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.
Damping of spikes in an array of coupled oscillators by injection of sinusoidal current is studied both electronically and numerically. The effect is investigated using an array consisting of thirty mean-field coupled FitzHugh–Nagumo-type oscillators. The results are considered as a possible mechanism of the deep brain stimulation used to avoid the symptoms of the Parkinson's disease.
A technique for stabilizing the steady states in an array of either the star coupled or the all-to-all coupled FitzHugh–Nagumo (FHN) oscillators is described. To control the whole array a single oscillator or a small fraction of the oscillators can be involved. The controller is a four-terminal device and includes an external active nonlinear oscillator implemented as a counterpart of an individual FHN oscillator and synchronized to the mean field of the array. Analytical, numerical, and experimental investigations have been performed.
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