Lotka-Volterra systems - Helen Christodoulidi 19/11/25
Lotka-volterra systems are systems used to show the population of 2 species, one predator, one prey. The populations of the 2 species change over time based on each other’s populations. For example if the prey species loses loads of its population then logically the predator species would also lose population as the predator would have less food.
The Lotka-volterra system consists of 2 differential equations, one controlling the rate of change for the predators, and one controlling the rate of change for the prey. The equations for the models are (x prey, y predator) the equation for the rate of change for prey is dx/dt = ax - �xy, dy/dt = -?y + dxy where, x is prey population, y is predator population, t is time, a,� and ? are constants that are greater than 0. Notably the prey increases based on prey and decreases based on predators, while predators decrease based on predators and increases based on prey.
The Hartman grobman theorem “asserts that near a hyperbolic equilibrium point, the behavior of a nonlinear dynamical system can be approximated by its linearized form” [1]. Essentially near an equilibrium point the system will be close to linear. Meaning that the populations of the predator and prey will stay relatively stable. If you draw a phase portrait for the model you will get cyclic patterns around the equilibrium point meaning that starting points for the model near to the equilibrium point will give stable patterns for predator and prey where the populations increase and decrease periodically. Points further away from this may converge to 0 instead leading to both species going extinct.
[1] Richard Murdoch Montgomery (2025). Understanding the Hartman-Grobman Theorem: A Gateway to Predicting Dynamical System Behavior Near Hyperbolic Equilibria. International Journal of Pure and Applied Mathematics Research, 5(1), 20-34. doi: 10.51483/IJPAMR.5.1.2025.20-34.
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The presentation is well put together but to improve it you could fix some of the grammatical mistakes and it has slightly informal phrasing. (2/3)
You have understood the context of the talk well but to improve you could expand on the Lotka-Volterra system and begin to talk about the model. (2/3)
You have stated about the talk about the models but not as to why the actual models matter for society, and you also could have made a connection with the Hartman-Grobman better instead of it being mentioned generically. (1/3)
You have stated an external quote from an external source but to improve you could perhaps maybe critically assess the disscusion instead of restating it. (3/3)
You have used language that is both able to be understood by both scientific and non-scientific audiences, however some terms still maybe misunderstood by non-scientific audiences such as phase portrait. (2/3)
Overall a good start to a blog but could do with a few adjustments (10/15)
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Good use of quotes and external referencing. Lay person would likely struggle with the mathematical equations though. I think something like the Rabbit-Fox example may also help with comprehension. Very concise however, and easy to read!
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It is clear you have understood the seminar well and that is shown throughout your writing. While we understand the equations and terms you have used, a lay person will not, but other than that it looks good