PřF:M6201 Non-linear dynamics - Course Information

M6201 Non-linear dynamics

Extent and Intensity

2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. Lenka Přibylová, Ph.D. (lecturer)

Guaranteed by

doc. RNDr. Lenka Přibylová, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science

Timetable

Wed 8:00–9:50 M5,01013

• Timetable of Seminar Groups:

M6201/01: Fri 13:00–14:50 MP1,01014

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Applied Mathematics for Multi-Branches Study (programme PřF, B-MA)
• Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
• Economics (programme ESF, N-MA)
• Financial and Insurance Mathematics (programme PřF, B-AM)
• Financial and Insurance Mathematics (programme PřF, B-MA)
• Finance Mathematics (programme PřF, N-AM)
• Finance Mathematics (programme PřF, N-MA)
• Mathematical Biology (programme PřF, B-BI)
• Mathematical Biology (programme PřF, B-EXB)
• Mathematical Biology (programme PřF, N-BI)
• Mathematical Biology (programme PřF, N-EXB)
• Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
• Mathematics - Economics (programme PřF, B-AM)
• Mathematics - Economics (programme PřF, N-AM)
• Modelling and Calculations (programme PřF, B-AM)
• Modelling and Calculations (programme PřF, B-MA)
• Profesional Statistics and Data Analysis (programme PřF, B-AM)
• Statistics and Data Analysis (programme PřF, B-AM)
• Statistics and Data Analysis (programme PřF, B-MA)
• Statistics and Data Analysis (programme PřF, N-AM)
• Statistics and Data Analysis (programme PřF, N-MA)

Course objectives

At the end of the course students should get familiar with: elements of bifurcation theory of continuous and discrete dynamical systems; basic nonlinear phenomena in continuous and discrete dynamics; some chosen models of real processes that will illustrate the nonlinear phenomena

Syllabus

• Dynamical systems (continuous and discrete)
• Linear and nelinear systems
• Systems dependent on parameters, bifurcations
• One-parameter bifurcations in continuous case (bifurcation saddle-node, hysteresis, pitchfork, transcritical, Hopf bifurcation)
• Multi-parameter bifurcation
• Reduction to a central manifold
• One-parameter bifurcations in discrete case (bifurcation fold, flip, period doubling and universality, deterministic chaos, Neimark-Sacker bifurcation)
• Poincaré mapping and cycle bifurcation
• Chaos in continuous systems

Literature

• e-lerningový text přednášky na ISu
• KUZNECOV, Jurij Aleksandrovič. Elements of applied bifurcation theory. 2nd ed. New York: Springer-Verlag, 1998, xviii, 591. ISBN 0387983821. info

Teaching methods

lectures followed by computer lab.

Assessment methods

Written exam followed by an oral one.

Language of instruction

Czech

Further Comments

Study Materials
The course is taught once in two years.

• Enrolment Statistics (Spring 2012, recent)
  
• Permalink: https://is.muni.cz/course/sci/spring2012/M6201