The Lotka-Volterra predator-prey model is one of the four models we teach all of our students (along with exponential growth, logistic growth, and competitive LV). It was proposed a century ago by Alfred J. Lotka (in this paper, published in 1920) and re-discovered by Vito Volterra in 1926.

In a new preprint$^1$, Carlos, Zach and I show that when we account for any intraspecific variability in the mortality rate of the predator or the vulnerability of the prey, we obtain globally stable dynamics—contrary to what found in the original model. Our equations can be extended in a number of ways, providing an alternative (or complementary) mechanism for the stabilization of food webs.

Stefano Allesina, Zachary R Miller & Carlos Andres Marcelo Serván
Intraspecific variation stabilizes classic predator-prey dynamics
bioRXiv, 2021

In a talk I gave back in March for the Ecology Live! series of the British Ecological Society, I spent a few minutes presenting these results:

$^1$ Developing the project took a very long time, mostly because finding Lyapunov functions requires—as Steve Strogatz put it—a good deal of “divine inspiration”. I have learned more on Lyapunov functions in the past year than in the rest of my life. My tentative conclusion is that Lyapunov functions are either the best thing since sliced bread or an elaborate method of torture, depending on whether you can dream up the right form (“croce e delizia!”).