**Network Systems and Dynamics**

**Course content**

Motivating examples
systems drawn from social networks, epidemics and from estimation
problems for
sensor networks. Basic concepts and results in matrix and graph theory,
with an emphasis on
Perron–Frobenius theory, algebraic graph theory and linear dynamical
systems. Consensus systems and averaging systems in discrete and
continuous time,
described by static and time-varying matrices dynamics. Positive and
compartmental systems, described by Metzler matrices. Flow
networks. Networks of phase oscillator systems with an emphasis on the
Kuramoto model and
models of power networks.

Population dynamic models, describing mutualism, competition and cooperation in
multi-species systems.

**Textbook**

Francesco Bullo, Lectures on Network Systems. Kindle Direct Publishing, 2020. ISBN 978-1-986425-64-3

**Other useful matherial for the preparation of the exam**

For the preparation of the exam, it is suggested to look at the moodle page of the course where you can find all the lectures that have been video recorded and the slides that have been produced during the lectures.

** **Examination methodology

For the final exam there are two options:

1. A standard oral exam on the program of the course that roughly coincides with the textbook, or more precisely with what I did during the lectures (it can be found in the slides avalilable in moodle).

2. You can choose a project that consists in the reading of one or two research papers and the writing of a report which summarizes the content and doing numerical experiments related to the subject. All this activity will be done under my supervision, namely, the choice of the project, the choice of the papers to read and the numerical experiments to be done. In case you choose to do the project, part of the oral exam will be the explanation of the report and and part will be a question on a limited portion of the program to be decided with me according to the difficulty of the project that has been chosen. You can fond the list of projects in the announcments in moodle.

During the course I will propose homeworks. If you do them, you will get one extra point for each homework that I will be consider done correctly.

**Dates of the oral exam**

22/6/2021 at 14.00

20/7/2021 at 14.00 (changed from the previous date that was 12/7/2021)

7/9/2021 at 14.00

Notice that the dates of the exam are flexible. For fixing the date and the time of the exam you have to write to me by email.