Noise-induced Phase Synchronization Research Articles

Critical behavior of noise-induced phase synchronization

We present for the first time in detail the set of the main critical exponents associated with the phase transition of the Kuramoto model under multiplicative noise action. This was done considering the equilibrium thermodynamics for the states of synchronization as well as the subsequent analysis of the critical behavior of the free energy and entropy of the model. We reinforce the concept of the synchronization field for a system of oscillators with multiplicative noise where an expression for the susceptibility is analytically obtained at the critical limit. These results complete the gap that was lacking in obtaining all the critical exponents associated with the phase transition of a Kuramoto-type model.

Thermodynamics aspects of noise-induced phase synchronization.

In this article, we present an approach for the thermodynamics of phase oscillators induced by an internal multiplicative noise. We analytically derive the free energy, entropy, internal energy, and specific heat. In this framework, the formulation of the first law of thermodynamics requires the definition of a synchronization field acting on the phase oscillators. By introducing the synchronization field, we have consistently obtained the susceptibility and analyzed its behavior. This allows us to characterize distinct phases in the system, which we have denoted as synchronized and parasynchronized phases, in analogy with magnetism. The system also shows a rich complex behavior, exhibiting ideal gas characteristics for low temperatures and susceptibility anomalies that are similar to those present in complex fluids such as water.

Performance Evaluation of a Sensor Network Synchronization Scheme based on Noise Induced Phase Synchronization

Performance Evaluation of a Sensor Network Synchronization Scheme based on Noise Induced Phase Synchronization

Natural Synchronization of Wireless Sensor Networks by Noise-Induced Phase Synchronization Phenomenon

SUMMARY We propose a natural synchronization scheme for wireless uncoupled devices, without any signal exchange among them. Our proposed scheme only uses natural environmental fluctuations, such as the temperature or humidity of the air, the environmental sounds, and so on, for the synchronization of the uncoupled devices. This proposed synchronization is realized based on the noise-induced synchronization phenomenon, uncoupled nonlinear oscillators synchronize with each other only by adding identical common noises to each of them. Based on the theory of this phenomenon, the oscillators can also be synchronized by noise sequences, which are not perfectly identical signals. Since the environmental natural fluctuations collected at neighboring locations are similar to each other and cross-correlation becomes high, our proposed scheme enabling synchronization only by natural environmental fluctuations can be realized. As an application of this proposed synchronization, we introduce wireless sensor networks, for which synchronization is important for reducing power consumption by intermittent data transmission. We collect environmental fluctuations using the wireless sensor network devices. Our results show that the wireless sensor network devices can be synchronized only by the independently collected natural signals, such as temperature and humidity, at each wireless sensor device.

Dispersal and noise: Various modes of synchrony in ecological oscillators

We use the theory of noise-induced phase synchronization to analyze the effects of dispersal on the synchronization of a pair of predator-prey systems within a fluctuating environment (Moran effect). Assuming that each isolated local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive a Fokker-Planck equation describing the evolution of the probability density for pairwise phase differences between the oscillators. In the case of common environmental noise, the oscillators ultimately synchronize. However the approach to synchrony depends on whether or not dispersal in the absence of noise supports any stable asynchronous states. We also show how the combination of partially correlated noise with dispersal can lead to a multistable steady-state probability density.

NOISE-INDUCED PHASE SYNCHRONIZATION AMONG ANALOG MOS OSCILLATOR CIRCUITS

In this paper, we experimentally demonstrate noise-induced phase synchronization among multiple electrical oscillator circuits constructed by discrete MOS devices, where multiple nonlinear oscillators can be synchronized with each other when they accept common pulse perturbations randomly distributed in time. We also show that nonidentical oscillator circuits have the same peak frequency in a power spectrum when they receive a common perturbation.

Noise-Induced Phase Synchronization among Simple Digital Counters

We demonstrate noise-induced phase synchronization among simple digital counters, aiming at its practical application to phase synchronization among isolated digital systems (driven by precise clock sources) accepting common noisy pulse sequences. We employ a simple digital up-counter where i) relaxation oscillations in nonlinear analog oscillators are emulated by linear counting and carry overflow in a low-bit digital counter and ii) the counter value, which is equivalent to the phase of the digitally emulated oscillator, is increased by the precise base clocks, as well as by external noisy pulses, and the autonomous increase of the value (by the base clock) is inhibited by the noisy pulses, depending on the phase of the counter at which the pulse is given. Through extensive Verilog simulations, we demonstrate that the proposed digital counters can be synchronized by applying a common noise sequence, even if initial values of both the counters and phases of the counter's base clocks have different values.

Effects of Demographic Noise on the Synchronization of a Metapopulation in a Fluctuating Environment

We use the theory of noise-induced phase synchronization to analyze the effects of demographic noise on the synchronization of a metapopulation of predator-prey systems within a fluctuating environment (Moran effect). Treating each local predator-prey population as a stochastic urn model, we derive a Langevin equation for the stochastic dynamics of the metapopulation. Assuming each local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive the steady-state probability density for pairwise phase differences between oscillators, which is then used to determine the degree of synchronization of the metapopulation.

Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise

We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system.

