Object
Title: Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response
Contributor:
Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Group publication title:
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
Resource Identifier:
DOI:
Pages:
Source:
AMCS, volume 23, number 2 (2013) ; click here to follow the link
Language:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Repository > Types of work > Articles
- Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS)
- Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2013)
Last modified:
Nov 5, 2024
In our library since:
Apr 11, 2024
Number of object content hits:
35
All available object's versions:
https://zbc.uz.zgora.pl/repozytorium/publication/88618
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International Journal of Applied Mathematics and Computer Science (AMCS)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 24 (2014)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23, number 1 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23, number 2 (2013)
- Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
| Edition name | Date |
|---|---|
| Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response | Nov 5, 2024 |
