Wavelet bifurcation analysis of dynamical systems

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Wavelet bifurcation analysis of dynamical systems : A case study in oscillations of Chara corallina transmembrane potential. / Postnikov, E. B.; Lavrova, A. I.; Kiseliov, R. V.; Plyusnina, T. Yu.

In: International Journal of Bifurcation and Chaos, Vol. 22, No. 12, 1250293, 01.01.2012.

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

BibTeX

@article{691aa4e2d1754d1fbab35debc6dfe611,

title = "Wavelet bifurcation analysis of dynamical systems: A case study in oscillations of Chara corallina transmembrane potential",

abstract = "We consider oscillations observed in the mathematical model describing the dynamics of transmembrane potential and changes of proton concentration outside and inside the cell of alga Chara corallina. This model shows sufficiently nonlinear regimes such as periods of birth/disappearance as well as parameter regions of chaotic motion. We perform bifurcation analysis of these complex oscillations via the Continuous Wavelet Transform with the Morlet wavelet. We show that this method, compared to classical bifurcation analysis allows to make numerical simulations at the continuous change of the key parameters and to obtain the spectral characteristics.",

keywords = "algae, chaos, membrane oscillations, Morlet wavelet",

author = "Postnikov, {E. B.} and Lavrova, {A. I.} and Kiseliov, {R. V.} and Plyusnina, {T. Yu}",

year = "2012",

month = jan,

day = "1",

doi = "10.1142/S0218127412502938",

language = "English",

volume = "22",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

number = "12",

}

RIS

TY - JOUR

T1 - Wavelet bifurcation analysis of dynamical systems

T2 - A case study in oscillations of Chara corallina transmembrane potential

AU - Postnikov, E. B.

AU - Lavrova, A. I.

AU - Kiseliov, R. V.

AU - Plyusnina, T. Yu

PY - 2012/1/1

Y1 - 2012/1/1

N2 - We consider oscillations observed in the mathematical model describing the dynamics of transmembrane potential and changes of proton concentration outside and inside the cell of alga Chara corallina. This model shows sufficiently nonlinear regimes such as periods of birth/disappearance as well as parameter regions of chaotic motion. We perform bifurcation analysis of these complex oscillations via the Continuous Wavelet Transform with the Morlet wavelet. We show that this method, compared to classical bifurcation analysis allows to make numerical simulations at the continuous change of the key parameters and to obtain the spectral characteristics.

AB - We consider oscillations observed in the mathematical model describing the dynamics of transmembrane potential and changes of proton concentration outside and inside the cell of alga Chara corallina. This model shows sufficiently nonlinear regimes such as periods of birth/disappearance as well as parameter regions of chaotic motion. We perform bifurcation analysis of these complex oscillations via the Continuous Wavelet Transform with the Morlet wavelet. We show that this method, compared to classical bifurcation analysis allows to make numerical simulations at the continuous change of the key parameters and to obtain the spectral characteristics.

KW - algae

KW - chaos

KW - membrane oscillations

KW - Morlet wavelet

UR - http://www.scopus.com/inward/record.url?scp=84872389739&partnerID=8YFLogxK

U2 - 10.1142/S0218127412502938

DO - 10.1142/S0218127412502938

M3 - Article

AN - SCOPUS:84872389739

VL - 22

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 12

M1 - 1250293

ER -

ID: 27612528

Wavelet bifurcation analysis of dynamical systems: A case study in oscillations of Chara corallina transmembrane potential

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