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Curricular information is subject to change
On completion of this module students should be able to:
- identify fixed points of nonlinear systems.
- use linear stability analysis to classify fixed points.
- plot trajectories and phase portraits.
- discuss the various forms of stability and the relevance of conservative systems and reversible systems.
- identify bifurcation points.
- classify and describe different types of bifurcations.
- identify limit points and limit cycles and apply the Poincare Bendixson theorem, Liapunov functions and Liénard's theorem.
- discuss chaotic systems and give some examples.
- Flows on the line
- Fixed points and stability
- Linear stability analysis
- Bifurcations: saddle-node, pitchfork, transcritical
- Classification of linear systems
- Phase portraits
- Conservative and reversible systems
- Limit cycles
- Poincaré-Bendixson theorem
- Hopf bifurcations
- Chaos: Lorenz equations, fractals, strange attractors
|Student Effort Type||Hours|
|Specified Learning Activities||
|Autonomous Student Learning||
Dynamical systems will be studied with the aid of python code.
Students are required to be write their own python code to solve equations, calculate data and generate plots.
All students are required to have their own laptop.
|Description||Timing||Component Scale||% of Final Grade|
|Examination: Final exam||2 hour End of Trimester Exam||Yes||Standard conversion grade scale 40%||No||
|Multiple Choice Questionnaire: Weekly quizzes||Throughout the Trimester||n/a||Standard conversion grade scale 40%||No||
|Assignment: 2 problem-solving assignments||Throughout the Trimester||n/a||Standard conversion grade scale 40%||No||
|Class Test: Class test||Week 7||n/a||Standard conversion grade scale 40%||No||
|Resit In||Terminal Exam|
|Spring||Yes - 2 Hour|
• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Online automated feedback
In-class activities and weekly quizzes provide students with regular feedback. Individual feedback will be given on assignments and class tests. The assessment structure is designed such that students will receive feedback on their previous assessment prior to submitting the next.
|Dr Áine Byrne||Lecturer / Co-Lecturer|
|Lecture||Offering 1||Week(s) - Autumn: All Weeks||Thurs 14:00 - 14:50|
|Lecture||Offering 1||Week(s) - Autumn: All Weeks||Tues 13:00 - 13:50|
|Lecture||Offering 1||Week(s) - Autumn: All Weeks||Wed 15:00 - 15:50|