Original title: Impact of a block structure on the Lotka-Volterra model
Authors: Maxime Clenet, François Massol, Jamal Najim
In this article, the author explores the Lotka-Volterra (LV) model, which is widely used to describe complex systems such as food webs or microbiomes. The model consists of a set of equations that link the abundances of different species within the system.
To understand how interactions between species affect equilibrium, the author focuses on the case of two communities. They use a large random interaction matrix with independent entries and a block variance profile. The diagonal blocks in the matrix represent interactions within each community, while the off-diagonal blocks represent interactions between communities.
By analyzing this model, the author investigates the existence of equilibrium and the possibility of some species disappearing (attrition) within each community. They also mention that information about systems with more than two communities is provided in the appendix.
Overall, this article provides insights into the dynamics of complex systems and how species interactions play a crucial role in determining their equilibrium.
Original article: https://arxiv.org/abs/2311.09470