Unit name | Advanced Nonlinear Dynamics and Chaos |
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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 |
Pre-requisites |
EMAT33100 Nonlinear Dynamics & Chaos |
Co-requisites |
None |
School/department | School of Engineering Mathematics and Technology |
Faculty | Faculty of Engineering |
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.
Aims:
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.
1 Summative Assessment, 100% - Summer Timed Assessment. This will assess all ILOs.