Dynamical Analysis of Holling Tanner Prey Predators Model with Add Food in Second Level Predators

This article discusses the Holling Tanner prey predator model and Holling type II response function with additional food in the second level predator. The dynamic analysis of the system begins with determining the equilibrium point, analyzing the stability of the equilibrium point, and numerical simulation with python. The results of the dynamic analysis obtain seven equilibrium points, namely E1 extinction in three populations, point E2 extinction in the population of prey and first level predator, point E3 extinction in the first and second level predator populations, point E4 extinction in the second level predator population, point E5 extinction in the first level predator population, and point E6 the three populations are not extinction. The results of the stability analysis around the equilibrium point E1, E2, E3 are shown to be saddle unstable, then E4, E5, E6 are asymptotically stable with certain conditions. Numerical simulation is applied to determine the validity of the analytical results. The simulation results illustrate changes in the system solution in the form of phase portraits. The bifurcation diagram of the numerical continuation of the maximum predation rate parameter of the second-level predator (β) shows the existence of Hopf bifurcation when maximum predation rate parameter of the second-level predator with β = 2.1014232 and Transcritical bifurcation when maximum predation rate parameter of the second-level predator with β = 3.197.