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13D061UND - Introduction to nonlinear dynamics

Course specification
Course title Introduction to nonlinear dynamics
Acronym 13D061UND
Study programme Electrical Engineering and Computing
Module Nanoelectronics and Photonics
Type of study doctoral studies
Lecturer (for classes)
Lecturer/Associate (for practice)
    Lecturer/Associate (for OTC)
      ESPB 9.0 Status elective
      Condition none
      The goal Introduce students to basic methods of theoretical, numerical and experimental approach in analysis of the nonlinear dynamics problems. Introduce with basic concepts of deterministic evolution, stability, phase portraits, fixed points, bifurcations, and regular and chaotic dynamics to make students capable for a basic analysis of nonlinear physical systems.
      The outcome After the completion of this course it is expected that students will be capable to apply theoretical methods of nonlinear dynamics for analyses the nonlinear systems in physics, biology, and chemistry, to perform numerical analysis of the stability nonlinear systems and processing of the experimental data.
      Contents
      Contents of lectures Basic concepts of the evolution and stability. Regular and chaotic dynamics. Low dimensional dynamical systems: central manifold and normal forms. Standard mapping, KAM theorem, fixed points, Poincare- Birkhoff theorem, bifurcation phenomena. Global and local chaos. Statistical concepts: local and global stochasticity, Lyapunov exponents and Kolmogorov–Sinai entropy.
      Contents of exercises Application of the methods of nonlinear dynamics in analysis wave propagation in nonlinear periodic systems: photonic crystals, optical lattices and Bose-Einstein condensates. Design the numerical code for a linear stability analysis and dynamical simulation of the nonlinear phenomena on the examples of simple nonlinear systems.
      Literature
      1. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, 1994, Perseus Books Publishing
      2. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2000, Springer
      3. P. Berge, Y. Pomeau, C. Vidal, Order within chaos, 1984, John Wiley & Sons
      Number of hours per week during the semester/trimester/year
      Lectures Exercises OTC Study and Research Other classes
      6
      Methods of teaching Lectures, consulting, defining the student project and guiding students during their work on the projects and preparation the presentations.
      Knowledge score (maximum points 100)
      Pre obligations Points Final exam Points
      Activites during lectures 0 Test paper 0
      Practical lessons 0 Oral examination 30
      Projects
      Colloquia 0
      Seminars 70