Introduction to Complex Systems

Summer 2016, Prof. Dirk Brockmann

Dirk Brockmann• email: dirk.brockmann@hu-berlin.de

• phone: +49 30 187542070

• office: Robert-Koch-Institute, Nordufer 20, 13353 Berlin

• hours: by appointment

• web: http://rocs.hu-berlin.de

• twitter: @DirkBrockmann

https://de.surveymonkey.com/r/3F7V86T

Survey

course language

german or english depending on your vote

http://rocs.hu-berlin.de

the module

Practical Course

Lecture

Seminar

Time

Lecture: 8:00-10:00am, Thursdays

Seminar: 8:00-10:00am, Fridays

Practical Course: 28.6.2015 - 8.7.2016

Location

the module

Practical Course

Lecture

Seminar

Lecture

lecture

70 %

30 %

Theoretic FoundationPhenomena

Theoretic Foundation

20 %

20 %

20 %

30 %

10 %

Dynamical Systems1d Flows2d flows1d mapsstochastic processes

Collective Motion 11 %

Growth 11 %

Critical Phenomena 11 %

Pattern Formation 22 %

Synchronization 11 %

Chaotic Systems 11 %

Dynamical Systems 11 %

Networks 11 %

Seminar

seminar• 25 minute presentations

• on research papers

• paper pool will be online

• flexible choice

• each students meets with Dirk once before presentation

• content

• presentation skill

Practical Course

netlogonetlogo is a simple to learn, platform independent, and free programming language that we will use frequently throughout this course. You will need to download a copy and install on your computer.

https://ccl.northwestern.edu/netlogo/

example

Homework IPlease go to the netlogo documentation page and study

1.) the three tutorials (models, commands, procedures) 2.) the Interface Guide 3.) the Programming Guide

On the netlogo documentation page, you'll find links to these on the left.

schedule

Grading

• one test will be given after the foundation as a test for you to check what you have learned

• At the end of your module a klausur will be given on the theoretic foundation and the phenomena

• your seminar presentation will count towards your final grade

Collective Motion 11 %

Growth 11 %

Critical Phenomena 11 %

Pattern Formation 22 %

Synchronization 11 %

Chaotic Systems 11 %

Dynamical Systems 11 %

Networks 11 %

what are complex systems?

Complex Systems

• simple rules generate complex behavior

Complex Behavior

• unpredictable

• structured

• emergent

• self-organized

• dynamic

• self-similar

• critical

• pattern forming

Complex Systems

• simple rules generate complex behavior

example: three species

example: network growth

example: the game of life

• cells can be dead or alive

• Every living cell considers 8 nearest neighbors and counts living neighbors K

• when K<2 the cell dies

• when K=2 or K=3 the cell lives

• when K>3 the cell dies

• a dead cell is born when 3 neighbors are alive

Topic Appertizers

Chaotic Systems

example: deterministic chaos

http://rocs.hu-berlin.de

fractals

synchronization

synchronization

traveling waves in measles epidemic

pattern formation

critical phenomena

lattice SIR model

• the system is a two dimensional lattice

• each lattice is in one of three states: S, I, R

• An infected lattice site can randomly turn into a recovered lattice site with probability B

• A neighboring S - I pair of sites can turn into an I - I pair with probability A

growth

self-organization

collective motion