Mathematical Methods and Models for the Applications
A.Y. 2018/2019
Learning objectives
A broad view of models, methods, phenomena and techniques related to low dimensional dynamical systems will be presented, with a particular emphasis on some elementary features of chaotic dynamics.
The aim of the course is to give to the student the ability to develop simple numerical tools useful to investigate the above quoted models, methods, phenomena and techniques.
The aim of the course is to give to the student the ability to develop simple numerical tools useful to investigate the above quoted models, methods, phenomena and techniques.
Expected learning outcomes
Ability to study mathematical models described by means of simple dynamical systems.
Ability to develop simple numerical tools to investigate low dimensional dynamical systems.
Ability to develop simple numerical tools to investigate low dimensional dynamical systems.
Lesson period: First semester
Assessment methods: Giudizio di approvazione
Assessment result: superato/non superato
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
First semester
Course syllabus
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.
4. Chaotic behaviour: hyperbolic maps and shadowing lemma; homoclinic points; 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.
4. Chaotic behaviour: hyperbolic maps and shadowing lemma; homoclinic points; symbolic dynamics.
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Laboratories: 24 hours
Lessons: 36 hours
Lessons: 36 hours
Professors:
Paleari Simone, Sansottera Marco
Professor(s)
Reception:
Contact me via email
Office 1039, 1st floor, Dipartimento di Matematica, Via Saldini, 50