Applied mathematics and modelling · Maths EE idea · Ambitious

Predator–prey cycles

A research question to start from

Why do solutions of the Lotka–Volterra equations cycle, and what changes when prey growth is limited?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

A conserved quantity explains the cycles; a modification changes the behaviour, giving a clear comparison.

Mathematics you would need

Systems of ODEs
Phase-plane analysis
Conserved quantities
Linearisation near equilibria

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Find equilibria and linearise.
Derive the conserved quantity and show orbits are closed.
Add logistic prey growth and analyse the new behaviour.

Scope and difficulty

Ambitious. Ambitious.

Pitfalls

Only numerical plots.
Ecology rather than mathematics.

Where to start reading

Search a library catalogue or a university's open lecture notes for: Lotka-Volterra conserved quantity closed orbits; logistic prey stability. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.