Mathematical Modeling and Stability of Predator-Prey Systems
Altair Santos de Oliveira Sobrinho, Camila Foga\c{c}a de Oliveira,, Carolina Massae Kita, \'Erica Regina Takano Natti, Neyva Maria Lopes Romeiro,, Eliandro Rodrigues Cirilo, Paulo Laerte Natti
TL;DR
This paper analyzes the stability and long-term behavior of predator-prey models, specifically Lotka-Volterra systems, using Lyapunov methods to assess equilibrium stability under perturbations.
Contribution
It introduces a Lyapunov-based approach to study the stability of Lotka-Volterra predator-prey models, providing new insights into their asymptotic behavior.
Findings
Established conditions for stability of predator-prey equilibria
Demonstrated asymptotic stability under certain perturbations
Provided a framework for analyzing similar ecological models
Abstract
This work investigated the stability and asymptotic behavior of some Lotka Volterra type models. We used the Liapunov method which consists in analyzing the stability of systems of ordinary differential equations (ODEs) around the equilibrium when they submitted to perturbations in the initial conditions
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