Lattice Gas ◽  
Small World ◽  
Partition Functions ◽  
Complete Class ◽  
Dimer Model ◽  
Scale Free ◽  
Matching Polynomial ◽  
Independence Polynomial ◽  
Classical Models ◽  
Explicit Formulae

The lattice gas model and the monomer-dimer model are two classical models in statistical mechanics. It is well known that the partition functions of these two models are associated with the independence polynomial and the matching polynomial in graph theory, respectively. Both polynomials have been shown to belong to the “[Formula: see text]-complete” class, which indicate the problems are computationally “intractable”. We consider these two polynomials of the Koch networks which are scale-free with small-world effects. Explicit recurrences are derived, and explicit formulae are presented for the number of independent sets of a certain type.

scholarly journals Analysis on Invulnerability of Wireless Sensor Network towards Cascading Failures Based on Coupled Map Lattice

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Xiuwen Fu ◽  
Yongsheng Yang ◽  
Haiqing Yao
Keyword(s):  
Random Network ◽  
Small World ◽  
Coupled Map Lattice ◽  
Wireless Sensor ◽  
Cascading Failures ◽  
Scale Free Network ◽  
Scale Free ◽  
Network Topologies ◽  
Free Network ◽  
Entire Network

Previous research of wireless sensor networks (WSNs) invulnerability mainly focuses on the static topology, while ignoring the cascading process of the network caused by the dynamic changes of load. Therefore, given the realistic features of WSNs, in this paper we research the invulnerability of WSNs with respect to cascading failures based on the coupled map lattice (CML). The invulnerability and the cascading process of four types of network topologies (i.e., random network, small-world network, homogenous scale-free network, and heterogeneous scale-free network) under various attack schemes (i.e., random attack, max-degree attack, and max-status attack) are investigated, respectively. The simulation results demonstrate that the rise of interference R and coupling coefficient ε will increase the risks of cascading failures. Cascading threshold values Rc and εc exist, where cascading failures will spread to the entire network when R>Rc or ε>εc. When facing a random attack or max-status attack, the network with higher heterogeneity tends to have a stronger invulnerability towards cascading failures. Conversely, when facing a max-degree attack, the network with higher uniformity tends to have a better performance. Besides that, we have also proved that the spreading speed of cascading failures is inversely proportional to the average path length of the network and the increase of average degree k can improve the network invulnerability.

Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains

2013 ◽  
Vol 110 (10) ◽  
Author(s):  
Ralph Stoop ◽  
Victor Saase ◽  
Clemens Wagner ◽  
Britta Stoop ◽  
Ruedi Stoop
Keyword(s):  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Cortical Columns

SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950010
Author(s):  
DAOHUA WANG ◽  
YUMEI XUE ◽  
QIAN ZHANG ◽  
MIN NIU
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Hierarchical Network ◽  
Scale Free

Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.

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