Experimental observation of stochastic resonancelike behavior of autonomous motion in weakly ionized rf magnetoplasmas

Canard resonance: on noise-induced ordering of trajectories in heterogeneous networks of slow-fast systems

We analyse the dynamics of a network of semiconductor lasers coupled via their mean intensity through a non-linear optoelectronic feedback loop. We establish experimentally the excitable character of a single node, which stems from the slow-fast nature of the system, adequately described by a set of rate equations with three well separated time scales. Beyond the excitable regime, the system undergoes relaxation oscillations where the nodes display canard dynamics. We show numerically that, without noise, the coupled system follows an intricate canard trajectory, with the nodes switching on one by one. While incorporating noise leads to a better correspondence between numerical simulations and experimental data, it also has an unexpected ordering effect on the canard orbit, causing the nodes to switch on closer together in time. We find that the dispersion of the trajectories of the network nodes in phase space is minimized for a non-zero noise strength, and call this phenomenon canard resonance.

Study of detecting mechanism of carbon nanotubes gas sensor based on multi-stable stochastic resonance model

The detecting mechanism of carbon nanotubes gas sensor based on multi-stable stochastic resonance (MSR) model was studied in this paper. A numerically stimulating model based on MSR was established. And gas-ionizing experiment by adding electronic white noise to induce 1.65 MHz periodic component in the carbon nanotubes gas sensor was performed. It was found that the signal-to-noise ratio (SNR) spectrum displayed 2 maximal values, which accorded to the change of the broken-line potential function. The experimental results of gas-ionizing experiment demonstrated that periodic component of 1.65 MHz had multiple MSR phenomena, which was in accordance with the numerical stimulation results. In this way, the numerical stimulation method provides an innovative method for the detecting mechanism research of carbon nanotubes gas sensor.

Temperature-resonant cyclotron spectra in confined geometries

We consider a two-dimensional gas of colliding charged particles confined to finite size containers of various geometries and subjected to a uniform orthogonal magnetic field. The gas spectral densities are characterized by a broad peak at the cyclotron frequency. Unlike for infinitely extended gases, where the amplitude of the cyclotron peak grows linearly with temperature, here confinement causes such a peak to go through a maximum for an optimal temperature. In view of the fluctuation-dissipation theorem, the reported resonance effect has a direct counterpart in the electric susceptibility of the confined magnetized gas.

Dynamics of an excitable glow-discharge plasma under external forcing

Glow discharge plasma in the excitable regime shows rich dynamical behavior under external forcing. By perturbing the plasma with a subthreshold sawtooth periodic signal, we obtained small subthreshold oscillations that showed resonance with the perturbation frequency. The resonance phenomenon can be useful to estimate characteristic of an excitable system. However, for suprathreshold perturbation, frequency entrainment was observed. In this case, the system showed harmonic frequency entrainment for the perturbation frequencies greater than the characteristic frequency of the system and the excitable behavior for the perturbation frequencies well below the characteristic frequency. The experiments were performed in a glow-discharge plasma where excitability was achieved at a suitable discharge voltage and gas pressure.

Modeling noise-induced resonance in an excitable system: an alternative approach

Recently, it has been observed [Md. Nurujjaman, Phy. Rev. E 80, 015201(R) (2009)] that in an excitable system, one can maintain noise-induced coherency in the coherence resonance by blocking the destructive effect of the noise on the system at higher noise level. This phenomenon of constant coherence resonance (CCR) cannot be explained by the existing way of simulation of the model equations of an excitable system with added noise. In this paper, we have proposed a general model which explains the noise-induced resonance phenomenon CCR as well as coherence resonance (CR) and stochastic resonance (SR). The simulation has been carried out considering the basic mechanism of noise-induced resonance phenomena: noise only perturbs the system control parameter to excite coherent oscillations, taking proper precautions so that the destructive effect of noise does not affect the system. In this approach, the CR has been obtained from the interference between the system output and noise and the SR has been obtained by adding noise and a subthreshold signal. This also explains the observation of the frequency shift of coherent oscillations in the CCR with noise level.

