Why choose this project topic?
A focused study of lyapunov examples gives you a specific question in dynamical systems. It compares linearisation with a constructed Lyapunov argument on a bounded family of equilibria. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.
When can a stated Lyapunov function establish local stability for selected planar equilibria that linearisation does not fully classify?
Agree the apparatus or dataset, comparison range and feasible measurement schedule for lyapunov examples with your supervisor.
Proposed project objectives
- 01Define the materials, variables and comparison conditions for lyapunov examples.
- 02Define each system and equilibrium, examine the Jacobian and construct candidate functions with explicit neighbourhoods.
- 03Evaluate the measurements or model outputs in relation to this question: When can a stated Lyapunov function establish local stability for selected planar equilibria that linearisation does not fully classify?
A suggested research approach
Define each system and equilibrium, examine the Jacobian and construct candidate functions with explicit neighbourhoods. Verify sign conditions and state whether the conclusion is stability, asymptotic stability or a weaker result. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.
What you will need
- A bounded family of planar differential systems
- Lyapunov and linearisation theorem statements
- Symbolic derivative and neighbourhood-sign checks
Keep your project scope clear
A failed candidate function does not prove instability, and a local certificate does not establish global attraction.
Mathematics project chapter outline
Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.
- Chapter 1Introduction
- Chapter 2Literature Review
- Chapter 3Theory and Methodology
- Chapter 4Results and Applications
- Chapter 5Summary, Conclusion and Recommendations
Turn this topic into your own final year project.
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