Various real-world phenomena are modeled as dynamical systems. In this course, starting with the elements of dynamical systems theory, destabilization of stationary states and emergence of spontaneous rhythmic or chaotic dynamics are explained, using mathematical models of real-world systems as examples.
The aim of this course is to provide knowledge on the elements of dynamical systems theory such as stability and bifurcation, as well as on the dynamical systems modeling of real-world phenomena. In particular, theoretical and numerical analysis of nonlinear oscillations will be discussed.
Dynamical systems, stability, nonlinear oscillations, chaos, synchronization
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
|Course schedule||Required learning|
|Class 1||Introduction / Phase space and flows||Understand the notion of phase space and flows|
|Class 2||One-dimensional dynamical systems||Understand the dynamics of one-dimensional systems|
|Class 3||Two-dimensional dynamical systems||Understand the dynamics on the two-dimensional phase plane|
|Class 4||Stability and bifurcation||Understand the linear stability analysis and destabilization of fixed points|
|Class 5||Limit-cycle oscillations||Understand the emergence of limit-cycle oscillations and typical examples|
|Class 6||Reduction methods||Understand the methods to simplify dynamical systems|
|Class 7||Synchronization||Understand the synchronization phenomena of nonlinear oscillations|
|Class 8||Chaos||Understand the emergence of chaos and its characterization|
Steven Strogatz, "Nonlinear dynamics and chaos", Westview press.
Kuramoto, "Chemical Oscillations, Waves, and Turbulence", Springer.
Hoppensteadt & Izhikevich, "Weakly Connected Neural Networks", Springer.
Grading will be based on the homework scores.
Elementary knowledge of mathematics and physics