# Non Linear Dynamical Systems

 Title ΜΗ ΓΡΑΜΜΙΚΑ ΔΥΝΑΜΙΚΑ ΣΥΣΤΗΜΑΤΑ / Non Linear Dynamical Systems Code ΜΑΕ204 Faculty Sciences School Physics Cycle / Level 1st / Undergraduate Teaching Period Winter Coordinator Georgios Vougiatzis Common No Status Active Course ID 40003023

 Academic Year 2017 – 2018 Class Period Winter Faculty Instructors Georgios Vougiatzis 39hrs Weekly Hours 3 Class ID 600100146
Course Type 2016-2020
• Background
• Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
• Face to face
Digital Course Content
Language of Instruction
• Greek (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
Keywords
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
Description
Use of computers for mathematical (symbolic) and numerical computations with Mathematica Use of e-mail and web-class
Course Organization