Doubly stochastic coherence in complex neuronal networks

White-noise-induced double coherence resonances in reduced Hodgkin-Huxley neuron model near subcritical Hopf bifurcation

Coherence resonance (CR) describes a counterintuitive phenomenon in which the optimal oscillatory responses in nonlinear systems are shaped by a suitable noise amplitude. This phenomenon has been observed in neural systems. In this research, the generation of double coherence resonances (DCRs) due to white noise is investigated in a three-dimensional reduced Hodgkin-Huxley neuron model with multiple-timescale feature. We show that additive white noise can induce DCRs from the resting state near a subcritical Hopf bifurcation. The appearance of DCRs is related to the changes of the firing pattern aroused by the increases of the noise amplitude. The underlying dynamical mechanisms for the appearance of the DCRs and the changes of the firing pattern are interpreted using the phase space analysis and the dynamics of the stable focus-node near the subcritical Hopf bifurcation. We find that the multiple-timescale dynamics is essential for generating the DCRs and different firing patterns. The results not only present a case in which noise can induce DCRs near a Hopf bifurcation but also provide its dynamical mechanism, which enriches the phenomena in nonlinear dynamics and provides further understanding on the roles of noise in neural systems with multiple-timescale feature.

Transition from double coherence resonances to single coherence resonance in a neuronal network with phase noise

The effect of phase noise on the coherence dynamics of a neuronal network composed of FitzHugh-Nagumo (FHN) neurons is investigated. Phase noise can induce dissimilar coherence resonance (CR) effects for different coupling strength regimes. When the coupling strength is small, phase noise can induce double CRs. One corresponds to the average frequency of phase noise, and the other corresponds to the intrinsic firing frequency of the FHN neuron. When the coupling strength is large enough, phase noise can only induce single CR, and the CR corresponds to the intrinsic firing frequency of the FHN neuron. The results show a transition from double CRs to single CR with the increase in the coupling strength. The transition can be well interpreted based on the dynamics of a single neuron stimulated by both phase noise and the coupling current. When the coupling strength is small, the coupling current is weak, and phase noise mainly determines the dynamics of the neuron. Moreover, the phase-noise-induced double CRs in the neuronal network are similar to the phase-noise-induced double CRs in an isolated FHN neuron. When the coupling strength is large enough, the coupling current is strong and plays a key role in the occurrence of the single CR in the network. The results provide a novel phenomenon and may have important implications in understanding the dynamics of neuronal networks.

Intrinsic noise induced coherence resonance in a glow discharge plasma

Experimental evidence of intrinsic noise induced coherence resonance in a glow discharge plasma is being reported. Initially the system is started at a discharge voltage (DV) where it exhibited fixed point dynamics, and then with the subsequent increase in the DV spikes were excited which were few in number and with further increase of DV the number of spikes as well as their regularity increased. The regularity in the interspike interval of the spikes is estimated using normalized variance. Coherence resonance was determined using normalized variance curve and also corroborated by Hurst exponent and power spectrum plots. We show that the regularity of the excitable spikes in the floating potential fluctuation increases with the increase in the DV, up to a particular value of DV. Using a Wiener filter, we separated the noise component which was observed to increase with DV and hence conjectured that noise can play an important role in the generation of the coherence resonance. From an anharmonic oscillator equation describing ion acoustic oscillations, we have been able to obtain a FitzHugh-Nagumo like model which has been used to understand the excitable dynamics of glow discharge plasma in the presence of noise. The numerical results agree quite well with the experimental results.

Enhanced corticomuscular coherence by external stochastic noise

Noise can have beneficial effects as shown by the stochastic resonance (SR) phenomenon which is characterized by performance improvement when an optimal noise is added. Modern attempts to improve human performance utilize this phenomenon. The purpose of the present study was to investigate whether performance improvement by addition of optimum noise (ON) is related to increased cortical motor spectral power (SP) and increased corticomuscular coherence. Eight subjects performed a visuomotor task requiring to compensate with the right index finger a static force (SF) generated by a manipulandum on which Gaussian noise was applied. The finger position was displayed on-line on a monitor as a small white dot which the subjects had to maintain in the center of a green bigger circle. Electroencephalogram from the contralateral motor area, electromyogram from active muscles and finger position were recorded. The performance was measured by the mean absolute deviation (MAD) of the white dot from the zero position. ON compared to the zero noise condition induced an improvement in motor accuracy together with an enhancement of cortical motor SP and corticomuscular coherence in beta-range. These data suggest that the improved sensorimotor performance via SR is consistent with an increase in the cortical motor SP and in the corticomuscular coherence.

Synchronization and stochastic resonance of the small-world neural network based on the CPG

According to biological knowledge, the central nervous system controls the central pattern generator (CPG) to drive the locomotion. The brain is a complex system consisting of different functions and different interconnections. The topological properties of the brain display features of small-world network. The synchronization and stochastic resonance have important roles in neural information transmission and processing. In order to study the synchronization and stochastic resonance of the brain based on the CPG, we establish the model which shows the relationship between the small-world neural network (SWNN) and the CPG. We analyze the synchronization of the SWNN when the amplitude and frequency of the CPG are changed and the effects on the CPG when the SWNN's parameters are changed. And we also study the stochastic resonance on the SWNN. The main findings include: (1) When the CPG is added into the SWNN, there exists parameters space of the CPG and the SWNN, which can make the synchronization of the SWNN optimum. (2) There exists an optimal noise level at which the resonance factor Q gets its peak value. And the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the noise intensity. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.

Information transmission in a neuron-astrocyte coupled model

A coupled model containing two neurons and one astrocyte is constructed by integrating Hodgkin-Huxley neuronal model and Li-Rinzel calcium model. Based on this hybrid model, information transmission between neurons is studied numerically. