Intermediate Noise Intensity Research Articles

Effects of noise on excitable dissipative solitons

We study the effects of noise on excitable DS found on nonlinear Kerr cavities, showing that the system exhibits coherence resonance, characterized by a maximum degree of regularity for intermediate noise intensities. This behavior is observed for two different ways of applying noise: an additive white uncorrelated spatio-temporal noise and including fluctuations in the intensity of an addressing beam.

Noise-reversed stability of Turing patterns versus Hopf oscillations near codimension-two conditions

Pattern formation induced by noise is a celebrated phenomenon in diverse reaction-diffusion systems. Here we report numerical simulations with the Lengyel-Epstein model for the chlorine dioxide-iodine-malonic acid reaction when perturbed with an external spatiotemporal stochastic forcing in the vicinity of the Hopf and Turing codimension-two bifurcation. Competition between Turing and Hopf modes gives rise to the generation of transient Turing patterns evolving to stationary global oscillations. This situation is reversed by the introduction of external fluctuations and Turing patterns become dominant in this case. The increase in the spatial coherence is found for intermediate noise intensity and small correlation length.

Pattern Synchronization in a Two-Layer Neuronal Network

Pattern synchronization in a two-layer neuronal network is studied. For a single-layer network of Rulkov map neurons, there are three kinds of patterns induced by noise. Additive noise can induce ordered patterns at some intermediate noise intensities in a resonant way; however, for small and large noise intensities there exist excitable patterns and disordered patterns, respectively. For a neuronal network coupled by two single-layer networks with noise intensity differences between layers, we find that the two-layer network can achieve synchrony as the interlayer coupling strength increases. The synchronous states strongly depend on the interlayer coupling strength and the noise intensity difference between layers.

STOCHASTIC SPIKING COHERENCE IN COUPLED SUBTHRESHOLD MORRIS-LECAR NEURONS

We consider a large population of globally coupled subthreshold Morris-Lecar neurons. By varying the noise intensity D, we numerically investigate stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings). As D passes a lower threshold, a transition from an incoherent to a coherent state occurs because of a constructive role of noise to stimulate coherence between noise-induced spikings. However, when passing a higher threshold of D, another transition from a coherent to an incoherent state takes place due to a destructive role of noise to spoil the spiking coherence. Such an incoherence-coherence-incoherence transition is well-described in terms of the order parameter which is just the mean square deviation of the global potential. In the coherent regime, we also characterize the degree of stochastic spiking coherence by using a coherence measure which reflects the degree of "resemblance" of the global potential to the local potential. Thus, stochastic spiking coherence with large coherence measure is found to occur over a large range of intermediate noise intensity.

SPATIOTEMPORAL COHERENCE RESONANCE IN A MAP LATTICE

We study the effects of parametric noise on a lattice network, which is locally modeled by a two-dimensional Rulkov map. We conclude that at some intermediate noise intensity, parametric noise can induce ordered circular patterns, which indicates the appearance of spatiotemporal coherence resonance in the studied lattice. With the observation of coherence-like manner in linear spatial cross-correlation, the coherence phenomena can be analyzed quantitatively.

Multiplicative-noise-induced coherence resonance via two different mechanisms in bistable neural models

The bistable FitzHugh-Nagumo (FHN) neural model driven by two multiplicative noises and one additive noise is investigated. Two different potential mechanisms for enhancing coherence of bistable FHN model are presented, that is, the first multiplicative noise changes the system from the bistable to the oscillatory regime, and the second multiplicative noise can enhance the symmetry of two stable states of the system. The two mechanisms are analytically or numerically explained. At any level of the second multiplicative noise, a maximal coherence have been found at some intermediate noise intensity of the first multiplicative noise. Only when the first multiplicative noise intensity is less than 0.0001 can a maximal coherence be obtained at some intermediate noise intensity of the second multiplicative noise. These coherence resonance phenomena have been understood in terms of the presented mechanisms.

Spatial coherence resonance on diffusive and small-world networks of Hodgkin–Huxley neurons

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin–Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining the impact of diffusive and small-world network topology that determines the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.

Characterization of Stochastic Spiking Coherence in Coupled Neurons

We consider a large population of globally coupled subthreshold Morris-Lecar neurons. By varying the noise intensity D, we investigate numerically stochastic spiking coherence (i.e., noise-induced coherence between neural spikings). As D passes a threshold, a transition from an incoherent to a coherent state occurs. This coherent transition is described in terms of the “thermodynamic” order parameter O, which concerns a macroscopic time-averaged fluctuation of the global potential. We note that such stochastic spiking coherence may be well visualized in terms of the raster plot of neural spikings (i.e., spatiotemporal plot of neural spikings), which is directly obtained in experiments. To quantitatively measure the degree of stochastic spiking coherence (seen in the raster plot), we introduce a new type of “spiking coherence measure,” Ms, by taking into consideration the average contribution of (microscopic) local neural spikings to the (macroscopic) global membrane potential. Hence, the spiking coherence measure may be regarded as a “statistical-mechanical” measure. Through competition between the constructive and the destructive roles of noise, stochastic spiking coherence is found to occur over a large range of intermediate noise intensities and to be well characterized in terms of the mutually complementary quantities of O and Ms. Particularly, Ms reflects the degree of stochastic spiking coherence seen in the raster plot very well.

Drift and diffusion in a periodic two-dimensional velocity field without attractors

We consider the transport of overdamped particles in a two-dimensional periodic velocity field. This field possesses extended lines of fixed points where the deterministic motion stops. Additive noise makes the lines penetrable and results in an oscillatory motion along tori. We characterize the stochastic motion by the probability distribution density, the stationary mean velocity, and the mean times of escape from bounded domains. For intermediate noise intensities, the fluctuations enhance the transport of the particles compared to the deterministic case. A fast dichotomic modulation of asymmetry enhances fluxes.

