Dynamical Systems often behave in a counter-intuitive fashion and are, therefore, complicated to predict, to organize and to regulate. The counter-intuitive behavior comes from nonlinear interactions between the system components.
This course provides a nutshell view on nonlinear dynamics, leading to a toolbox for understanding and simulating complex situations.
Starting from high-school level mathematics (basic calculus, probabilities etc.) this course will introduce ideas from nonlinear dynamics and illustrate, how this perspective had led to breakthroughs in identifying the organizing principles behind dynamical observations.
The basic questions we will discuss have an immediate appeal to industrial systems: Why can a single feedback loop lead to oscillations? When does a chain of processes become unstable? What are the limits for accurate predictions in nonlinear systems?
Topics include the stability analysis in systems of ordinary differential equations; conditions of oscillations; deterministic chaos; agent-based models and cellular automata; dynamic processes on networks.
In all these cases it will be shown, how the abstract theoretical concepts are linked with explicit observations and how these concepts can help understand processes in industrial systems.