A Leslie-Gower type predation model with hyperbolic functional response and cooperation between predators
Abstract
In this paper, we propose a Leslie-Gower type predator-prey model with hunting cooperation between
predators. This interaction is described by a nonlinear, autonomous, Kolmogorov-type system of ordinary
differential equations with a hyperbolic functional response. The existence of a positively invariant region,
the delimitation of the trajectories, the existence of a single positive equilibrium point, and the presence
of a heteroclinic curve were established. Considering a topologically equivalent system, the nature of the
equilibrium (0,0) is examined. Moreover, the basin of attraction of (0,0) and the stability of all nonnegative
points are analyzed. Furthermore, the solutions are very sensitive to the initial conditions, since there is a
separatrix curve that divides the trajectories. Finally, numerical simulations are performed to validate the
analytical results.
Keywords
Bifurcación, cooperación, estabilidad, Leslie-Gower, separatriz
Author Biography
Francisco Javier Reyes Bahamon
FRANCISCO JAVIER REYES BAHAMÓN
FECHA DE NACIMIENTO 05 de Febrero de 1990
LUGAR DE NACIMIENTO Neiva – Huila
CÉDULA DE CIUDADANIA 1.075.242.683 de Neiva
ESTADO CIVIL Soltero
OCUPACIÓN Docente de Matemáticas
CALLE 70A No. 25-137 TEL: 3219004454
NEIVA– HUILA
Licenciado en Matemáticas de la Universidad Surcolombiana, Maestría en Matemática Aplicada de la Universidad Nacional de Colombia, Estudiante de doctorado en Matemáticas de la Universidad Nacional de Colombia sede Manizales.
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