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Unit information: Nonlinear Dynamics and Chaos in 2018/19

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Unit name Nonlinear Dynamics and Chaos
Unit code EMAT33100
Credit points 10
Level of study H/6
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Gross
Open unit status Not open
Pre-requisites

EMAT20200 Engineering Mathematics 2

Co-requisites

None

School/department Department of Engineering Mathematics
Faculty Faculty of Engineering

Description

Description: Based on a format of lively lectures combined with experiments and computer demonstrations, this unit introduces students of all disciplines to chaos theory and the profound effect that this field has had on a wide range of application areas. The course focuses on geometric techniques for analysing a system, thereby avoiding cumbersome algebraic manipulations. Of particular interest are qualitative changes of the dynamics as parameters are changed, which allows you to describe ways that a system can become chaotic.

Aims: This unit is intended to alert students to the complicated behaviour that can occur in simple systems and to equip them with the straightforward mathematical tools to analyse simple nonlinear systems. Additionally, the students will be introduced to a range of numerical methods that will allow them to investigate more complicated systems arising from real-world problems.

Intended learning outcomes

Be able to analyze the stability of stationary solutions of ordinary differential equation systems and discrete time maps, locate critical parameter values at which the stability changes and interpret the implications of these transitions for the dynamics of the system.

Demonstrate an understanding of advanced concepts of nonlinear dynamics such as for instance higher codimension bifurcations.

Be able to apply methods of nonlinear dynamics to analyze and understand the dynamics of real world systems.

Teaching details

Lectures

Assessment Details

Two-hour written examination: 100% (all learning outcomes)

Reading and References

  • Steven H. Strogatz, Nonlinear Dynamics and Chaos, with Applications in Physics, Biology, Chemistry, and Engineering, Addison-Wesley, 1994
  • J.M.T. Thompson & H.B. Stewart, Nonlinear Dynamics and Chaos, Wiley, 2002
  • John Guckenheimer & Philip J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York, 1986
  • Yuri A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer-Verlag, New York, 1995, 1998
  • Robert L. Devaney, An Introduction to Chaotic Dynamical Systems, Perseus Publishing Co., 1989
  • H.-O. Peitgen, H. Jürgens & D. Saupe, Chaos and Fractals, New Frontiers of Science, Springer-Verlag, New York, 1992

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