PERFORMANCE OF THE LOTKA-VOLTERRA AND HOLLING MODEL APPLIED TO PREY-PREDATOR SYSTEMS

Borda A.E.G. · Revista de la Facultad de Ciencias (2022) · DOI: 10.15446/rev.fac.cienc.v11n1.90452

Resumen

In this work, the critical condition of the Lotka-Volterra model was demonstrated, starting from the formal assumption of prey-predator growth in a 1: 1 ratio, using the Runge-Kutta method and assuming hypothetical values of the positive fixed constants A (growth rate prey), B (rate at which predators destroy prey), C (death rate of predators), and D (rate at which predators increase by consuming prey, respectively); interacting with each other in the ecosystem, in such a way that the dependence of the variables x (prey) and y (predator) as a function of time was estimated through the dx/dt and dy/dt differentials. A Holling type II functional response predator-prey model was considered, observing that the predator had saturation and a period of time was necessary for the capture, according to the differential curves of trajectories and direction fields; the conclusive result is the prey variable that is superimposed on the predator variable, adjusting the values to a collinearity as a function of time. This study aimed to implement the Lotka-Volterra and Holling Model to be applied to prey-predator systems.

Instituciones: Universidad Nacional San Luis Gonzaga