Noise-invoked resonances near a homoclinic bifurcation in the glow discharge plasma

Stochastic resonance (SR) and coherence resonance (CR) have been studied experimentally in discharge plasmas close to a homoclinic bifurcation. For the SR phenomenon, it is observed that a superimposed subthreshold periodic signal can be recovered via stochastic modulations of the discharge voltage. Furthermore, it is realized that even in the absence of a subthreshold deterministic signal, the system dynamics can be recovered and optimized using noise. This effect is defined as CR in the literature. In the present experiments, induction of SR and CR is quantified using the absolute mean difference and normalized variance techniques, respectively.

Colored-noise-induced Hopf bifurcations in predator-prey communities

A broad class of (N+1) -species ratio-dependent predator-prey stochastic models, which consist of one predator population and N prey populations, is considered. The effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise. In the framework of the mean-field theory, approximate self-consistency equations for prey-populations mean density and for predator-population density are derived (to the first order in the noise variance). In some cases, the mean field exhibits Hopf bifurcations as a function of noise correlation time. The corresponding transitions are found to be reentrant, e.g., the periodic orbit appears above a critical value of the noise correlation time, but disappears again at a higher value of the noise correlation time. The nonmonotonous dependence of the critical control parameter on the noise correlation time is found, and the conditions for the occurrence of Hopf bifurcations are presented. Our results provide a possible scenario for environmental-fluctuations-induced transitions between the oscillatory regime and equilibrium state of population sizes observed in nature.

Coherence resonance near a Hopf bifurcation

We report on the observation of coherence resonance for a semiconductor laser with short optical feedback close to Hopf bifurcations. Noise-induced self-pulsations are documented by distinct Lorentzian-like features in the power spectrum. The character of coherence is critically related to the type of the bifurcation. In the supercritical case, spectral width and height of the peak are monotonic functions of the noise level. In contrast, for the subcritical bifurcation, the width exhibits a minimum, translating into resonance behavior of the correlation time in the pulsation transients. A theoretical analysis based on the generic model of a self-sustained oscillator demonstrates that these observations are of general nature and are related to the fact that the damping depends qualitatively different on the noise intensity for the subcritical and supercritical case.

Canard Explosion and Coherent Biresonance in the Rate Oscillation of CO Oxidation on Platinum Surface

The relationship between canard explosion and coherent biresonance is analyzed by numerically investigating a temporal dynamical model of CO oxidation on Pt surface. Canard explosion, manifesting itself by a dramatic change in the amplitude and period of a periodic orbit within a very narrow interval of a control parameter, is the result of multiple time scales in a dynamical system and is common in excitable systems. Coherent biresonance, namely, two peaks on the signal-to-noise ratio (SNR) curve when varying noise intensity, is a novel phenomenon of coherent resonance which is well-known in excitable systems. When the control parameter is varied from a stable fixed point, crossing the supercritical Hopf bifurcation, one of the peaks that corresponds to relatively larger noise intensity, keeps a constant height and position, while the other becomes higher and moves to lower noise level. When we consider the case in which two control parameters are perturbed by independent noise simultaneously, an interesting picture of one valley between two ridges appears on the 3D surface of SNR.

Fokker-Planck analysis of stochastic coherence in models of an excitable neuron with noise in both fast and slow dynamics

We provide a detailed and quantitative Fokker-Planck analysis of noise-induced periodicity (stochastic coherence, also known as coherence resonance) in both a discrete-time model and a continuous-time model of excitable neurons. In particular, we show that one-dimensional models can explain why the effects of noise added to the fast and slow dynamics of the models are dramatically different. We argue that such effects should occur in any excitable system with two or more distinct time scales and need to be taken into account in experiments investigating stochastic coherence.

Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model

We study noise-induced resonance effects in the leaky integrate-and-fire neuron model with absolute refractory period, driven by a Gaussian white noise. It is demonstrated that a finite noise level may either maximize or minimize the regularity of the spike train. We also partition the parameter space into regimes where either or both of these effects occur. It is shown that the coherence minimization at moderate noise results in a flat spectral response with respect to periodic stimulation in contrast to sharp resonances that are observed for both small and large noise intensities.

