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Unit information: Advanced Nonlinear Dynamics and Chaos in 2018/19

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Unit name Advanced Nonlinear Dynamics and Chaos
Unit code EMATM0001
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Professor. Champneys
Open unit status Not open
Pre-requisites

EMAT33100 Nonlinear Dynamics & Chaos

Co-requisites

None

School/department Department of Engineering Mathematics
Faculty Faculty of Engineering

Description

Students will be introduced to more advanced methods in nonlinear dynamics and shown further applications of this work to real systems. They will be taken to the frontiers of the subject, ready to deal with some of its most challenging problems. Material covered in this course will be selected from Centre manifolds, normal forms, codimension-one and two bifurcating, circle maps, KAM theorem, Smale horseshoes, symbolic dynamics, homoclinic bifurcations, 'Shilnikov-type' bifurcations, control of chaos, many routes to chaos, symplectic numerical methods, principles of numerical path-following methods including the importance of unstable solutions, computation of global bifurcations, C-bifurcations in piecewise continuous systems, Lyapunov exponents and chaotic attractors.

Aims:

The aim of the unit is to introduce students to advanced methods in nonlinear dynamics, covering maps, ordinary and partial differential equations. Students will also be shown applications of the theory to real-world systems. They will be taken to the frontiers of the subject, ready to deal with some of its most challenging problems.

The particular topics covered in the unit will be driven by current research. Potential topics include global bifurcation theory and computation, resonance and invariant tori, centre manifolds, KAM theory, Smale horseshoes, 'Shilnikov-type' bifurcations, principles of numerical path-following methods, bifurcations in piecewise smooth systems, systems with delay, Lyapunov exponents and chaotic attractors, Green's functions, inverse scattering, pattern formation, nonlinear waves, localisation, solitons and breathers.

Intended learning outcomes

  1. To have familiarity with a variety of research topics in applied nonlinear dynamics, covering both ordinary and differential equations, and maps
  2. To be equipped with a set of analytical and numerical tools for analysing bifurcations, chaos and other nonlinear effects in systems arising from applications

Teaching details

Lectures

Assessment Details

Exam 75%. 2 labs of 12.5% each

Reading and References

  • Elements of Applied Bifurcation Theory (2nd Ed)
  • Yu. A. Kuznetsov, Springer, 1998

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