Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons

The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied. When the neurons are set in the subthreshold regime near the firing threshold, the additive noise induces limit cycles. The coherence of the system is optimized by the noise. The coupling of the network can enhance CR in two different ways. In particular, when the coupling is strong enough, the synchronization of the system is induced and optimized by the noise. This synchronization leads to a high and wide plateau in the local CR curve. A bell-shaped curve is found for the peak height of power spectra of the spike train, being significantly different from a monotonic behavior for the single neuron. The local-noise-induced limit cycle can evolve to a refined spatiotemporal order through the dynamical optimization among the autonomous oscillation of an individual neuron, the coupling of the network, and the local noise.     

Collective temporal coherence for subthreshold signal encoding on a stochastic small-world Hodgkin-Huxley neuronal network

We study the collective temporal coherence of a small-world network of coupled stochastic Hodgkin-Huxley neurons. Previous reports have shown that network coherence in response to a subthreshold periodic stimulus, thus subthreshold signal encoding, is maximal for a specific range of the fraction of randomly added shortcuts relative to all possible shortcuts, p, added to an initially locally connected network. We investigated this behavior further as a function of channel noise, stimulus frequency and coupling strength. We show that temporal coherence peaks when the frequency of the external stimulus matches that of the intrinsic subthreshold oscillations. We also find that large values of the channel noise, corresponding to small cell sizes, increases coherence for optimal values of the stimulus frequency and the topology parameter p. For smaller values of the channel noise, thus larger cell sizes, network coherence becomes insensitive to these parameters. Finally, the degree of coupling between neurons in the network modulates the sensitivity of coherence to topology, such that for stronger coupling the peak coherence is achieved with fewer added short cuts.     

Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons

We study nontrivial effects of noise on synchronization and coherence of a chaotic Hodgkin-Huxley model of thermally sensitive neurons. We demonstrate that identical neurons which are not coupled but subjected to a common fluctuating input (Gaussian noise) can achieve complete synchronization when the noise amplitude is larger than a threshold. For nonidentical neurons, noise can induce phase synchronization. Noise enhances synchronization of weakly coupled neurons. We also find that noise enhances the coherence of the spike trains. A saddle point embedded in the chaotic attractor is responsible for these nontrivial noise-induced effects. Relevance of our results to biological information processing is discussed.     

Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin-Huxley neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the spiking coherence of Newman-Watts small-world networks of stochastic Hodgkin-Huxley (HH) neurons and investigate the relations between the coupling strength and channel noise when coherence resonance (CR) occurs. It is found that, when the amplitude of TPCS is varied, the spiking induced by channel noise can exhibit CR and coherence bi-resonance (CBR), and the CR moves to a smaller patch area (bigger channel noise) when the amplitude increases; when the frequency of TPCS is varied, the intrinsic spiking can exhibit CBR and multiple CR, and the CR always occurs when the frequency is equal to or multiple of the spiking period, manifesting as the locking between the frequencies of the intrinsic spiking and the coupling strength. These results show that TPCS can greatly enhance and optimize the intrinsic spiking coherence, and favors the spiking with bigger channel noise to exhibit CR. This implies that, compared to constant coupling strength, TPCS may play a more efficient role for improving the time precision of the information processing in stochastic neuronal networks.     

Stochastic resonance in an ion channel following the non-Arrhenius gating rate

Stochastic resonance (SR) is a novel cooperative phenomenon occurring in nonlinear systems due to coupling of an ambient noise and an external signal. Biological systems may use SR mechanism to detect the signal efficiently from an external environment. A number of studies have addressed the SR in artificial ion channels considering external voltages as noises. More important than these external noises is the internal, thermal noise which changes the channel conformations essential for biological functions. In this work, we consider that the channel gating rates follow a non-Arrhenius temperature dependence derived from experimental data of a real biological channel. Using the Monte-Carlo simulations, we find that in this channel SR occurs near a physiological temperature in a very distinctive manner compared with that for the Arrhenius gating model.     

