Complex Systems and Self-Organization

Complex systems as systems in which complex and qualitatively new behaviours emerge from the interaction of simple building blocks. Self-organisation and self-organising criticality as a process in complex systems. The notion of a critical state as a zero-dimensional state in parameter space using the example of the percolation problem. Scale-invariance and fractality as a property of systems at criticality. Fractal dimension, multifractality, self-affinity. Bak-Tang-Wiesenfeld sandpile model where the system itself moves towards criticality. Forward and inverse avalanches and their size distributions. Bak-Sneppen model: a one-dimensional model of biological evolution. The Kardar-Parisi-Zhang model of surface growth. Self-organization in geophysics: erosion, tectonics and earthquakes. Self-organization in astrophysics and plasma physics. Self-organisation in society and economy. Scale-free networks as one of the outcomes of self-organization. Main properties and characteristics of scale-free networks.

NB! This course will take place in spring semester 2025/2026 which starts on 2nd of February and ends on 15th of June (you can find that information under start date section). TalTech's timetables for spring semester 2026 will be published at the beginning of January via tunniplaan.taltech.ee.

After completing this course, the student:

• recognizes the general characteristics of complex systems and uses them in his/her field of research;
• describes the most important complex systems and understands their functioning;
• describes the processes that lead to self-organisation and their manifestations of self-organisation.

Final assessment can consist of one test/assignment or several smaller assignments completed during the whole course. After declaring a course the student can re-sit the exam/assessment once. Assessment can be graded or non-graded. For specific information about the assessment process please get in touch with the contact person of this course. For specific information about grade transfer please contact your home university

not

• Per Bak „How Nature Works: the science of self-organized criticality“. https://doi.org/10.1007/978-1-4757-5426-1.
• Raúl Sánchez, David Newman „A Primer on Complex Systems“. https://doi.org/10.1007/978-94-024-1229-1.

lectures, exercises