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Excitable dynamics and threshold sets in nonlinear systems.

Michal Voslar1, Igor Schreiber

  • 1Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Prague Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech Republic.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2004
PubMed
Summary

We define a quantitative threshold for excitable systems, distinguishing large excitatory responses from small nonexcitatory ones. This method uses numerical techniques to analyze chemical reaction dynamics and their excitability limits.

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Area of Science:

  • Chemical kinetics
  • Nonlinear dynamics
  • Theoretical chemistry

Background:

  • Excitable systems exhibit distinct responses to perturbations.
  • Previous work established foundational concepts for analyzing these systems.
  • Understanding response thresholds is crucial for predicting system behavior.

Purpose of the Study:

  • To quantitatively define a threshold separating excitatory and nonexcitatory responses in excitable systems.
  • To develop and apply numerical methods for finding this threshold in two-variable systems.
  • To investigate threshold phenomena and the loss of excitability in a chemical reaction model.

Main Methods:

  • Formulating the threshold set as a boundary value problem with a maximum separation rate condition.

Related Experiment Videos

  • Employing multiple shooting and continuation methods for solving the nonlinear problem.
  • Analyzing the bromate-sulfite-ferrocyanide chemical reaction system.

    • Main Results:

    • A quantitative threshold set was identified for the excitable system.
    • A bifurcation diagram was constructed, illustrating how excitability can vanish.
    • The numerical findings were compared with experimental data.

    Conclusions:

    • The developed numerical method effectively determines the excitability threshold.
    • The study provides insights into the conditions under which excitability is lost.
    • The findings are relevant to understanding threshold phenomena in various excitable systems.