Theory of Dynamics In-Phase Locking and Quasi-Period Synchronization in Two Mutually Coupled Multi-Quantum-Well Lasers

We study dynamics in two mutually coupling multi-quantum-well lasers. We carry out theoretical and numerical analysis of synchronization, anti-synchronization, in-phase locking in the two identical lasers but detuning, in detain. It is proved that the coupling level determines stability of the lasers by analyzing the eigenvalueequation. Critical case of locking is discussed via the phase difference equation. Quasi-period and stable states in the two lasers are investigated via varying the current, detuning and coupling level.     

Phase locking and chaotic synchronization in an array of three lasers

A linear array of three lasers that are coupled mutually in space is investigated. It is shown that the phase of the laser fields is locked with intermediate coupling while the laser intensities are totally chaotic and chaotically synchronized. When the intensities of lasers reenter the regime of chaotic synchronization at smaller coupling constant, the laser fields show low degree of phase locking. The phase differences in the fields between three lasers show rich patterns when the coupling is changed. Received 3 August 2001 and Received in final form 27 September 2001     

Phase synchronization and its transition in two coupled bursting neurons: theoretical and numerical analysis

It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris--Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.     

Constructive influence of noise-flatness in correlation ratchets

The influence of noise-flatness on overdamped motion of Brownian particles in a 1D periodic system with a simple sawtooth potential subjected to both unbiased thermal noise and three-level telegraph noise is considered. The exact formula for the stationary probability flux (current) is presented. The phenomenon of multiple current reversals and some topological properties of the hypersurface of zero current in the parameter space of noises are investigated and illustrated by phase diagrams. The conditions for the existence of four current reversals versus the switching rate of nonequilibrium noise are given. An alternative interpretation of the results in terms of cross-correlation between two dichotomous noises is presented.     

低分析频率压缩光的实验制备

基于PPKTP晶体的阈值以下光学参量振荡(OPO)过程,制备了共振于铷原子D1线795 nm的压缩真空态光场,研究了分析频率处于千赫兹范围的主要噪声来源,特别是795 nm激光及其二次谐波397.5 nm激光在晶体内吸收引起的非线性损耗增加和系统热不稳定的问题(397.5 nm激光处于PPKTP晶体透光范围边缘,具有高于其他波长数倍的吸收系数).以795 nm和1064 nm为例,分析了非线性损耗及晶体内热效应对压缩度的影响.受限于以上因素,795 nm压缩光很难得到1064 nm波段同样的压缩度.探测系统中的噪声耦合则限制了压缩频带.实验上对分析频率为千赫兹的经典噪声进行了有效控制,通过使用真空注入的OPO、垂直偏振及反向传输的腔长锁定光、低噪声的平衡零拍探测器、高稳定度的实验系统及量子噪声锁定等方法,最终在2.6—100 kHz的分析频段得到了约2.8 dB的795 nm压缩真空.该压缩光可用作磁场测量系统的探测光以提高测量灵敏度.     

Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators

We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models.     

Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Resonance assisted synchronization of coupled oscillators: frequency locking without phase locking

Frequency locking without phase locking of two coupled nonlinear oscillators is experimentally demonstrated. This synchronization regime is found for two coupled laser modes, beyond the phase-locking range fixed by Adler's equation, because of a resonance mechanism. Specifically, we show that the amplitudes of the two modes exhibit strong fluctuations that produce average frequency synchronization, even if the instantaneous phases are unlocked. The experimental results are in good agreement with a theoretical model.     

Effects of the network structure and coupling strength on the noise-induced response delay of a neuronal network

The Hodgkin-Huxley (H-H) neuron model driven by stimuli just above threshold shows a noise-induced response delay with respect to time to the first spike for a certain range of noise strengths, an effect called “noise delayed decay” (NDD). We study the response time of a network of coupled H-H neurons, and investigate how the NDD can be affected by the connection topology of the network and the coupling strength. We show that the NDD effect exists for weak and intermediate coupling strengths, whereas it disappears for strong coupling strength regardless of the connection topology. We also show that although the network structure has very little effect on the NDD for a weak coupling strength, the network structure plays a key role for an intermediate coupling strength by decreasing the NDD effect with the increasing number of random shortcuts, and thus provides an additional operating regime, that is absent in the regular network, in which the neurons may also exploit a spike time code.     

