Analysis of Local Stability for Discrete Lotka-Volterra Models
DOI:
https://doi.org/10.5433/1679-0375.2025.v46.53574Keywords:
Lotka-Volterra, mathematical modeling, population dynamics, stability of discrete systemsAbstract
This paper applies the stability theory of discrete systems to a predator–prey model with a specific structure, formulated directly in discrete time. This approach offers didactic and computational advantages for modeling ecological systems with non-overlapping generations, contrasting with methods that discretize continuous models. This direct formulation captures the inherently discrete nature of ecological monitoring and non-overlapping generations, while presenting particular analytical challenges. Through linearization and spectral analysis, we obtain explicit stability conditions for the system's three equilibria: total extinction, which is always unstable; predator exclusion; and coexistence, whose local behaviors depend on conditions among biotic parameters. The results provide practical criteria for predicting population persistence, offering a foundation for applied studies in control and conservation.
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