Open AccessA model of predator-prey differential equation with time delay
Author(s) -
Husna Arifah,
Kus Prihantoso Krisnawan
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1320/1/012001
Subject(s) - fixed point , mathematics , predation , logistic function , stability (learning theory) , bifurcation , functional response , predator , equilibrium point , ordinary differential equation , control theory (sociology) , differential equation , mathematical analysis , statistics , nonlinear system , physics , ecology , computer science , biology , control (management) , quantum mechanics , machine learning , artificial intelligence
This paper purposes are forming a predator-prey model with delay, examining the stability of the fixed points, and observing the presence of bifurction of the fixed point. The predator-prey models formed by using a type II-Holling function and a logistic equation. Holling function is a function that shows the predation level of a predator against its prey. This level of predation depends on how the predator searches, captures, and finally processes the food. The stability of fixed points of the predator-prey model with this delay observed through its model linearity. And the bifurcation is indicated by the sign changing of eigen values over the change of parameter value and from the decrease of the number of fixed points. The results show that at a certain value of parameter the 3 fixed points decreased to only 2 fixed points. At this certain parameter value, the first fixed point is saddle and the second one is degenerate. The system indicating undergoes a transcritical bifurcation.