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چكيده انگليسي :

Synchronization in All to all Bipartite and Achlioptas Networks Student name Sara Parastegari Email address s parastegari@ph iut ac ir Date of submission 1389 01 30 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Dr KeivanAghababaeiSamani@iut ac ir AbstractSynchronization phenomena in population of interacting elements are the subject of intense research efforts inphysics chemistry biology and social scince Synchronized states are very important in networks of phaseoscillators most of real systems such as biological and social systems can be modeled by a complex network andelementary units of the system are displayed by nodes and edges represent interactions between them A successfulapproach to the problem of synchronization consist of modeling each member of population as an oscillator Here the synchronization phenomena are introduced then the Kuramoto model is designed One of the interestingquestions in the Kuramoto model is the stability of solutions both synchronized and incoherent states In this thesis by a synchronized state we mean a state in wich all to of the oscillators oscillate with the same frequency this is alsocalled a frequency locked state The aim of this thesis is investigating the role of topology and properties ofnetworks such as Erdos Renyi network scale free network with Barabasi Albert model and the so called Achlioptasnetworks on synchronization The Kuramoto model is applied on all to all networks with unimodal and bimodalfrequency distributions The diagram of order parameter as a function of time is drawn for synchronized state andthe threshold of synchronization Furthermore this diagram shows that when coupling constant k is less than athreshold value the system is not synchronize and by increasing coupling constant the system reached to thesynchronization threshold if coupling constant is more than threshold value Bipartite networks are introduced andthe Kuramoto model is studied for these networks with bimodal frequency distribution Time evaluation of orderparameter is drawn for synchronized and asynchronized modes While coupling constant is less than threshold thesystem is asynchronized and by increasing coupling costant the system will inter to synchronization Finally thescale free and random networks are introduce and time evaluation of order parameter are compared in two networks When evaluation the diagram is compare for scale free and random networks it will be found that the scale freenetwork reaches sooner than random network to synchronization The Growth Achlioptas process is introduced Firstdefine an Achliptas growth process The goal is to construct a random network of N nodes and given degreesequence k1 k2 kN If links are placed randomaly the procedure can be carried out with the configurationmodel Here instead the criterion to add links is different The random and scale free networks and designed withGrowth Achlioptas process and the Kuramoto model are applied on these two networks Furthermore diagramorder parameter depending on the time are drawn and compared to scale free and random networks that was madewith Growth Achlioptas process Links between nodes are introduce in order to produce a scale free and randomgraph with given exponent for the degree distribution For the scale free and random networks that are made byAchlioptas method it is found that the scale free networks reach sooner than random network to synchronization Key words Network Synchronization Unimodal frequency distribution Bimodal frequency distribution Grow Achlioptas

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