Project Dynamical Systems
Faculteit  Science and Engineering 
Jaar  2017/18 
Vakcode  WIIPDS07 
Vaknaam  Project Dynamical Systems 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Project Dynamical Systems  
Leerdoelen  1. The student has a profound understanding of planar linear systems and he/she can classify equilibria using the tracedeterminant plane and the conjugacy classes of linear systems. 2. The student can identify elementary bifurcations of equilibria and knows criteria for the occurrence of these bifurcations. 3. The student is familiar with main theorems like the HartmanGrobman theorem, the stable curve theorem for saddles of planar systems, the PoincareBendixson theorem, the Lyapunov stability theorem and the Lasalle invariance principle and is able to apply them to basic examples. 4. The student knows about the mathematical characteristics of chaotic behavior and is able to prove them for simple examples. 5. The student is able to apply and/or further develop the theory provided in the lectures in a project work. With some supervision by the lecturer the student is able to work on the project independently within a small group. The student is able to present this project work in a written and an oral form. 

Omschrijving  This course comprises an introduction to dynamical systems theory. Dynamical systems theory is concerned with how systems evolve in time. As such it has many applications in all the sciences. The time evolution can be continuous or discrete. In the former case it is described by ordinary differential equations, in the later case it is described by the iteration of a map from the system's state space to itself. In many applications it is difficult to find explicit solutions of such systems. Instead one is more interested in the qualitative behavior of solutions. This behavior often concerns the question of how the solutions explore the state space of the system, i.e. from where to where do they evolve, do they behave regularly (like periodic or quasiperiodic ) or irregularly (like showing a sensitive dependence on initial condition and other features). The irregular behavior is often referred to as chaotic behavior. Often there are special solutions (like fixed points or periodic orbits) which form the organizing centers in the state space in the sense that they determine the qualitative behavior of the other solutions. In dynamical systems theory one is moreover often interested in whether and know the qualitative behavior persists or changes if system parameters are varied. In this course a part of the mathematical framework is provided which is required to answer these questions. This is mainly done in the form of lectures. In the second half of the course the students will also work in small groups on a project which involves an application or an extension of the theory provided in the lectures. The groups write a report on their project and present the project work in a talk.  
Uren per week  
Onderwijsvorm 
Bijeenkomst (S), Hoorcollege (LC), Werkcollege (T)
(lectures, problem classes and indiviual meetings of teams of students with the lecturer.) 

Toetsvorm 
Presentatie (P), Schriftelijk tentamen (WE), Verslag (R)
(Oral and written presentation of the project work, and a final written exam. The final grade is composed as 0.40 E + 0.1 T + 0.5 R where E, T and R are the marks for the written exam, the talk and the report, respectively.) 

Vaksoort  bachelor  
Coördinator  prof. dr. H. Waalkens  
Docent(en)  prof. dr. H. Waalkens  
Verplichte literatuur 


Entreevoorwaarden  Prior knowledge from the courses, Calculus 1, Calculus 2 and Ordinary Differential Equations is required.  
Opmerkingen  The course prepares for courses in Systems and Control and advanced courses in Dynamical Systems Theory.  
Opgenomen in 
