Bifurcation, chaos analysis and control in a discrete-time predator–prey system
Abstract The dynamical behavior of a discrete-time predator–prey model with modified Leslie–Gower and Holling’s type II schemes is investigated on the basis of the normal form method as well as bifurcation and chaos theory. The existence and stability of fixed points for the model are discussed. It...
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Online Access: | http://link.springer.com/article/10.1186/s13662-019-1950-6 |
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doaj-534d4f398bf34e0e8972eaf5e2a46d152020-11-25T01:20:11ZengSpringerOpenAdvances in Difference Equations1687-18472019-01-012019112210.1186/s13662-019-1950-6Bifurcation, chaos analysis and control in a discrete-time predator–prey systemWeiyi Liu0Donghan Cai1School of Mathematics and Statistics, Wuhan UniversitySchool of Mathematics and Statistics, Wuhan UniversityAbstract The dynamical behavior of a discrete-time predator–prey model with modified Leslie–Gower and Holling’s type II schemes is investigated on the basis of the normal form method as well as bifurcation and chaos theory. The existence and stability of fixed points for the model are discussed. It is showed that under certain conditions, the system undergoes a Neimark–Sacker bifurcation when bifurcation parameter passes a critical value, and a closed invariant curve arises from a fixed point. Chaos in the sense of Marotto is also verified by both analytical and numerical methods. Furthermore, to delay or eliminate the bifurcation and chaos phenomena that exist objectively in this system, two control strategies are designed, respectively. Numerical simulations are presented not only to validate analytical results but also to show the complicated dynamical behavior.http://link.springer.com/article/10.1186/s13662-019-1950-6Predator–prey modelLocal stabilityNeimark–Sacker bifurcationMarotto’s chaosBifurcation controlChaos control |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Weiyi Liu Donghan Cai |
spellingShingle |
Weiyi Liu Donghan Cai Bifurcation, chaos analysis and control in a discrete-time predator–prey system Advances in Difference Equations Predator–prey model Local stability Neimark–Sacker bifurcation Marotto’s chaos Bifurcation control Chaos control |
author_facet |
Weiyi Liu Donghan Cai |
author_sort |
Weiyi Liu |
title |
Bifurcation, chaos analysis and control in a discrete-time predator–prey system |
title_short |
Bifurcation, chaos analysis and control in a discrete-time predator–prey system |
title_full |
Bifurcation, chaos analysis and control in a discrete-time predator–prey system |
title_fullStr |
Bifurcation, chaos analysis and control in a discrete-time predator–prey system |
title_full_unstemmed |
Bifurcation, chaos analysis and control in a discrete-time predator–prey system |
title_sort |
bifurcation, chaos analysis and control in a discrete-time predator–prey system |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2019-01-01 |
description |
Abstract The dynamical behavior of a discrete-time predator–prey model with modified Leslie–Gower and Holling’s type II schemes is investigated on the basis of the normal form method as well as bifurcation and chaos theory. The existence and stability of fixed points for the model are discussed. It is showed that under certain conditions, the system undergoes a Neimark–Sacker bifurcation when bifurcation parameter passes a critical value, and a closed invariant curve arises from a fixed point. Chaos in the sense of Marotto is also verified by both analytical and numerical methods. Furthermore, to delay or eliminate the bifurcation and chaos phenomena that exist objectively in this system, two control strategies are designed, respectively. Numerical simulations are presented not only to validate analytical results but also to show the complicated dynamical behavior. |
topic |
Predator–prey model Local stability Neimark–Sacker bifurcation Marotto’s chaos Bifurcation control Chaos control |
url |
http://link.springer.com/article/10.1186/s13662-019-1950-6 |
work_keys_str_mv |
AT weiyiliu bifurcationchaosanalysisandcontrolinadiscretetimepredatorpreysystem AT donghancai bifurcationchaosanalysisandcontrolinadiscretetimepredatorpreysystem |
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1725134958935146496 |