Dynamical Systems
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA03105 
Vaknaam  Dynamical Systems 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Dynamical Systems  
Leerdoelen  At the end of the course, the student is able to: 1. 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. identify elementary bifurcations of equilibria and can recite criteria for the occurrence of these bifurcations. 3. 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. knows about the mathematical characteristics of chaotic behavior and is able to prove them for simple examples. 

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.  
Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(If the mark for the final exam is 4.5 or higher then the grade for the course will be max(FE, 0.3 HW + 0.7 FE) where FE and HW are the grades for the final exam and homework assignments, respectively. If the mark for the final exam is lower than 4.5 then the grade for the course will be the mark for the final exam. The HW does not count in case of a resit exam.) 

Vaksoort  bachelor  
Coördinator  Prof. Dr. H. Waalkens  
Docent(en)  Prof. Dr. H. Waalkens  
Verplichte literatuur 


Entreevoorwaarden  Knowledge assumed: from the courses, Calculus 1, Calculus 2, Linear Algebra 1, Linear Algebra 2, and Linear Systems  
Opmerkingen  The course prepares for courses in Systems and Control and advanced courses in Dynamical Systems Theory. This course was registered last year with course code WBMA19005 

Opgenomen in 
