Course Information
TitleΜΗ ΓΡΑΜΜΙΚΑ ΔΥΝΑΜΙΚΑ ΣΥΣΤΗΜΑΤΑ / Non Linear Dynamical Systems
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
CoordinatorGeorgios Vougiatzis
Course ID40003023

Programme of Study: UPS of School of Physics (2012-today)

Registered students: 104
OrientationAttendance TypeSemesterYearECTS
CoreBasic Election745

Class Information
Academic Year2019 – 2020
Class PeriodWinter
Faculty Instructors
Instructors from Other Categories
Weekly Hours3
Class ID
Type of the Course
  • Background
  • Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
  • Face to face
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Instruction, Examination)
Learning Outcomes
In the end of the lectures, the students 1) should have become familiar with the basic theory and methods used for the study of nonlinear dynamical systems in Physics and in other sciences. 2) learn to recognize the usefulness of analytical mathematical methods and their limits and how to manage computational methods. 3) under a systematic way, they come in contact with the modern theory of chaos. 4) since software of symbolic mathematics and numerical computations is widely used, they get this particular mastery too, which is very useful for their scientific field.
General Competences
  • Apply knowledge in practice
  • Generate new research ideas
Course Content (Syllabus)
Introduction to Dynamical systems, analytic and numerical approach - The programming tool "Mathematica" · Analytic and Numerical solution of Differential equations with Mathematica · Basic notions of the Dynamical systems - Phase space - Classification of systems and trajectories. · Conservative systems of one degree of freedom - oscillations · Autonomous linear systems 2x2 · Autonomous nonlinear systems - Stability of equilibrium points and phase space diagrams. Applications (Lotka-Voltera models) · Limit cycles. Application to electrical circuit oscillators (Van der Pol) · Bifurcations · Linear perturbed oscillators – Periodic and quasi-periodic trajectories, limit cycles and Poincare maps. · Conservative Oscillators – Poincare maps - Homoclinic chaos. · Limit cycles and strange attractor in dissipative Duffing equation · Discrete dynamical systems · Summary and Discussion
Nonlinear differential equations, Dynamical systems, chaos
Educational Material Types
  • Slide presentations
  • Book
  • Computer programs
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Communication with Students
Use of computers for mathematical (symbolic) and numerical computations with Mathematica Use of e-mail and web-class
Course Organization
Reading Assigment301
Student Assessment
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Course Bibliography (Eudoxus)
ΔΥΝΑΜΙΚΑ ΣΥΣΤΗΜΑΤΑ Κωδικός Βιβλίου στον Εύδοξο: 86195706 Έκδοση: 1/2019 Συγγραφείς: ΑΝΑΣΤΑΣΙΟΥ ΣΤΑΥΡΟΣ ΜΠΟΥΝΤΗΣ ΑΝΑΣΤΑΣΙΟΣ ΕΙΣΑΓΩΓΗ ΣΤΑ ΜΗ ΓΡΑΜΜΙΚΑ ΔΥΝΑΜΙΚΑ ΣΥΣΤΗΜΑΤΑ Κωδικός Βιβλίου στον Εύδοξο: 320107 Συγγραφείς: ΓΕΩΡΓΙΟΣ ΒΟΥΓΙΑΤΖΗΣ, ΕΥΘΥΜΙΑ ΜΕΛΕΤΛΙΔΟΥ Ελληνικά Ακαδημαϊκά Ηλεκτρονικά Συγγράμματα και Βοηθήματα - Αποθετήριο "Κάλλιπος"
Additional bibliography for study
Επιπρόσθετο υλικό στην ιστοσελίδα του μαθήματος
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