Analysis of noise-induced phase synchronization in nervous systems: from algorithmic perspective

In many cases, a key step in neuronal information processing is phase synchronization of neurons (as oscillators). Substantial evidence suggests that an universal mechanism is behind the synchronization. Recently, stochastic equations were proposed to model the synchronization. However, it is unclear what force ultimately drives this universal mechanism. From algorithmic perspective, we analyze solutions of these stochastic equations. The result enhances the current analysis for the phase synchronization; importantly, it shows that noise is the ultimate driving force.

Geometric framework for phase synchronization in coupled noisy nonlinear systems

A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behavior through a change of stability via a Hopf bifurcation entails the spontaneous appearance of a gauge structure in the system, arising from the evolution of the slow dynamics, but induced by the fast variables. The conditions for the oscillators to be synchronised in phase are obtained. The role of weak noise appears to be to drive the system towards a more synchronized behavior. Our analysis provides a framework to explain recent experimental observations on noise-induced phase synchronization in coupled nonlinear systems.

Noise Induced Phase Synchronization of a General Class of Limit Cycle Oscillators

We consider the effect of weak additive noise to a general class of limit cycle oscillators. Employing phase reduction method, the largest Lyapunov exponent of the noise driven oscillators are shown to be negative for a broad class of oscillators, which implies that identical limit cycle oscillators driven by a common additive noise can achieve phase synchronization without direct mutual interactions. Generalization of the results including the effect of colored noise and the effect of noise to spatially extended systems are also discussed.

Understanding synchronization induced by “common noise”

Noise-induced synchronization refers to the phenomenon where two uncoupled, independent nonlinear oscillators can achieve synchronization through a “common” noisy forcing. Here, “common” means identical. However, “common noise” is a construct which does not exist in practice. Noise by nature is unique and two noise signals cannot be exactly the same. How to justify and understand this central concept in noise-induced synchronization? What is the relation between noise-induced synchronization and the usual chaotic synchronization? Here we argue and demonstrate that noise-induced synchronization is closely related to generalized synchronization as characterized by the emergence of a functional relation between distinct dynamical systems through mutual interaction. We show that the same mechanism applies to the phenomenon of noise-induced (or chaos-induced) phase synchronization.

Robustness of the Noise-Induced Phase Synchronization in a General Class of Limit Cycle Oscillators

We show that a wide class of uncoupled limit-cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven synchronizing state. The result shows that such a synchronization can be achieved in a broad class of oscillators with little constraint on their intrinsic property. On the other hand, the leaky integrate-and-fire neuron oscillators do not belong to this class, generating intermittent phase slips according to a power law distribution of their intervals.

Noise-induced synchronization for phase turbulence

Phase turbulence is suppressed by applying common noise additively to the Kuramoto–Sivashinsky type equation, and the noise-induced phase synchronization is realized. The noise strength necessary for the suppression of phase turbulence is evaluated theoretically.

Experimental study of noise-induced phase synchronization in vertical-cavity lasers.

We report the experimental evidence of noise-induced phase synchronization in a vertical-cavity laser. The polarized laser emission is entrained with the input periodic pump modulation when an optimal amount of white, Gaussian noise is applied. We characterize the phenomenon, evaluating the average frequency of the output signal and the diffusion coefficient of the phase difference variable. Their values are roughly independent of the different wave forms of periodic input, provided that a simple condition for the amplitudes is satisfied. The experimental results are compared with numerical simulations of a Langevin model.

NOISE-INDUCED PHASE SYNCHRONIZATION: THEORETICAL AND EXPERIMENTAL RESULTS

The beneficial role fluctuations can play in the process of phase synchronization is analyzed in terms of a model with binary input and output signals. Special attention is paid to the relation between noise-induced phase synchronization and the well-known phenomenon of stochastic resonance. Analytic predictions are compared with experimental data from a vertical cavity surface emitting laser. Various measures for aperiodic stochastic resonance, frequency entrainment and stochastic phase synchronization reveal a satisfactory agreement between theory and experiment.

Frequency and phase synchronization in stochastic systems.

The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and compared with each other with special attention paid to their robustness with respect to noise. We review the results of an analytic approach describing noise-induced phase synchronization in a thermal two-state system. In this context exact expressions for the mean frequency and the phase diffusivity are obtained that together determine the average length of locking episodes. A recently proposed method to quantify frequency synchronization in noisy potential systems is presented and exemplified by applying it to the periodically driven noisy harmonic oscillator. Since this method is based on a threshold crossing rate pioneered by Rice the related phase velocity is termed the Rice frequency. Finally, we discuss the relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator.

Noise-induced phase synchronization and synchronization transitions in chaotic oscillators.

Whether common noise can induce complete synchronization in chaotic systems has been a topic of great relevance and long-standing controversy. We first clarify the mechanism of this phenomenon and show that the existence of a significant contraction region, where nearby trajectories converge, plays a decisive role. Second, we demonstrate that, more generally, common noise can induce phase synchronization in nonidentical chaotic systems. Such a noise-induced synchronization and synchronization transitions are of special significance for understanding neuron encoding in neurobiology.

Noise-induced phase synchronization enhanced by dichotomic noise.

We study the nonlinear response of a stochastic bistable system driven by both a weak periodic signal and a dichotomic noise in terms of stochastic phase synchronization. We show that the effect of noise-induced phase synchronization can be significantly enhanced by the addition of a dichotomic noise.