Channel noise-induced temporal coherence transitions and synchronization transitions in adaptive neuronal networks with time delay

Using spike-timing-dependent plasticity (STDP), we study the effect of channel noise on temporal coherence and synchronization of adaptive scale-free Hodgkin-Huxley neuronal networks with time delay. It is found that the spiking regularity and spatial synchronization of the neurons intermittently increase and decrease as channel noise intensity is varied, exhibiting transitions of temporal coherence and synchronization. Moreover, this phenomenon depends on time delay, STDP, and network average degree. As time delay increases, the phenomenon is weakened, however, there are optimal STDP and network average degree by which the phenomenon becomes strongest. These results show that channel noise can intermittently enhance the temporal coherence and synchronization of the delayed adaptive neuronal networks. These findings provide a new insight into channel noise for the information processing and transmission in neural systems.     

Noise enhanced phase synchronization and coherence resonance in sets of chaotic oscillators with weak global coupling

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic R?ssler oscillators are verified experimentally with an array of chaotic electrochemical oscillators.     

Suppression of Chaos and Phase Locking in Two Coupled Nonidentical Neurons under Periodic Input

Dynamical behaviour of two coupled neurons with at least one of them being chaotic is presented. Bifurcation diagrams and Lyapunov exponents are calculated to diagnose the dynamical behaviour of the coupled neurons with the increasing coupling strength. It is found that when the coupling strength increases, a chaotic neuron can be controlled by the coupling between neurons. At the same time, phase locking is studied by the maxima of the differences of instantaneous phases and average frequencies between two coupled neurons, and the inherent connection of phase locking and the suppression of chaos is formulated. It is observed that the onset of phase locking is closely related to the suppression of chaos. Finally, a way for suppression of chaos in two coupled nonidentical neurons under periodic input is suggested.     

Study on phase synchronization of stochastic chaotic system

This paper detects and characterizes the diverse roles played by bounded noise in chaotic phase synchronization (CPS) of weakly coupled nonlinear stochastic systems. Analysis of a paradigmatic model of two bidirectional coupled three-level food chains is carried out by various statistical measures such as Shannon entropy and mutual information. The results indicate that inside the synchronous regime, CPS is considerably reduced under the influence of bounded noise; near the onset of phase synchronization, temporal phase locking is diversely changed with the increase of noise, i.e., either weak or strong noise also degrades the degree of CPS, while intermediate noise enhances CPS remarkably, and an optimal noise intensity is detected that maximizes the enhancement.     

Analysis of phase synchronization of chaotic oscillations in terms of symbolic CTQ-analysis

The application of symbolic CTQ-analysis for studying synchronization of chaotic oscillations is considered. This approach differs substantially from its analogs since it makes it possible to diagnose and measure quantitatively the characteristics of intermittency regimes in synchronization of chaotic systems and, hence, to analyzer the temporal structure of synchronization. The application of the symbolic analysis apparatus based on the T alphabet to systems with phase locking and synchronization of time scales is demonstrated for the first time. As an example, a complex system of two mutually coupled nonidentical Rössler oscillators in the helical chaos regime with attractors having an ill-conditioned phase is considered. The results show that the method considered here makes it possible to reliably diagnose synchronism sooner than a phase locking and/or time-scale synchronization threshold is detected.     

Coherence resonance and synchronization of Hindmarsh-Rose neurons with noise

Noise effects on coherence resonance and synchronization of Hindmarsh-Rose (HR) neuron model are studied. The coherence resonance of a single HR neuron with Gaussian white noise added to the membrane potential is investigated in situations before, near and after the Hopf bifurcation, separately, with the external direct current as a bifurcation parameter. It is shown that even though there is no coupling between neurons, uncoupled identical HR neurons driven by a common noise can achieve complete synchronization when the noise intensity is higher than a critical value. Furthermore, noise also enhances complete synchronization of weakly coupled neurons. It is concluded that synchronization in bursting neurons is easier to be induced than in spiking ones, and coupling enhances the sensitivity of synchronization of neurons to noise stimulus.