Nonlinear dynamics of two-dimensional sinusoidal discrete map

Chuang BI; Qian ZHANG; Yong XIANG; Jingmei WANG

doi:10.1109/ICCCAS.2013.6765377

Nonlinear dynamics of two-dimensional sinusoidal discrete map

Chuang BI, Qian ZHANG, Yong XIANG, Jingmei WANG

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

3 Citations (Scopus)

Abstract

A new two-dimensional sinusoidal discrete map is achieved by nonlinearly coupling a sinusoidal map and a cubic map. The fixed points are obtained based on this two-dimensional sinusoidal discrete map, and the stability of the system is analyzed to study the complex nonlinear dynamic behavior of the system and the evolution of their attractors. The research results indicate that there are complex nonlinear physical phenomena in this two-dimensional sinusoidal discrete map, such as symmetry breaking bifurcation, Hopf bifurcation, and flip bifurcation. Furthermore, bifurcation mode coexisting and the evolution of the attractors of the system are analyzed by using the bifurcation diagram, the Lyapunov exponent diagram and phase portraits when the control parameters of the system are varied.

Original language	English
Title of host publication	Proceedings of the 2013 International Conference on Communications, Circuits and Systems (ICCCAS)
Publisher	IEEE
Pages	438-441
Number of pages	4
ISBN (Electronic)	9781479930517
DOIs	https://doi.org/10.1109/ICCCAS.2013.6765377
Publication status	Published - Nov 2013
Externally published	Yes
Event	2013 International Conference on Communications, Circuits and Systems, ICCCAS 2013 - Chengdu, China Duration: 15 Nov 2013 → 17 Nov 2013

Conference

Conference	2013 International Conference on Communications, Circuits and Systems, ICCCAS 2013
Country/Territory	China
City	Chengdu
Period	15/11/13 → 17/11/13

Keywords

Bifurcation
Limit-cycles
Chaos
Nonlinear dynamical systems
Stability analysis
Couplings
Discrete-time systems

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10.1109/ICCCAS.2013.6765377

Cite this

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title = "Nonlinear dynamics of two-dimensional sinusoidal discrete map",

abstract = "A new two-dimensional sinusoidal discrete map is achieved by nonlinearly coupling a sinusoidal map and a cubic map. The fixed points are obtained based on this two-dimensional sinusoidal discrete map, and the stability of the system is analyzed to study the complex nonlinear dynamic behavior of the system and the evolution of their attractors. The research results indicate that there are complex nonlinear physical phenomena in this two-dimensional sinusoidal discrete map, such as symmetry breaking bifurcation, Hopf bifurcation, and flip bifurcation. Furthermore, bifurcation mode coexisting and the evolution of the attractors of the system are analyzed by using the bifurcation diagram, the Lyapunov exponent diagram and phase portraits when the control parameters of the system are varied.",

keywords = "Bifurcation, Limit-cycles, Chaos, Nonlinear dynamical systems, Stability analysis, Couplings, Discrete-time systems",

author = "Chuang BI and Qian ZHANG and Yong XIANG and Jingmei WANG",

year = "2013",

month = nov,

doi = "10.1109/ICCCAS.2013.6765377",

language = "English",

pages = "438--441",

booktitle = "Proceedings of the 2013 International Conference on Communications, Circuits and Systems (ICCCAS)",

publisher = "IEEE",

note = "2013 International Conference on Communications, Circuits and Systems, ICCCAS 2013 ; Conference date: 15-11-2013 Through 17-11-2013",

}

BI, C, ZHANG, Q, XIANG, Y & WANG, J 2013, Nonlinear dynamics of two-dimensional sinusoidal discrete map. in Proceedings of the 2013 International Conference on Communications, Circuits and Systems (ICCCAS). IEEE, pp. 438-441, 2013 International Conference on Communications, Circuits and Systems, ICCCAS 2013, Chengdu, China, 15/11/13. https://doi.org/10.1109/ICCCAS.2013.6765377

TY - GEN

T1 - Nonlinear dynamics of two-dimensional sinusoidal discrete map

AU - BI, Chuang

AU - ZHANG, Qian

AU - XIANG, Yong

AU - WANG, Jingmei

PY - 2013/11

Y1 - 2013/11

N2 - A new two-dimensional sinusoidal discrete map is achieved by nonlinearly coupling a sinusoidal map and a cubic map. The fixed points are obtained based on this two-dimensional sinusoidal discrete map, and the stability of the system is analyzed to study the complex nonlinear dynamic behavior of the system and the evolution of their attractors. The research results indicate that there are complex nonlinear physical phenomena in this two-dimensional sinusoidal discrete map, such as symmetry breaking bifurcation, Hopf bifurcation, and flip bifurcation. Furthermore, bifurcation mode coexisting and the evolution of the attractors of the system are analyzed by using the bifurcation diagram, the Lyapunov exponent diagram and phase portraits when the control parameters of the system are varied.

AB - A new two-dimensional sinusoidal discrete map is achieved by nonlinearly coupling a sinusoidal map and a cubic map. The fixed points are obtained based on this two-dimensional sinusoidal discrete map, and the stability of the system is analyzed to study the complex nonlinear dynamic behavior of the system and the evolution of their attractors. The research results indicate that there are complex nonlinear physical phenomena in this two-dimensional sinusoidal discrete map, such as symmetry breaking bifurcation, Hopf bifurcation, and flip bifurcation. Furthermore, bifurcation mode coexisting and the evolution of the attractors of the system are analyzed by using the bifurcation diagram, the Lyapunov exponent diagram and phase portraits when the control parameters of the system are varied.

KW - Bifurcation

KW - Limit-cycles

KW - Chaos

KW - Nonlinear dynamical systems

KW - Stability analysis

KW - Couplings

KW - Discrete-time systems

UR - http://www.scopus.com/inward/record.url?scp=84898783784&partnerID=8YFLogxK

U2 - 10.1109/ICCCAS.2013.6765377

DO - 10.1109/ICCCAS.2013.6765377

M3 - Conference paper (refereed)

AN - SCOPUS:84898783784

SP - 438

EP - 441

BT - Proceedings of the 2013 International Conference on Communications, Circuits and Systems (ICCCAS)

PB - IEEE

T2 - 2013 International Conference on Communications, Circuits and Systems, ICCCAS 2013

Y2 - 15 November 2013 through 17 November 2013

ER -

Nonlinear dynamics of two-dimensional sinusoidal discrete map

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Keywords

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