Barrier crossing driven by Lévy noise: Universality and the role of noise intensity

We study the barrier crossing of a particle driven by white symmetric Lévy noise of index alpha and intensity D for three different generic types of potentials: (a) a bistable potential, (b) a metastable potential, and (c) a truncated harmonic potential. For the low noise intensity regime we recover the previously proposed algebraic dependence on D of the characteristic escape time, T_{esc} approximately C(alpha)D;{mu(alpha)} , where C(alpha) is a coefficient. It is shown that the exponent mu(alpha) remains approximately constant, mu approximately 1 for 0<alpha<2 ; at alpha=2 the power-law form of T_{esc} changes into the known exponential dependence on 1D ; it exhibits a divergencelike behavior as alpha approaches 2. In this regime we observe a monotonous increase of the escape time T_{esc} with increasing alpha (keeping the noise intensity D constant). The probability density of the escape time decays exponentially. In addition, for low noise intensities the escape times correspond to barrier crossing by multiple Lévy steps. For high noise intensities, the escape time curves collapse for all values of alpha . At intermediate noise intensities, the escape time exhibits nonmonotonic dependence on the index alpha , while still retaining the exponential form of the escape time density.

Associative memory and segmentation in the neural system under stimulation of stochastic or chaotic perceptual singals

We present in this paper some results on the temporal segmentation and retrieval of stored memories or patterns using neural networks composed of spiking neurons. Respecting the working environment，we present the network with stochastic or chaotic stimuli as their extremely working conditions and also with noise. We attempt to give an explanation to the function of memory retrieval of the brain system, where the stimuli usually may not be constant, sinusoidal or periodic, but rather chaotic or stochastic. For an input pattern which is a superposition of several stored patterns, it is shown that the proposed neuronal network model is capable of segmenting out each pattern one after another as synchronous firings of a subgroup of neurons，and if a corrupted input pattern is presented, the network is shown to be able to retrieve the perfect one，that is it has the function of associative memory. By thorougly adjusting the parameters, such as the coupling strength and the intensity of the noise, the temporal segmentation attains its optimal performance at intermediate noise intensity，which reminds of the stochastic resonance observed in the coupled spiking neuronal networks.

Thoughts out of noise

We study the effects of additive Gaussian noise on the behaviour of a simple spatially extended system, which is locally modelled by a nonlinear two-dimensional iterated map describing neuronal dynamics. In particular, we focus on the ability of noise to induce spatially ordered patterns, i.e. the so-called noise-induced pattern formation. For intermediate noise intensities, the spatially extended system exhibits ordered circular waves, thereby clearly manifesting the constructive role of random perturbations. The emergence of observed noise-induced patterns is explained with simple arguments that are obtained by analysing the typical spatial scale of patterns evoked by various diffusion coefficients. Since discrete-time systems are straightforward to implement and require modest computational capabilities, the present study describes one of the most fascinating and visually compelling examples of noise-induced self-organization in nonlinear systems in an accessible way for graduate or even advanced undergraduate students attending a nonlinear dynamics course.

Phase Transitions Driven by State-Dependent Poisson Noise

Nonlinear systems driven by state-dependent Poisson noise are introduced to model the persistence of climatic anomalies in land-atmosphere interaction caused by the soil-moisture dependence of the frequency of rainfall events. It is found that these systems may give rise to bimodal probability distributions, while the state variable randomly persists around the preferential states because of transient dynamics that are opposite to the long-term behavior. Mean-field analysis and numerical simulations of the spatially distributed systems reveal a symmetry-breaking bifurcation for sufficiently strong spatial diffusive couplings and intermediate noise intensities. In such conditions, the initial development of spatial patterns is followed by a stable configuration, selected on the bases of the initial conditions in correspondence of the remnants of the modes of the uncoupled system.

Noise-induced bifurcations and chaos in the average motion of globally-coupled oscillators

A system of coupled master equations simplified from a model of noise-driven globally coupled bistable oscillators under periodic forcing is investigated. In the thermodynamic limit, the system is reduced to a set of two coupled differential equations. Rich bifurcations to subharmonics and chaotic motions are found. This behavior can be found only for certain intermediate noise intensities. Noise with intensities which are too small or too large will certainly spoil the bifurcations. In a system with large though finite size, the bifurcations to chaos induced by noise can still be detected to a certain degree.

Reentrant transitions in globally coupled active rotators with multiplicative and additive noises

We study the nonequilibrium phenomena in globally coupled active rotators with multiplicative and additive noises. It is shown that at a critical value of the multiplicative noise intensity the system undergoes noise-induced transition from a one-cluster state to a two-cluster state. Additive noise suppresses the effect of the multiplicative noise on the system, increasing the critical value of the multiplicative noise intensity. The system shows a reentrant transition at intermediate additive noise intensity.

Nonequilibrium Phenomena in Globally Coupled Active Rotators with Multiplicative and Additive Noises

We investigate noise-induced phase transitions in globally coupled active rotators with multiplicative and additive noises. In the system there are four phases, stationary one-cluster, stationary two-cluster, moving one-cluster, and moving two-cluster phases. It is shown that multiplicative noise induces a bifurcation from one-cluster phase to two-cluster phase. Pinning force also induces a bifurcation from moving phase to stationary phase suppressing the multiplicative noise effect. Additive noise reduces both effects of multiplicative noise and pinning force urging the system to the stationary one-cluster phase. The frustrated effects of pinning force and additive and multiplicative noises lead to a reentrant transition at intermediate additive noise intensity. Nature of the transition is also discussed.