In a previous paper [L. M. Ladino, E. I. Sabogal, Jose C. Valverde,
General functional response and recruitment in a predator-prey system
with capture on both species, Math. Methods Appl. Sci. 38(2015)
2876-2887], a mathematical model for a predator-prey model with
general functional response and recruitment including capture on both
species was formulated and analyzed. However, the global asymptotic
stability (GAS) of this model was only partially resolved. In the
present paper, we provide a rigorously mathematical analysis for the
complete GAS of the predator-prey model. By using the Lyapunov stability
theory in combination with some nonstandard techniques of mathematical
analysis for dynamical systems, the GAS of equilibria of the model is
determined fully. The obtained results not only provide an important
improvement for the population dynamics of the predator-prey model but
also can be extended to study its modified versions in the context of
fractional-order derivatives. The theoretical results are supported and
illustrated by a set of numerical examples.
A new study for the global asymptotic stability of a general predator-prey model