Dynamical Systems and Non-Linear Dynamics
Full course description
The course Dynamical Systems and Nonlinear Dynamics will provide you an introduction into the analysis and visualization of the complex behavior of dynamical systems . We will look at a many features of nonlinear systems, starting from first-order differential equations, covering phase-plane analysis and eventually study the famous Lorenz-equations. Topics will include fixed points and stability, numerical methods, bifurcations, oscillators, attractors, chaos, fractals and recurrence analysis. The theory will always be supported by many practical examples and applications, and assignments will be mostly done with the help of the computer, using MATLAB and/or Octave. Journal clubs will provide further insight into various applications of dynamical systems theory in the field of Systems Biology.
This course aims to provide a solid basis for the understanding of the behavior of dynamical systems and to provide tools to visualize and analyze these systems, with a limited amount of fundamental mathematical theory. The focus will be on practical applications of the theory, by analyzing and visualizing systems using the computer. Participants will learn to use MATLAB/Octave to define, analyze and visualize dynamic behavior in multiple ways, study the effect of parameter changes and initial conditions, see how deterministic chaos can arise in relatively simple systems, have fun with fractals and discover recurrent patterns in biomedical signals. Prerequisites are an introductory level of calculus and physiology, as covered by the courses Mathematics of Biological Systems and Biology and Physiology.
The course will be given following the material discussed in: Steven H. Strogatz, Nonlinear Dynamics and Chaos, 2nd edition. Students are strongly recommended to obtain a copy of this book, as it provides a gentle but thorough introduction into the analysis of nonlinear systems with many examples from physics, biology, chemistry and engineering.