Магистратура
2022/2023
Анализ нелинейных динамических систем
Лучший по критерию «Новизна полученных знаний»
Статус:
Курс обязательный (Математика)
Направление:
01.04.01. Математика
Кто читает:
Кафедра фундаментальной математики
Когда читается:
1-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Станкевич Наталия Владимировна
Прогр. обучения:
Математика
Язык:
английский
Кредиты:
6
Контактные часы:
56
Course Syllabus
Abstract
The course will study numerical and analytical methods for the study of various nonlinear phenomena in dynamical systems. The phenomenon of dynamic chaos, including multidimensional, synchronization, multistability and others will be considered. Numerical modeling of the behavior of dynamic systems is planned as part of the course
Learning Objectives
- The purpose of the course is to gain knowledges of the analysis of nonlinear dynamic systems, both analytical and numerical methods.
- Get acquainted with various non-linear dynamical systems and study their complex behavior.
- Study nonlinear phenomena: multistability and synchronization.
Expected Learning Outcomes
- A student knows the history of the discipline and subfields
- A student studies analytical methods for the analysis of nonlinear mappings. Learn the main bifurcations of non-linear mappings. Study application package for numerical bifurcation analysis of nonlinear mappings - XPP AUTO. Prepare programs for the analysis of nonlinear mappings.
- A student studies analytical methods for the analysis of nonlinear flow dynamical systems. Learn types of equilibrium points, main bifurcation. Study application package for numerical bifurcation analysis.
- A student learns multi-frequency and chaotic behavior. Make numerical simulations of models with chaotic and multi-frequency quasiperiodic oscillations.
- A student studies phenomena synchronization. Learn asymptotic methods for analyzing synchronization in ensembles of coupled oscillators.
- A student learns models with hyperbolic chaos. Study models, and character time series and phase portraits.
Course Contents
- Introduction
- Discrete dynamical systems
- Flow dynamical systems
- Numerical methods for analyzing dynamical systems
- Complex behavior in dynamical systems
- Synchronization
- Hyperbolic chaos
Assessment Elements
- Analysis of nonlinear mappings
- Analysis of nonlinear flow dynamical systems
- Base analysis of nonlinear systems
- Numerical simulation of nonlinear mappings
- Numerical simulations of 2D and 3D flow dynamical systems
- Complete synchronization in autonomous ensembles of oscillators
- Numerical simulations of multi-dimensional dynamical systems
- Numerical simulation of models with hyperbolic dynamics
- Assimpotic methods for detecting complete synchrinization
- Test - Nonlinear dynamical systems
Interim Assessment
- 2022/2023 2nd module0.05 * Test - Nonlinear dynamical systems + 0.15 * Base analysis of nonlinear systems + 0.125 * Numerical simulation of nonlinear mappings + 0.05 * Complete synchronization in autonomous ensembles of oscillators + 0.05 * Analysis of nonlinear flow dynamical systems + 0.15 * Numerical simulations of multi-dimensional dynamical systems + 0.125 * Numerical simulations of 2D and 3D flow dynamical systems + 0.1 * Numerical simulation of models with hyperbolic dynamics + 0.05 * Analysis of nonlinear mappings + 0.15 * Assimpotic methods for detecting complete synchrinization
Bibliography
Recommended Core Bibliography
- Differential dynamical systems, Meiss, J. D., 2007
- Discrete dynamical systems, Galor, O., 2010
- Dynamical systems and chaos, Broer, H., 2011
Recommended Additional Bibliography
- • R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Benjamin/Cum-. (2015). Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.20873EF4