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Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique

Author

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  • Elena Adomaitienė
  • Skaidra Bumelienė
  • Gytis Mykolaitis
  • Arūnas Tamaševičius

Abstract

We suggest employing the first-order stable RC filters, based on a single capacitor, for control of unstable fixed points in an array of oscillators. A single capacitor is sufficient to stabilize an entire array, if the oscillators are coupled strongly enough. An array, composed of 24 to 30 mean-field coupled FitzHugh–Nagumo (FHN) type asymmetric oscillators, is considered as a case study. The investigation has been performed using analytical, numerical, and experimental methods. The analytical study is based on the mean-field approach, characteristic equation for finding the eigenvalue spectrum, and the Routh–Hurwitz stability criteria using low-rank Hurwitz matrix to calculate the threshold value of the coupling coefficient. Experiments have been performed with a hardware electronic analog, imitating dynamical behavior of an array of the FHN oscillators.

Suggested Citation

  • Elena Adomaitienė & Skaidra Bumelienė & Gytis Mykolaitis & Arūnas Tamaševičius, 2017. "Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique," Complexity, Hindawi, vol. 2017, pages 1-8, September.
    • Handle: RePEc:hin:complx:4324879
    DOI: 10.1155/2017/4324879
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