### Courses

##### Last Updated:
10/03/2019 - 15:02

## IAM529 - Applied Nonlinear Dynamics

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Yurdahan Güler
Prerequisites: Consent of Instructor(s)

#### Course Catalogue Description

The course consists of a detailed description of continuous and discrete dynamical systems. We shall combine the introduction to the general theory with the consideration of bifurcations and chaos, the most important subtopics. The analysis of appropriate mechanical, physical, economic and biological models is an essential part of almost every lecture of the course. To support the course numerical and computational toolbox will be used.

#### Course Objectives

• The aim of this course is to study mathematical basis of dynamical systems to prepare students for further investigations in related fields.

#### Course Learning Outcomes

Student, who passed the course satisfactorily will:

• learn the basic concepts of dynamical systems
• have the ability to do research in related fields

#### Tentative (Weekly) Outline

1. Linear Dynamical Systems

1. Fundamental Theorem of Continuous Systems
2. A Review of Eigenvectors, Eigenvalues
3. A Qualitative Investigation of Planar Systems
4. Stability of Linear Systems
2. Nonlinear Dynamical Systems
1. A Short review of Manifold Approach
2. Fixed Points and Phase Flow
3. Local Nonlinear Systems, Linearization
4. Stability of Nonlinear Systems, Hyperbolic, Non-hyperbolic Cases
5. Limit Cycles, the Poincaré Map
6. Liapunov Function
7. The Hartman-Grobman Theorems
3. Bifurcations and Hamiltonian Systems
1. One Dimensional Bifurcations, Saddle Node, Pitchfork, Transcritical Bufircations
2. The Hopf Bifurcations
3. Hamiltonian Flows
4. Classification of Flows
5. Examples
4. Chaos and Fractals
1. The Lorenz Equations, and Chaos on a Strange Attractor
2. Lorenz Map
3. The Cantor Set, Dimension of Fractals

#### Course Textbook(s)

• Stephen Lynch, Dynamical Systems with Applications using MATLAB, Birkhäuser Basel, 2014
• James D. Meiss, Differential Dynamical Systems, SIAM, 2007

#### Supplementary Materials and Resources

• Books:
• J. Jost, Dynamical Systems:Examples of Complex Behaviour, Springer, 2005
• S. H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, 2nd edition, Westview Press, 2015
• Resources:
• Lecture Notes: Furthermore, lecture notes and recent research articles will be provided during the course.
• MATLAB Student Version is available to download on MathWorks website, http://www.mathworks.com, or METU FTP Severs (Licenced)