Mathematical Modeling of Collective Behavior 1000-1S19MCB
Collective dynamics is mathematical description of large groups of individuals interacting with each other in a nonlocal manner. Examples of such phenomena are found in ecology (flocks of birds, schools of fish), economy (distribution of goods), sociology (reaching of agreement in a group, opinion formation), robotics (control of autonomous drons) and other fields.
The goal of the seminar is to introduce students to mathematical aspects of above described phenomena. We will learn most recent methods analysing particular models. The students' presentations
will be based on carefully chosen research papers with mathematical difficulty increasing from classical theory of ordinary differential equations to partial differential equations with nonlocal operators.
Type of course
Prerequisites (description)
Learning outcomes
Student:
- Knowns what basic models of collective dynamics
- Is aware of current open mathematical problems in collective dynamics
- Is able to apply standard techniques and is aware of more advanced ones
- Is able to find information related to given problem and present it
- Understands a potential of mathematics as a language of a unified description of seemingly unrelated phenomena.
Assessment criteria
Attendance and presentation.
Bibliography
Active Particles vol. 1 and vol. 2, N. Bellomo, P.Degond and E. Tadmor (eds)
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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