Creator:
Chen, Qiaoling ; Teng, Zhidong ; Hu, Zengyun
Contributor:
Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Title:
Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response
Group publication title:
Subject and Keywords:
discrete prey?predator model ; flip bifurcation ; Hopf bifurcation ; saddle-node bifurcation ; OGY chaotic control
Abstract:
The dynamics of a discrete-time predator?prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. ; Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations in period-2, 4, 8, 16, quasi-periodic orbits, an attracting invariant circle, an inverse period-doubling bifurcation from the period-32 orbit leading to chaos and a boundary crisis, a sudden onset of chaos and a sudden disappearance of the chaotic dynamics, attracting chaotic sets and non-attracting sets. ; We also observe that when the prey is in chaotic dynamics the predator can tend to extinction or to a stable equilibrium. Specifically, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Date:
Resource Type:
DOI:
Pages:
Source:
AMCS, volume 23, number 2 (2013) ; click here to follow the link