Atnaujinkite slapukų nuostatas

El. knyga: Dynamical Systems on Networks: A Tutorial

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on simple situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. 

This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks.

 

Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow

of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics, and co-Director of MACSI, at the University of Limerick, Ireland.

 

Recenzijos

This book by Porter and Gleeson is an excellent tutorial of dynamical systems interconnected as networks. the book under review is highly recommended for students and researchers new to the dynamical systems view of networks. The authors take the best possible approach to presenting a problem for a very large audience. (Juan Gonzalo Bajaras-Ramrez, Mathematical Reviews, February, 2017) 

The book is a relatively concise tutorial and a summary of references for the study of dynamical systems on networks. This tutorial may serve as an accompanying source for the introduction to the field Dynamical systems on networks. (Serhiy Yanchuk, zbMATH 1369.34001, 2017)

1 Introduction: How Does Nontrivial Network Connectivity Affect Dynamical Processes on Networks?
1(2)
2 A Few Basic Concepts
3(2)
3 Examples of Dynamical Systems
5(24)
3.1 Percolation
6(2)
3.1.1 Site Percolation
6(1)
3.1.2 Bond Percolation
6(1)
3.1.3 K-Core Percolation
7(1)
3.1.4 "Explosive" Percolation
7(1)
3.1.5 Other Types of Percolation
8(1)
3.2 Biological Contagions
8(3)
3.2.1 Susceptible--Infected (SI) Model
9(1)
3.2.2 Susceptible--Infected--Susceptible (SIS) Model
10(1)
3.2.3 Susceptible--Infected--Recovered (SIR) Model
10(1)
3.2.4 More Complicated Compartmental Models
10(1)
3.2.5 Other Uses of Compartmental Models
11(1)
3.3 Social Contagions
11(4)
3.3.1 Threshold Models
13(1)
3.3.2 Other Models
14(1)
3.4 Voter Models
15(2)
3.5 Interlude: Asynchronous Versus Synchronous Updating
17(2)
3.6 Coupled Oscillators
19(5)
3.7 Other Dynamical Processes and Phenomena
24(5)
4 General Considerations
29(18)
4.1 Master Stability Condition and Master Stability Function
29(7)
4.2 Other Approaches for Studying Dynamical Systems on Networks
36(1)
4.3 Discrete-State Dynamics: Mean-Field Theories, Pair Approximations, and Higher-Order Approximations
37(8)
4.3.1 Node-Based Approximation for the SI Model
37(2)
4.3.2 Degree-Based MF Approximation for the SI Model
39(2)
4.3.3 Degree-Based MF Approximation for a Threshold Model
41(3)
4.3.4 Discussion of MF Approximation for Discrete-State Dynamics
44(1)
4.4 Additional Considerations
45(2)
5 Software Implementation
47(2)
5.1 Stochastic Simulations (i.e., Monte Carlo Simulations)
47(1)
5.2 Differential-Equation Solvers for Theories
48(1)
6 Dynamical Systems on Dynamical Networks
49(4)
7 Other Resources
53(2)
8 Conclusion, Outlook, and Open Problems
55(2)
A Appendix: High-Accuracy Approximation Methods for General Binary-State Dynamics
57(10)
A.1 High-Accuracy Approximations for Binary-State Dynamics
57(2)
A.1.1 Stochastic Binary-State Dynamics
57(2)
A.2 Approximation Methods for General Binary-State Dynamics
59(2)
A.3 Monotonic Dynamics and Response Functions
61(6)
A.3.1 Monotonic Threshold Dynamics
61(1)
A.3.2 Response Functions for Monotonic Binary Dynamics
62(2)
A.3.3 Cascade Conditions
64(3)
References 67