Effect of external noise correlation in optical coherence resonance

Noise-induced symmetry breaking in a network of excitable ecological systems

Noise-induced symmetry breaking has barely been unveiled on the ecological grounds, though its occurrence may elucidate mechanisms responsible for maintaining biodiversity and ecosystem stability. Here, for a network of excitable consumer-resource systems, we show that the interplay of network structure and noise intensity manifests a transition from homogeneous steady states to inhomogeneous steady states, resulting in noise-induced symmetry breaking. On further increasing the noise intensity, there exist asynchronous oscillations, leading to heterogeneity crucial for maintaining a system's adaptive capacity. The observed collective dynamics can be understood analytically in the framework of linear stability analysis of the corresponding deterministic system.

Practical lineshape of a laser operating near an exceptional point

We present a practical laser linewidth broadening phenomenon in the viewpoint of high sensitivity of an exceptional point (EP). A stochastic simulation model is implemented to describe the fluctuations in the cavity resonance frequencies. The linewidth originated from external noises are maximized at the EP. The linewidth enhancement factor behaves similarly to the Petermann factor although the Petermann effect is not considered. In the long coherence time limit, the power spectral density of the laser exhibits a splitting in the vicinity of the EP although the cavity eigenfrequencies coalesce at the EP.

Roles of external noise correlation in optimal intracellular calcium signaling

The dynamics of a minimal calcium model, which is subjected to white noise or colored noise, was investigated. For white noise, coherence of noise-induced calcium oscillations reached a maximum at an optimal noise intensity, characterizing coherence resonance. Higher resonance peaks could be observed at lower noise intensity when a control parameter is tuned to approach a bifurcation point. For colored noise, a maximal coherence of the oscillations was found for suitable values of both the intensity and the correlation time. Moreover, the coherence of the oscillations exhibited two maxima at two values of noise intensity (correlation time) for appropriate noise correlation time (intensity). In addition, a quantitative description of the effects of noise correlation time on the resonance behavior was presented. The resonance behavior, which is induced either by white noise or colored noise, was interpreted by terms of height and relative width of a spectral peak.

Control of spiking regularity in a noisy complex neural network

The effects of spatiotemporally correlated noise on the regularity of spiking oscillations are studied in a network composed of Fitz-Hugh-Nagumo neurons. The spiking regularity of the neural network becomes the best at a moderate noise intensity, indicating the occurrence of coherence resonance (CR). The CR in a Watts-Strogatz small-world network is further improved by adding a small fraction of long-range connections. Given a set of temporal correlation constant tau and spatial correlation length lambda of the noise, there exists an optimal network topology randomness, at which the spiking oscillations show the best regularity. The optimal randomness of the network topology at different tau and lambda varies in a narrow range. Changing lambda does not affect the optimal tau for achieving the most regular spike train, whereas varying tau, the best spiking regularity emerges at different optimal lambda.

Synchronization of noisy delayed feedback systems with delayed coupling

Synchronization of delayed coupled and stochastically perturbed systems with delayed nonlinear feedback is studied, using as an example circular chains of three and four delayed coupled Ikeda oscillators. It is proved that in the case of multiplicative noise the exact synchronization in the mean occurs for sufficiently large coupling, and an analytic estimate of the sufficient coupling is given. The sufficiency condition is compared with numerical computations, and typical effects of noise on the exact and some generalized types of synchronization are illustrated.

Double coherence resonance in neuron models driven by discrete correlated noise

We study the influence of correlations among discrete stochastic excitatory or inhibitory inputs on the response of the FitzHugh-Nagumo neuron model. For any level of correlation, the emitted signal exhibits at some finite noise intensity a maximal degree of regularity, i.e., a coherence resonance. Furthermore, for either inhibitory or excitatory correlated stimuli, a double coherence resonance is observable. Double coherence resonance refers to a (absolute) maximum coherence in the output occurring for an optimal combination of noise variance and correlation. All of these effects can be explained by taking advantage of the discrete nature of the correlated inputs.

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 in excitable electronic circuits in the presence of colored noise

We give evidence of coherence resonance in an excitable electronic circuit whose dynamics obeys the FitzHugh-Nagumo model system, under the application of different noise sources, ranging from Gaussian white noise to colored 1/f2 noises. The resonance behavior can be significantly reinforced when experimental parameters are tuned in order to place the stable fixed point closer to the excitability threshold of spiking behavior, as well as when the time scales of the circuit are properly modified. A quantitative description of the effects of noise correlations in inducing the resonant behavior is provided.

Noise-induced wave nucleations in an excitable chemical reaction

We study both experimentally and numerically the temporal coherence of noise-induced wave nucleations in excitable media subjected to external fluctuations with finite correlation time. The experiments are performed with the light-sensitive variant of the Belousov-Zhabotinsky (BZ) reaction forced by an exponentially correlated dichotomous fluctuating illumination. We find that there exists an optimal correlation time for which nucleations coherence reaches a maximum. The same behavior is obtained in numerical simulations with a stochastic Oregonator model, modified to describe the light-sensitive BZ reaction.

Delay-induced resonances in an optical system with feedback

We study the influence of the delay time in the response of a delayed feedback system to external periodic driving. The nonlinear system we consider is a semiconductor laser with optical feedback operating in the low-frequency fluctuation regime. We numerically examine the consequences of varying the external cavity length of the system when a weak modulation is introduced through the laser's pump current. The harmonic modulation is seen to lead to a partial periodic entrainment of power dropouts, and the distribution of time intervals between the dropouts exhibits resonances with certain delay times. In other words, the response of the system to the external modulation is enhanced for particular values of the external cavity length. The same effect can be observed in the presence of noise, indicating that stochastic resonance can be enhanced or degraded depending on the feedback time.

Doubly stochastic coherence via noise-induced symmetry in bistable neural models

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance.

Coherence and anticoherence resonance tuned by noise

We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity.

Stochastic entrainment of optical power dropouts

We show that the natural pulsed behavior, in the form of sudden power dropouts, exhibited by semiconductor lasers subject to optical feedback can be entrained by the joint action of external noise and weak periodic driving. These power dropouts, which in the absence of forcing do not occur periodically, acquire the periodicity of the harmonic driving for an optimal amount of external noise, in what constitutes a form of stochastic resonance. This phenomenon is analyzed by means of a generalized Lang-Kobayashi model with external nonwhite noise in the modulated pump current, in terms of both the temporal correlation and the amplitude of the noise.