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
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
|Course schedule||Required learning|
|Class 1||Introduction / Phase space and flows||Notion of phase space and flows|
|Class 2||Gradient, Hamiltonian, and one-dimensional dynamical systems||Dynamics of gradient, Hamiltonian, and one-dimensional dynamical systems|
|Class 3||Stability and bifurcation||Notions of stability, linear stability analysis and bifurcation of fixed points|
|Class 4||2-dimensional systems||Dynamics on the two-dimensional phase plane|
|Class 5||Limit-cycle oscillations||Emergence of limit-cycle oscillations and typical examples|
|Class 6||Reduction methods and synchronization||Methods to simplify dynamical systems and analyzing synchronization phenomena of nonlinear oscillations|
|Class 7||Chaotic dynamics||Emergence of chaotic dynamics 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