Estudio de la ecuación logística integrando respuestas funcionales de tipo Holling

Abstract

This work presents a qualitative study of the logistic equation when integrated with Holling-type functional responses I, II, and III. The dynamic properties of the resulting systems are analyzed, including the existence and stability of equilibrium points. For each case, the ecological implications of the model are discussed, representing predator-prey interactions and environmental carrying capacity. The analysis is complemented by visualizations using phase diagrams, which provide a graphical interpretation of the qualitative solutions of the studied models. This approach reveals the dynamic richness that can emerge even from mathematically simple models, highlighting the relevance of functional responses in ecological modeling. Furthermore, the qualitative analysis of differential equations is emphasized as an essential tool for understanding nonlinear systems, allowing the identification of global behaviors, regions of growth or extinction, and the comparison of the impact of different predation forms. This type of study offers a solid foundation for applications in theoretical ecology, conservation, and natural resource management.