2026-10-06T10:25:07Z https://api.figshare.com/v2/oai

oai:figshare.com:article/31292701 2026-09-30T10:39:34Z category_28846 category_25789 portal_753 item_type_1 month_year_09_2026

Develop stability theory of generalised Lotka-Volterra models Richard Pretorius (23156464) Modelling and simulation Computational modelling and simulation in earth sciences Lyapunov functions Ecological modelling Lotka-Volterra models Ecological communities Functional responses SDG 12 Responsible consumption and production SDG 13 Climate action SDG 15 Life on land <p dir="ltr">These are the figures from the dissertation, "Nonlinear paths to persistence : the stability of generalised Lotka-Volterra models".</p><p dir="ltr">The dataset examines the long-term dynamics of ecological communities modeled using a generalized Lotka-Volterra model. 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. Worked examples illustrate these results and their ecological interpretations. </p> 2026-09-30T10:39:34Z Image Figure 10.25403/UPresearchdata.31292701.v1 https://figshare.com/articles/figure/Develop_stability_theory_of_generalised_Lotka-Volterra_models/31292701 CC BY 4.0