Controlling Equilibrium and Synchrony in Arrays of FitzHugh– Nagumo Type Oscillators

We present a case study of the FitzHugh–Nagumo (FHN) type model with a strongly asymmetric activation function. The proposed model is an electronically rather than a biologically inspired approach. The asymmetric exponential model imitates the shape of spikes in real neurons better than the classical FHN model with a cubic van der Pol activation function. An array of mean-field coupled non-identical FHN type oscillators is considered. The effect of mutual synchronization (phase locking) of units, originally oscillating at their individual frequencies, is demonstrated. Several feedback control methods, including stable tracking filter technique, mean field nullifying, and repulsive coupling are shown either to stabilize unstable equilibrium states or to suppress synchrony of the coupled FHN oscillators. The stability of the equilibrium states is analyzed by employing the eigenvalues, obtained from the characteristic equation, and by using the diagonal minors of the Routh–Hurwitz matrix. Nonlinear differential equations are solved numerically

Destroying synchrony in an array of the FitzHugh–Nagumo oscillators by external DC voltage source

A control method for desynchronizing an array of mean-field coupled FitzHugh–Nagumo-type oscillators is described. The technique is based on applying an adjustable DC voltage source to the coupling node. Both, numerical solution of corresponding nonlinear differential equations and hardware experiments with a nonlinear electrical circuit have been performed

Inhibition of spikes in an array of coupled FitzHugh–Nagumo oscillators by external periodic forcing

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

Application of ultrafast Schottky diodes to high megahertz chaotic oscillators

The considered chaotic oscillator consists of an amplifier, 2nd order LC resonator, Schottky diode and an extra capacitor in parallel to the diode. The diode plays the role of a nonlinear device. Chaotic oscillations are demonstrated numerically and experimentally at low as well as at high megahertz frequencies, up to 250 MHz

Suppressing Activity of an Array of Coupled Fitzhugh-Nagumo Oscillators

An extremely simple method for stabilizing unstable steady states in an array of coupled neuronal FitzHugh– Nagumo type oscillators is described. A two-terminal electronic feedback controller has been developed. The feed- back circuit, when coupled to an array of oscillators, damps the spiking neurons, thus does away with the effect of synchronization. Both, numerical simulations and hardware experiments with the electronic circuits have been performed. The results for an array of three mean-field coupled FitzHugh–Nagumo oscillators are presented

"Indoor" protection of electronic systems by means of high-pass negative feedback

An extremely simple first order RC high-pass filter is suggested to suppress harmful radio frequency oscillations, induced by high power electromagnetic pulses. Specifically, a broadband single stage transistor amplifier with a parasitic wiring inductance and also the parasitic junction and mounting capacitances are investigated both numerically and experimentally in the very high and ultrahigh frequency bands

80-dB microwave noise from an avalanche transistor circuit

Extremely high ‘excess noise ratio’ of 80 dB is observed from an avalanche transistor circuit, operating in a random pulse mode. Broadband noise spectrum measured from 30 MHz to 1 GHz exhibits good flatness with the nonuniformity of only + - 1 dB. Experiments have been performed with the silicon bipolar junction microwave transistors. An analog circuit model is proposed and investigated

Suppressing activity of an array of coupled FitzHugh–Nagumo oscillators

An extremely simple method for stabilizing unstable steady states in an array of coupled neuronal FitzHugh– Nagumo type oscillators is described. A two-terminal electronic feedback controller has been developed. The feed- back circuit, when coupled to an array of oscillators, damps the spiking neurons, thus does away with the effect of synchronization. Both, numerical simulations and hardware experiments with the electronic circuits have been performed. The results for an array of three mean-field coupled FitzHugh–Nagumo oscillators are presented