Abstract:
The logistic model can be applied in the field of biological studies to
investigate population growth problems and some important aspects
of the ecological situation. This model is a growth model with a
limited population growth rate, and ecologists describe this rate as
carrying capacity. Carrying capacity can be interpreted as the ideal
population size, where individuals in the population can live properly
in their environment. The growth rate of a population can be
influenced by the harvesting factor, in this case, it is assumed that
harvesting is not constant. The effect of the harvest on the growth
rate can be analyzed mathematically by using the Holling type III
functional response. In this paper, describe the formation of a logistic
model taking into account the effects of harvesting, using the Holling
type III functional response. Then, perform a nondimensional process
in the model, namely simplifying a model that has four parameters to
a model that only has two parameters. Next, determine the
equilibrium point of the model, perform a stability analysis at that
equilibrium point, and investigate the possibility of bifurcation. As
result, first obtained a logistic model which has two non-dimensional
parameters, where one of the equilibrium points is zero and is
unstable. Next, determine another equilibrium point through an
implicit equation and investigate its stability through simulation.
Finally, obtained two equilibrium points, which are fold bifurcation.
Keywords:
Logistic Model, Harvesting, Holling Type III, Equilibrium, Stability Analysis, Fol Bifurcation.
