Ghost stochastic resonance in vertical-cavity surface-emitting lasers: experiment and theory

Experimental evidence of vibrational resonance in a multistable system

Experimental evidence of vibrational resonance in a multistable vertical-cavity surface-emitting laser (VCSEL) is reported. The VCSEL is characterized by a coexistence of four polarization states and driven by low-frequency (LF) and high-frequency (HF) periodic signals. In these conditions a series of resonances on the low frequency depending on the HF amplitude is observed. The location of resonances in a parameter space (dc current, amplitude of HF signal) is experimentally studied. For a fixed value of the dc current an evolution of the resonance curves with an increase of the LF amplitude is experimentally investigated.

Ghost resonance in the chaotic Chua's circuit

We experimentally investigate the ghost resonance phenomenon in the electronic circuit of Chua operating in the chaotic regime. The circuit can be stimulated to jump between two single-scroll attractors by an external periodic signal with an amplitude above an intrinsic threshold. For subthreshold signals, jumps between the chaotic attractors can be promoted by a superposed white noise. We show that the circuit output can exhibit a well-defined ghost resonance signature, i.e., a resonance on a frequency that is absent in a multicomponent input signal, when the amplitudes of the input components are properly related. Further, we show that ghost resonance can be induced by the Chua's circuit's own chaotic dynamics when it is driven by a suprathreshold multicomponent signal without the need of an external noise source.

Spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model

The phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered. Two of them, here so-called sensory neurons, are driven by noise and subthreshold periodic signals with different ratio of frequencies, and its outputs plus noise are applied synaptically to a third neuron, so-called interneuron. We present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron. We find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter-firing intervals statistics densities that are very distinctive from densities obtained using tones with ratios that are known to be dissonant. In other words, at the output of the interneuron, inharmonious signals give rise to blurry spike trains, while the harmonious signals produce more regular, less noisy, spike trains. Theoretical results are compared with numerical simulations.

Experimental study of resonant activation in a noisy bistable vertical-cavity surface-emitting laser with strong periodic excitation

An experimental evidence of the phenomenon of resonance activation (RA) in bistable semiconductor vertical-cavity surface-emitting laser (VCSEL) with a high level of internal noise under strong periodic excitation is presented. It is shown that the mean switching period (MSP) between polarization states passes through a minimum depending on the modulation frequency. From comparing frequency dependencies of the MSP and the coefficient of variation it is demonstrated for different conditions that resonance activation and stochastic resonance (SR) occur at different optimal values of the modulation frequency. The influence of the signal amplitude, the level of noise in VCSEL and asymmetry of bistable quasipotential are also experimentally studied. For large enough modulation amplitudes, RA and SR are accompanied by the phenomenon of the mean switching frequency locking.

Ghost resonance in a pool of heterogeneous neurons

We numerically study the subharmonic response of a heterogeneous pool of neurons to a pair of independent inputs. The neurons are stimulated with periodic pulse trains of frequencies f(1)=2 Hz and f(2)=3 Hz, and with inharmonic pulses whose frequencies f(1) and f(2) are equally shifted an amount Delta f. When both inputs are subthreshold, we find that the neurons respond at a frequency equal to f(2)-f(1) in the harmonic situation (Delta f=0), that increases linearly with Delta f in the inharmonic case. Thus the neurons detect a frequency not present in the input; this effect is termed "ghost resonance". When one of the inputs is slightly suprathreshold the ghost resonance persists, but responses related with the frequency of the suprathreshold input also emerge. This behavior must be taken into account in experimental studies of signal integration and coincidence detection by neuronal pools.

Coincidence detection of inharmonic pulses in a nonlinear crystal

Two trains of light pulses at periods that are equally shifted from the harmonics of a missing fundamental are combined in a nonlinear crystal. As a result of a noncollinear phase-matched second-order nonlinear generation, a new train of pulses is obtained. When the temporal width of the input pulses is large, the frequency of the resulting pulse train follows the observations from classical experiments on the perception of virtual pitch by the brain. On the other hand, when the width of the input pulses is small, the generated pulse train exhibits much lower frequencies, analogous to those observed in the motor neural system. Our experimental setup allows us to explore, systematically and continuously, the transition between these two regimes, while at the same time to demonstrate that the functionalities that have been observed in the nervous system are similar to the ones we observe from coincidence detection in quadratic nonlinear systems.

Ghost stochastic resonance with distributed inputs in pulse-coupled electronic neurons

We study experimentally the phenomenon of ghost stochastic resonance in pulse-coupled excitable systems, for input signals distributed among different elements. Specifically, two excitable electronic circuits are driven by different sinusoidal signals that produce periodic spikes at distinct frequencies. Their outputs are sent to a third circuit that processes these spiking signals and is additionally perturbed by noise. When the input signals are harmonics of a certain fundamental (that is not present in the inputs) the processing circuit exhibits, for an optimal amount of noise, a resonant response at the frequency of the missing fundamental (ghost frequency). In contrast with the standard case in which the signals being directly integrated are sinusoidal, this behavior relies here on a coincidence-detection mechanism. When the input signals are homogeneously shifted in frequency, the processing circuit responds with pulse packages composed of spikes at a frequency that depends linearly on the frequency shift. Expressions for the dependence of the package period and duration on the frequency shift and spike width, respectively, are obtained. These results provide an experimental verification of a recently proposed mechanism of binaural pitch perception.