I.The Basic Information of the Course
Course Number:202012420019
EnglishName of theCourse：Complex networks and dynamical systems
ChineseName of theCourse：复杂网络与动力系统
In-classHours andAllocation32hours, including26hoursforlectures,and6hours for presentation and discussion.
Credit(s):2
Semester: thesecond semester
Applied discipline:Science andEngineeringDiscipline,
Participants：Academicmaster and doctoral students
Way of evaluation:project report and presentation
Language:English
Majors：Scienceand engineering majors
CourseOpening Department: College of Mathematical Sciences
II.Prerequisite Course
Mathematical analysis, Advanced algebra, Functional analysis, Ordinary differential equation
III. The Objectives and Requirements of the Course
1)This course is an optional course. Theobjectiveof this course is to help students to understand some basic concepts and metrics of complex networks.
2)Through the study of this course, the students will be able todevelop and analyze some epidemic models.
3)Students will acquire the ability to search and read the literature related to the research problem independently. For the concepts and theories not understood in the literature, they can independently find the sources, andsolve the problem by themselves.
4)Students should be able to write code for the models and analysis independently.
IV. The Content of the Course
Complex networks is a new field of science widely applied to information technology networks, including internet, electric power networks, mobile phone networks, transportation networks including airline network and railway networks, friendship networks in the field of social networks, river networks, biological networks including neural networks, protein networks. In the recent decade, rapid progress has been made in network theory and techniques, especially in the topological structure of networks.
This course mainly introduces the historical background of epidemics, basic concepts in complex networks, modelling epidemics on complex networks, and the approaches of modelling and analysis under different network structures. This course mainly focuses on the idea of modelling, dynamical analysis, and biological interpretations. The contents are as follows.
Chapter 1.Preliminaries:networksand graphs
1.1What is a network
1.2Basic concepts ingraph theory
1.3Statistical characterization of networks
1.4Weightednetworks
1.5 Real word systems
In this chapter, taking road traffic as an example, the related concepts of network are introduced. When explaining the introduction of complex networks, we take the hot topic, such as the road traffic as the entry point, review the rapid development of society and the transformation of traffic problems, encourage students to develop ideas, actively practice, and design solutions to solve traffic congestion problems. Inspire students' creativity, and at the same time advocate students to actively care about others, and consciously carry forward and practice socialist core values.
Chapter2.Networks models
2.1 Randomness and network models
2.2 Exponential random graphs
2.3 Evolving networks and the non-equilibrium approach
Taking the social network as an example to introduce the nature of the network. When explaining the nature of the network, we introduce a six-degree separation, which means that on average you only needsixpeople to connect with anyone in any corner of the world. Inspire the students to promote the peace of the world.
Chapter 3. Introduction to dynamical processes and simulations
3.1 A microscopicapproachto dynamical phenomena
3.2 Equilibrium and non-equilibrium systems
3.3 Approximation solutions of the Master Equation
3.4Agent-based modeling and numerical simulations
Chapter 4 Resilience and Robustness of networks
4.1Percolation in complex networks
4.2Damage and resilience in complex networks
4.3Targeted attacks on large degree networks
Chapter 5 Epidemic spreading in population networks
5.1 epidemic models
5.2 Epidemics in heterogeneous networks
5.3 Immunization of heterogeneous networks
Taking the infectious disease, Malaria, as an example, the problem of establishing and analyzing infectious disease models is introduced.
When introducing the application of complex networks, we introduce modelling the transmission of Malaria, remind students to pay attention to their own health, and let the students further understand that only a heathy person can help promote the sustainable development of society and better serve the people, and better contribute to the country.
V. Reference Books, Reference Literatures, and Reference Materials
Text Books
1.Alain Barrat,n Barrat, Marc Barthélemy, and Alessandro Vespignani. Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge,2008
2.Zhen Jin,Guiquan Sun, Maoxing Liu. Modelling and analysis of dynamical epidemic models.Science Press, China，2014.
Syllabus designer:
Signature of the associate dean in charge of teaching：
Date：July 3, 2020
中文
