Bifurcation analysis and chaos in a discrete reduced Lorenz system

E. M. Elabbasy; A. A. Elsadany; Yue Zhang

doi:10.1016/j.amc.2013.11.088

Bifurcation analysis and chaos in a discrete reduced Lorenz system

E. M. Elabbasy
, A. A. Elsadany
, Yue Zhang

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

Abstract

In this paper, the discrete reduced Lorenz system is considered. The dynamical behavior of the system is investigated. The existence and stability of the fixed points of this system are derived. The conditions for existence of a pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. The complex dynamics, bifurcations and chaos are displayed by numerical simulations.

Original language	English
Pages (from-to)	184-194
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	228
DOIs	https://doi.org/10.1016/j.amc.2013.11.088
State	Published - 1 Feb 2014
Externally published	Yes

Keywords

Chaotic behavior
Discrete Lorenz system
Lyapunov exponents
Neimark-Sacker bifurcation

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10.1016/j.amc.2013.11.088

Cite this

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title = "Bifurcation analysis and chaos in a discrete reduced Lorenz system",

abstract = "In this paper, the discrete reduced Lorenz system is considered. The dynamical behavior of the system is investigated. The existence and stability of the fixed points of this system are derived. The conditions for existence of a pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. The complex dynamics, bifurcations and chaos are displayed by numerical simulations.",

keywords = "Chaotic behavior, Discrete Lorenz system, Lyapunov exponents, Neimark-Sacker bifurcation",

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AU - Elabbasy, E. M.

AU - Elsadany, A. A.

AU - Zhang, Yue

PY - 2014/2/1

Y1 - 2014/2/1

N2 - In this paper, the discrete reduced Lorenz system is considered. The dynamical behavior of the system is investigated. The existence and stability of the fixed points of this system are derived. The conditions for existence of a pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. The complex dynamics, bifurcations and chaos are displayed by numerical simulations.

AB - In this paper, the discrete reduced Lorenz system is considered. The dynamical behavior of the system is investigated. The existence and stability of the fixed points of this system are derived. The conditions for existence of a pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. The complex dynamics, bifurcations and chaos are displayed by numerical simulations.

KW - Chaotic behavior

KW - Discrete Lorenz system

KW - Lyapunov exponents

KW - Neimark-Sacker bifurcation

UR - https://www.scopus.com/pages/publications/84890465284

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DO - 10.1016/j.amc.2013.11.088

M3 - Article

AN - SCOPUS:84890465284

SN - 0096-3003

VL - 228

SP - 184

EP - 194

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Bifurcation analysis and chaos in a discrete reduced Lorenz system

Abstract

Keywords

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