Lotka-Volterra System by Helen Christodoulidi 19/11/2025
Ever wondered why predator and prey populations seem to rise, fall, and manage to stay perfectly balanced? On the 19th of November 2025, Helen Christodoulidi held a seminar about the mathematics behind predator-prey models, specifically Lotka-Volterra systems.
Lotka-Volterra systems are at the core of modelling predator-prey populations and are widely used in industry including ecology, biology, and finance. The name Lotka-Volterra comes from the mathematicians Alfred J. Lotka and Vito Volterra who independently contributed to the dynamics of population. The model consists of two differential equations (DE’s), one that models the prey and the other, predators. These DE’s depend on one another, so fluctuations in the predator population effect the prey population, and vice versa.
The Hartman-Grobman Theorem [1] is a fundamental result of a dynamical system and allows us to solve a Lotka-Volterra model to visualise its periodic solutions. Helen Christodoulidi worked through an example by hand and derived solutions that show hyperbolic lines on a phase diagram. Another way to view these solutions are periodically which show adjacent, asymmetric waves that rise and fall proportionally to one another [2]. Other solutions show similar waves but at different heights, suggesting one population is more sensitive than the other.
An application of the Lotka-Volterra system is in real world epidemics, specifically COVID 19. The system is tweaked slightly to model the susceptible and infected. New periodic solutions were derived showing different wave forms which peaked then decayed overtime. Helen Christodoulidi’s presentation included real data and graphs from GOV.UK that showed the exact same peak and decay in the infected population.
The seminar rounded off by showing solutions to a 4D Lotka-Volterra system and showed 3D projections of the solutions that demonstrate bounded (co-existence) and unbounded (not all survive) chaos [3]. In the end, Lotka-Volterra systems define the sensitivity between balance and extinction of two species.
[1] Perko, L. (2000). Differential equations and dynamical systems. New York: Springer.
[2] GeeksforGeeks (2025) Lotka-Volterra Model of Predator-Prey Relationship. Available at: https://www.geeksforgeeks.org/biology/lotka-volterra-model-of-predator-prey-relationship/
[3] Christodoulidi, H., Hone, A.N., & Kouloukas, T.E. (2019). A new class of integrable LotkaVolterra systems. Journal of Computational Dynamics.
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following the mark scheme criteria
overall presentation 3/3 date, name of speaker and title are correct
Accurate reporting 3/3 i think you captured the information well
Accurate contextualisation 3/3 i think you talked about real world applications well
Additional external sources 2/3 good use of sources would recommend an additional reference
writing style 2/3 good style but for me some words might need explaining for a layperson but i could be wrong
overall well done!
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Good grammar and gave title and date. Successfully explained Lotka-Volterra systems and their uses concisely but it still made perfect sense. Would be suitable for a lay audience in my opinion since they didn’t focus too much on where the maths came from, but more so why it’s there and what it tells us, which helps it be easy to follow and understand.
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Speaker’s name, title and date all included. Spelling and grammar are both good, except for ‘the wave forms’; this should be one word: waveforms. The way that your report is structured flows smoothly and logically. The blog report summarises the seminar well and highlights how mathematical modelling can be applied to real-world scenarios. It is clear from this that you have understood the seminar’s central message. In terms of context, I like that you focused on COVID-19, something that has impacted us all. Could you have expanded on this by discussing the implications of the mathematical modelling for public health? This would provide more evidence of the importance of such modelling. Your references are strong and relevant, but you haven’t included a direct quote; this is a prerequisite in the marking criteria. I think the writing style is mostly appropriate for a lay audience, but some parts could be explained more thoroughly, for example, ‘hyperbolic lines on a phase diagram’. As a 3rd year physics student, I understand what this means and can picture it in my mind, could you say the same for the layperson? All in all, it is a good, solid blog report that I enjoyed reading, and hopefully, I have given you a couple of valid points to think about and perhaps further improve it.