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

E. B. Postnikov, A. I. Lavrova, R. V. Kiseliov, T. Yu Plyusnina

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number1250293
JournalInternational Journal of Bifurcation and Chaos
Volume22
Issue number12
DOIs
StatePublished - 1 Jan 2012
Externally publishedYes

Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

Keywords

  • algae
  • chaos
  • membrane oscillations
  • Morlet wavelet

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