Coherence resonance with multiple peaks in a coupled FitzHugh-Nagumo model

Coherence resonance in a coupled excitable system is studied, through both a computer simulation and a circuit experiment, using a piecewise linear version of the FitzHugh-Nagumo model. White noise is added to the first element and spikes are accordingly generated and transmitted to the second element. The mean, standard deviation, and coefficient of variation of the interspike intervals in the second element have multiple peaks as the noise strengthens, when the coupling strength is small. This results from the phase locking to the spikes that the noise generates.

Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise

We demonstrate the effect of coherence resonance in a heterogeneous array of coupled Fitz Hugh-Nagumo neurons. It is shown that coupling of such elements leads to a significantly stronger coherence compared to that of a single element. We report nontrivial effects of parameter heterogeneity and spatial independence of noise on array-enhanced coherence resonance; especially, we find that (i) the coherence increases as spatial correlation of the noise decreases, and (ii) inhomogeneity in the parameters of the array enhances the coherence. Our results have the implication that generic heterogeneity and background noise can play a constructive role to enhance the time precision of firing in neural systems.

Self-organized waves in annular rf weakly magnetized dusty plasmas

Self-organized waves and the associated dust particle motion are studied experimentally in a low-pressure annular rf weakly magnetized dusty discharge system. Low-frequency drift waves with strong modulation on plasma density and dark space (sheath) width, traveling azimuthally with mode number m=1, are self-excited. Period-n and quasiperiodic states are also observed at higher rf power. Dust particles in the liquid state show collective elliptical cyclic motion in the low-frequency ionization-drift wave but respond only weakly to waves with frequencies above 50 Hz. When dust is added to a dust-free magnetized discharge in which there exists an ionization drift wave at 20 KHz, the wave amplitude is reduced and the frequency is down shifted.

Self-organized oscillations of strongly coupled dust coulomb clusters in plasma traps

The self-organized oscillation of a strongly coupled dust Coulomb cluster with an elongated cross section in a weakly ionized rectangular plasma trap is investigated. Through an inverse supercritical bifurcation at the low rf power end, a low-frequency (about 5 Hz) limit cycle oscillation of the whole cluster associated with the intracluster compressional lattice wave and phase-locked oscillation of the glow intensity distribution is observed. It is caused by the interplay of the dust motion and the shrinking and expanding of the confining dark space.

Instabilities in a magneto-optical trap: noise-induced dynamics in an atomic system

The instabilities observed in the atomic cloud of a magneto-optical trap are experimentally studied through the dynamics of the center of mass location and the cloud population. Two dynamical components are identified: a slow, stochastic one affects both variables, and a fast, deterministic one affects only the center of mass location. A one-dimensional stochastic model taking into account the shadow effect is developed from these observations and reproduces the experimental behavior. It is shown that instabilities are driven by noise and present stochastic resonancelike characteristics.

Intrawell stochastic resonance versus interwell stochastic resonance in underdamped bistable systems

We show that, for periodically driven noisy underdamped bistable systems, an intrawell stochastic resonance can exist, together with the conventional interwell stochastic resonance, resulting in a double maximum in the power spectral amplitude at the forcing frequency as a function of the noise intensity. The locations of the maxima correspond to matchings of deterministic and stochastic time scales in the system. In this paper we present experimental evidence of these phenomena and a phemonological nonadiabatic description in terms of a noise-controlled nonlinear dynamic resonance.

Microscopic Particle Motions in Strongly Coupled Dusty Plasmas

The microscopic particle motions from the crystal to the disordered state of a dusty plasma with micrometer-sized silicon dioxide particle suspensions in a radio-frequency glow discharge system were studied through an optical microimaging system. Small-amplitude random motion around the lattice sites of the crystal state, relative domain motion with varying boundaries, cooperative hopping in the liquid state, and highly disordered motion with increasing radio-frequency power were observed. Chaotic states with different spatial scales under the coherent and stochastic coupling between dust particles and self-organized background plasma fluctuations were also demonstrated.