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Unit information: Advanced Nonlinear Dynamics and Chaos in 2021/22

Unit name Advanced Nonlinear Dynamics and Chaos
Unit code EMATM0001
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Professor. Champneys
Open unit status Not open

EMAT33100 Nonlinear Dynamics & Chaos



School/department Department of Engineering Mathematics
Faculty Faculty of Engineering

Description including Unit Aims

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 abstract definition of dynamical system, structural stability and topological definition of bifurcation, centre manifolds, normal forms, analysis of codimension-one and two bifurcations, periodic orbits and Poincare maps, quasi-periodic motion, resonance and parametric resonance, circle maps, KAM theory & Arnold tongues, synchronisation of oscillators, Smale horseshoes, symbolic dynamics, homoclinic bifurcations, 'Shilnikov-type' bifurcations, principles of numerical path-following method and bifurcation analysis, non-smooth bifurcations in piecewise continuous systems, fractals, Lyapunov exponents and chaotic attractors.


  1. 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.
  2. 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, ractals, Lyapunov exponents and chaotic attractors, quasi-periodic motion, sychronisation of coupled oscillators.

Intended Learning Outcomes

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

Teaching Information

Teaching will be delivered through a combination of synchronous and asynchronous sessions, including lectures, supported by live online sessions, problem sheets and self-directed exercises.

Assessment Information

1 Summative Assessment, 100% - Summer Exam. This will assess all ILOs.


If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

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How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.