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

الملخص EN

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.