Develop stability theory of generalised Lotka-Volterra models

Unlike the classical Lotka-Volterra model, our generalised Lotka-Volterra framework allows for non-linear growth rates and interaction functions, thereby providing a more realistic mathematical model of ecological communities.

Stability is studied via two complementary approaches in this dataset : eigenvalue analysis and Lyapunov functions. While eigenvalue-based criteria offer limited ecological insight, our two Lyapunov functions yield concrete stability conditions. The first globally characterises equilibria under strictly competitive or cooperative interactions, while the second yields only local results to a broader class of communities.