Course Details in 2024/25 Session

Module Title	LC Chaos in Discrete and Continuous Systems
School	Physics and Astronomy
Department	Physics & Astronomy
Module Code	03 33948
Module Lead	Martin Long
Level	Certificate Level
Credits	10
Semester	Semester 2
Pre-requisites
Co-requisites
Restrictions	None
Exclusions
Description	This module provides a mathematical introduction to the phenomena of chaos in non-linear systems. The first half of the module looks at the effects of non-linearity in mechanical systems described by differential equations, and discrete systems described by iterated maps. The logistic map is examined in detail, and the period-doubling route to chaos described. The concept of fractals, and their occurrence in chaotic systems is developed. The second half of the module covers some of these concepts in more detail. The origin of period-doubling and universality in the logistic map is identified. The phase space description of dynamical systems is refined by classifying their fixed points using matrix techniques. Finally, the phenomena of limit cycles, strange attractors and bifurcations are discussed.
Learning Outcomes	By the end of the module students should be able to: Recognise non-linearity in a difference or differential equation. Sketch the phase portrait of a second order non-linear differential equation. Identify the fixed points of an iterated map, and perform a linear stability analysis. Define and construct fractals, and determine their Hausdorff dimension. Identify and classify the fixed points of one- and two-dimensional dynamical systems. Understand universality and Feigenbaum constants in the period-doubling route to chaos. Define and understand strange attractors and their fractal properties. Perform a matrix linear stability analysis for fixed points of a dynamical system. Define and understand bifurcations in the behaviour of dynamical systems.
Assessment	33948-01 : Exam : Exam (Centrally Timetabled) - Written Unseen (70%) 33948-02 : Assessed problems : Coursework (20%) 33948-03 : Chaos Lab : Coursework (10%)
Assessment Methods & Exceptions	Class Test (30%); 1.5 hours Examination (70%)
Other
Reading List