The course aims at providing the fundamentals of models, methods and mathematical tools used to study low dimensional dynamical systems, even those presenting a chaotic behaviour, also in connection with applicative problems. This will be pursued with the aid of laboratory sessions, where suitable numerical schemes will be developed.
Expected learning outcomes
At the end of the course, the students should be able to study simple dynamical systems representing mathematical models also arising from applicative problems, and should be able to develop suitable numerical tools supprting the aforementioned study.
Lesson period: First semester
(In case of multiple editions, please check the period, as it may vary)
1. One dimensional discrete systems: fixed points and periodic orbits; attractors and repulsors; stability; bifurcations; logistic model of population dynamics; chaotic and symbolic dynamics.
2. Two dimensional systems: stationary orbits; linear systems; stability of equilibria; asymptotic orbits; strange attractors; relations with differential equations; Poincare' index and section; bifurcations.
3. Oscillations: forced and dumped linear systems; nonlinear oscillations; averaging method; limit cycles and Van der Pol oscillator; synchronization; resonances; Henon-Heiles model.
The final examination consists of an oral exam and of the evaluation of all the activities performed during the lab sessions.
- In the oral exam, the student will be required to illustrate results presented during the course, in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them. -The lab exam is based on the activities done in each lab session.
The examination is passed if the oral part is successfully passed and if the lab activities are positively evaluated. Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.
Further options for the examination could be discussed at the beginning of the course.