Nonlinear Dynamics

Nonlinearity and nonlinear world. Nonlinear mathematical models. Basic theory of ODEs and practical numerical integration. Attractors, bifurcations. Mathematically determined chaos. Orbit and the Feigenbaum diagrams, the Lorenz section, the Poincaré section. Fractality, fractal structures. Recurrence maps and feedback loops. The Mandelbrot set, and the Fatou and Julia sets their connection to nonlinear dynamical systems. Fractal dimensions. The universal route to chaos via period doubling cascade. Identification of chaotic processes. Analytical and numerical methods, the Lyapunov exponent. Entropy. Horizon of predictability. Examples from physics, mechanics, biology and ecology. Applications of chaos theory and fractal geometry.

NB! This course will take place in autumn semester 2024/2025 which starts on 2nd of September and ends 26th of January (you can find that information under Start date section). The real course start and end dates will be announced at the beginning of September at the latest.

After completing this course, the student:

• recognises and analyses nonlinear systems and chaotic regimes;
• explains the fundamentals and concepts used in nonlinear dynamics.

Final assessment can consist of one test/assignment or several smaller assignments completed during the whole course. After declaring a course the student can re-sit the exam/assessment once. Assessment can be graded or non-graded. For specific information about the assessment process please get in touch with the contact person of this course. For specific information about grade transfer please contact your home university

• S.H. Strogatz, Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition, Avalon Publishing, 2014.
• K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos: An Introduction to Dynamical Systems, Springer, 2000.
• Ü. Lepik, J. Engelbrecht, Kaoseraamat, Teaduste Akadeemia Kirjastus, 1999.

lectures, exercises