1. SylabUZ
2. Faculty of Physics and Astronomy
3. winter term 2018/2019
4. Physics and Astronom - PhD studies
5. Lecture III-A

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Lecture III-A - course description

Aim of the course

Presentation of the methods used in the modern inter-disciplinary fields of science dealing with chaitic processes in complex physical and biologicl systems. The applications of these methods include the turbulence in liquids and cosmic plasma, irregularities in biological systems, dynamics of the population growth, chemical reactions, motion of stellar clusters, dynamics of transportation and many others. The lecture will also include the phenomena of bifurcation, fractals and systems with self-organizing criticality.

Prerequisites

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Knowledge of physics and mathematics at the Master of Science level.

Scope

• Flows and differential equations.

• Constant points, sadle points and bifurcation. .

• Non-linear and dampened oscillators.

• Bifurcations and catastrophes..

• Phase portraits and Poincare maps.

• Lorenz equations and mapping.

• Strange atractors.

• Lyapunov exponents and the origins of chaos.

• Discrete and iterative maps.

• Fractals and correlative exchanges.

• Stochastic systems.

• Self-organizing criticality systems.

Teaching methods

Lecture, discussion.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

Positive grade from the final exam.

Recommended reading

[1] E. Ott, Chaos w układach dynamicznych, WNT Warszawa 1997.

[2] S. H. Strogatz, Nonlinear Dynamics and Chaos, Perseus Books, 1994

[3] Armin Fuchs, Nonlinear Dynamics in Complex Systems, Springer, 2013.

Further reading

[1] G. L. Baker i J. P. Gollub, Wstęp do dynamiki układów chaotycznych, PWN, 1993.

[2] M. J. Aschwanden (editor) Self-organized Criticality Systems, Open Academic Press, 2013.

Notes

Modified by dr Joanna Kalaga (last modification: 10-07-2018 12:30)