Two-parameter bifurcation analysis of the discrete Lorenz model

Javad Alidousti; Zohre Eskandari; Zakieh Avazzadeh; J. A. Tenreiro Machado

doi:10.1002/mma.7969

Two-parameter bifurcation analysis of the discrete Lorenz model

Javad Alidousti
, Zohre Eskandari
, Zakieh Avazzadeh^*
, J. A. Tenreiro Machado

^*Corresponding author for this work

Department of Applied Mathematics

Shahrekord University
Polytechnic of Porto

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

2 Citations (Scopus)

Abstract

This paper studies the bifurcation analysis of the discrete time Lorenz system considering its generalization for two control parameters. The one- and two-parameter bifurcations of the system, including pitchfork, period-doubling, Neimark–Sacker, 1:2, 1:3, and 1:4 resonances, are surveyed thoroughly. The critical coefficients are computed to analyze the nondegeneracy of listed bifurcations and predict their bifurcation scenarios. The numerical continuation method reveals complex dynamics including bifurcations up to 16th iterations. The results show an excellent agreement between the analytical predictions and the numerical observations.

Original language	English
Journal	Mathematical Methods in the Applied Sciences
DOIs	https://doi.org/10.1002/mma.7969
Publication status	Accepted/In press - 2021

Keywords

Lorenz system
Neimark–Sacker
critical coefficient
numerical continuation
period doubling
strong resonances

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10.1002/mma.7969

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@article{9a8a78c8d25047dab58be75661560c33,

title = "Two-parameter bifurcation analysis of the discrete Lorenz model",

abstract = "This paper studies the bifurcation analysis of the discrete time Lorenz system considering its generalization for two control parameters. The one- and two-parameter bifurcations of the system, including pitchfork, period-doubling, Neimark–Sacker, 1:2, 1:3, and 1:4 resonances, are surveyed thoroughly. The critical coefficients are computed to analyze the nondegeneracy of listed bifurcations and predict their bifurcation scenarios. The numerical continuation method reveals complex dynamics including bifurcations up to 16th iterations. The results show an excellent agreement between the analytical predictions and the numerical observations.",

keywords = "Lorenz system, Neimark–Sacker, critical coefficient, numerical continuation, period doubling, strong resonances",

author = "Javad Alidousti and Zohre Eskandari and Zakieh Avazzadeh and \{Tenreiro Machado\}, \{J. A.\}",

note = "Publisher Copyright: {\textcopyright} 2021 John Wiley \& Sons, Ltd.",

year = "2021",

doi = "10.1002/mma.7969",

language = "English",

journal = "Mathematical Methods in the Applied Sciences",

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T1 - Two-parameter bifurcation analysis of the discrete Lorenz model

AU - Alidousti, Javad

AU - Eskandari, Zohre

AU - Avazzadeh, Zakieh

AU - Tenreiro Machado, J. A.

PY - 2021

Y1 - 2021

N2 - This paper studies the bifurcation analysis of the discrete time Lorenz system considering its generalization for two control parameters. The one- and two-parameter bifurcations of the system, including pitchfork, period-doubling, Neimark–Sacker, 1:2, 1:3, and 1:4 resonances, are surveyed thoroughly. The critical coefficients are computed to analyze the nondegeneracy of listed bifurcations and predict their bifurcation scenarios. The numerical continuation method reveals complex dynamics including bifurcations up to 16th iterations. The results show an excellent agreement between the analytical predictions and the numerical observations.

AB - This paper studies the bifurcation analysis of the discrete time Lorenz system considering its generalization for two control parameters. The one- and two-parameter bifurcations of the system, including pitchfork, period-doubling, Neimark–Sacker, 1:2, 1:3, and 1:4 resonances, are surveyed thoroughly. The critical coefficients are computed to analyze the nondegeneracy of listed bifurcations and predict their bifurcation scenarios. The numerical continuation method reveals complex dynamics including bifurcations up to 16th iterations. The results show an excellent agreement between the analytical predictions and the numerical observations.

KW - Lorenz system

KW - Neimark–Sacker

KW - critical coefficient

KW - numerical continuation

KW - period doubling

KW - strong resonances

UR - https://www.scopus.com/pages/publications/85120637417

U2 - 10.1002/mma.7969

DO - 10.1002/mma.7969

M3 - Article

AN - SCOPUS:85120637417

SN - 0170-4214

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

ER -

Two-parameter bifurcation analysis of the discrete Lorenz model

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Keywords

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