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 2025/2026 which starts on 1st of September and ends on 25th of January (you can find that information under Start date section). TalTech's timetables for Autumn semester 2025 will be published at the end of June via tunniplaan.taltech.ee. Switch the page to English and use "Search" and "Open detailed search" to find your course. NB! Some courses are taught by several lecturers during the same semester. Make sure that the course name and lecturer/teacher infromation of your course match with the information given in the Course Catalogue.

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

None.

• 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