Applied theory of dynamical systems

2021/2022

Academic Year

ENG

Instruction in English

4

ECTS credits

Delivered at:

Department of Fundamental Mathematics (Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod))

Course type:

Compulsory course

When:

4 year, 1, 2 module

Instructor

Turaev, Dmitry

Course Syllabus

Abstract

The course is designed as an introduction to the applied aspects of the modern theory of dynamical systems. A rigorous presentation of the theory of global bifurcations in multidimensional systems and its application to problems of biology will be given. The fundamentals of the dynamics of partial differential equations and the theory of dynamical systems under the action of random perturbations will be presented.

Learning Objectives

• Explore the following topics: Theory of global bifurcations, Dynamics in biology, Nonlinear partial differential equations and infinite dimensional dynamical systems, Stochastic processes and noise in dynamical systems.

Expected Learning Outcomes

• Know the basic provisions of the theory and be able to solve problems on this topic.

Course Contents

• Theory of global bifurcations
• Dynamics in biology
• Nonlinear partial differential equations and infinite dimensional dynamical systems
• Stochastic processes and noise in dynamical systems

Assessment Elements

• Итоговый устный опрос
• Реферат

Interim Assessment

• 2021/2022 2nd module
  0.7 * Итоговый устный опрос + 0.3 * Реферат

Bibliography

Recommended Core Bibliography

• Dynamical Systems on 2- and 3-Manifolds, XXVI, 295 p., Grines, V. Z., Medvedev, T. V., Pochinka, O. V., 2016
• Grines V., Medvedev Timur, Pochinka O. Dynamical Systems on 2- and 3-Manifolds. Switzerland : Springer, 2016.

Authors

• KARATETSKAYA EFROSINIYA YUREVNA
• POCHINKA OLGA VITALEVNA
• CHEBOCHKO NATALYA GEORGIEVNA