Nonlinear Dynamics and Chaos
| Code | School | Level | Credits | Semesters |
| PHYS4008 | Physics and Astronomy | 4 | 10 | Autumn UK |
- Code
- PHYS4008
- School
- Physics and Astronomy
- Level
- 4
- Credits
- 10
- Semesters
- Autumn UK
Summary
In this module, you will learn about a range of topics in nonlinear dynamics and chaos in particular: dynamical systems of various dimensions (one, two and three dimensions), stability and bifurcations of nonlinear dynamical systems, generic features of chaotic systems, characterisation of chaotic systems, nonlinear mappings and fractals. Chaos theory is of crucial importance in all branches of natural science, in social science and economics, and even in healthcare and art. We will see that extremely simple dynamical systems, that obey simple deterministic laws of motion, often exhibit highly complex and erratic behaviour that depends critically on how the system is set in motion. We will investigate chaotic motion in a range of systems. The behaviour of these systems will lead us naturally into an exploration of fractal patterns and self-similarity in dynamical systems and nonlinear maps.
Target Students
Students in the 3rd year of Physics programmes. Students in the 3rd or 4th year of Mathematical Physics, Chemistry and Molecular Physics,orNatural Sciences programmes.
Classes
This module is based on a series of lectures in the autumn semester.
Assessment
- 100% Exam 1 (2-hour): In-person Exam (January)
Assessed by end of autumn semester
Educational Aims
This module aims to extend students’ knowledge of classical mechanics in regimes where simple linear behaviour is replaced by more complex nonlinear dynamics. Students will encounter the way in which nonlinear deterministic systems can exhibit essentially random behaviour because of exponential sensitivity to initial conditions.Learning Outcomes
Knowledge and Understanding
On successful completion of the module, students will have enhanced their:
• A1 knowledge of nonlinear dynamical systems and chaos
• A2 knowledge and understanding of the scientific method.
• A3 understanding of how the basic principles of classical mechanics are applied in a range of situations.
• A4 knowledge of phase space methods for the analysis of physical problems
Intellectual Skills
On successful completion of the module, students will have demonstrated their ability to:
• B1 apply techniques of analytical mechanics to the quantitative analysis of physical situations.
• B2 apply high levels of numeracy and analysis.
• B3 apply techniques of problem solving.
Professional/Practical Skills
On successful completion of the module, students will have demonstrated their ability to:
• C1 formulate problems in nonlinear dynamics using appropriate mathematical language.
Transferable/Key Skills
On successful completion of the module, students will have demonstrated their ability to:
• D1 develop appropriate strategies for study, including the use of library, human, and electronic sources of information.