Delay Feedback Control of the Lorenz-Like System

Delay Feedback Control of the Lorenz-Like System

We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direct...

Full description

Bibliographic Details
Main Authors: Qin Chen, Jianguo Gao
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2018/1459272
id doaj-b36e9b66394c4050bc83b57971d61c5f
record_format Article
spelling doaj-b36e9b66394c4050bc83b57971d61c5f2020-11-24T22:30:30ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/14592721459272Delay Feedback Control of the Lorenz-Like SystemQin Chen0Jianguo Gao1Department of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021, ChinaDepartment of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021, ChinaWe choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems.http://dx.doi.org/10.1155/2018/1459272
collection DOAJ
language English
format Article
sources DOAJ
author Qin Chen
Jianguo Gao
spellingShingle Qin Chen
Jianguo Gao
Delay Feedback Control of the Lorenz-Like System
Mathematical Problems in Engineering
author_facet Qin Chen
Jianguo Gao
author_sort Qin Chen
title Delay Feedback Control of the Lorenz-Like System
title_short Delay Feedback Control of the Lorenz-Like System
title_full Delay Feedback Control of the Lorenz-Like System
title_fullStr Delay Feedback Control of the Lorenz-Like System
title_full_unstemmed Delay Feedback Control of the Lorenz-Like System
title_sort delay feedback control of the lorenz-like system
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2018-01-01
description We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems.
url http://dx.doi.org/10.1155/2018/1459272
work_keys_str_mv AT qinchen delayfeedbackcontrolofthelorenzlikesystem
AT jianguogao delayfeedbackcontrolofthelorenzlikesystem
_version_ 1725740709318754304

Similar Items