PřF:F6180 Introd. to nonlinear dynamics - Course Information

F6180 Introduction to nonlinear dynamics

Extent and Intensity

2/1/0. 2 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).

Teacher(s)

doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)

Guaranteed by

doc. Mgr. Jiří Chaloupka, Ph.D.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science

Timetable

Mon 10:00–11:50 Fcom,01034

• Timetable of Seminar Groups:

F6180/01: Mon 12:00–12:50 Fcom,01034

Prerequisites

F5030 Intro. to Quantum Mechananics
Basic knowledge from introductory courses of mathematics, physics, theoretical mechanics and ordinary differential equations.

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

• Biophysics (programme PřF, M-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives

This lecture is an introductory course of nonlinear dynamics dealing with solution of some simple classical systems with added nonlinear terms and deterministic chaos.

Learning outcomes

After passing this course the students should be able to:
- list and explain basic methods of solving classical systems, e.g. examining their phase portraits;
- apply these methods in case of systems with nonlinear terms;
- interpret the behavior of a dynamic system based on its phase trajectories;
- define and also classify a given problem leading to deterministic chaos.

Syllabus

• 1)Dynamical systems with discrete and continuous time evolution. Autonomous equations. State space, flow in phase space, fixed points, phase portraits,classification of linear systems, application to nonlinear systems.
• 2)Some one-dimensional nonlinear systems (Duffing oscillator, mathematical pendulum,forced oscillator).
• 3)Hamiltonian systems: integrability, invariants, periodic solutions, invariant tori and deterministic chaos, KAM theorem. Toda lattice,Hénon-Heiles potential, convex billiards.
• 4)One-dimensional maps: logistic equation, bifurcations, period-doubling , Feigenbaum theory.
• 5)Dissipative systems: time evolution in phase space, divergence theorem, Lyapunov exponents, strange attractors (Hénon, Lorenz, Rösler),fractal dimension.

Literature

• HORÁK, Jiří and Ladislav KRLÍN. Deterministický chaos a matematické modely turbulence. 1. vyd. Praha: Academia, 1996, 444 s. ISBN 8020004165. info
• KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995, 207 s. ISBN 8021011300. info
• HILBORN, Robert C. Chaos and nonlinear dynamics : an introduction for scientists and engineers. New York: Oxford University Press, 1994, 654 s. ISBN 0195088166. info
• LICHTENBERG, Allan J. and M. A. LIEBERMAN. Reguljarnaja i stochastičeskaja dinamika. New York: Springer-Verlag, 1983, 499 s. ISBN 0387907076. info

Teaching methods

Lecture + individual work on PC

Assessment methods

Demands for colloquium: oral testing of the knowledge gained, based on the individual work during the semester presentation.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Information on course enrolment limitations: F5030

Teacher's information

http://monoceros.physics.muni.cz/~jancely

• Enrolment Statistics (autumn 2021, recent)
  
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