Nonlinear Dynamics and Stochastic Processes with Applications

Reader: Benjamin Friedrich

Time: Every Tuesday 16.40 (6.DS )

Room: PHY/B214 (Häckelstrasse 3 on main campus)

Web: https://www.cfaed.tu-dresden.de/friedrich-group-teaching

Abstract

Nonlinear dynamical systems are studied in many fields of physics, engineering, electronics, and economics, including classical mechanics, biological physics and control theory. The theory of nonlinear dynamics provides a way of geometric thinking to identify dynamic steady states and oscillations in dynamical systems. It allows to assess the stability of these steady states and their behavior under change of control parameters, often without the need to solve dynamical equations explicitly.

This will be a first course in nonlinear dynamics, with a focus on geometric aspects and applications. Key theoretical concepts of dynamical systems theory will be introduced and illustrated by examples from physics, biology, and computer science. In a second part of the lecture, we will give an introduction to stochastic processes and study dynamics and robustness of nonlinear systems in the presence of noise.

Topics
Stability analysis, bifurcation theory, oscillators and synchronization, pattern formation, introduction to chaos, introduction to stochastic processes, Langevin and Fokker-Planck formalism, application to first passage time problems and Kramer’s escape rate theory.

Prerequisites

Ordinary Differential Equations, Multi-variate calculus

Literature

• Strogatz: Nonlinear Dynamics and Chaos, Westview, 2001 (gebraucht ab 20€)
• Risken: The Fokker-Planck Equation, Springer, 1996
• Stratonovich: Topics in the Theory of Random Noise, Martino, 2014
• Ott: Chaos in Dynamical Systems, Cambridge University Press, 2002
• VanKampen: Stochastic Processes in Physics and Chemistry, North-Holland, 2007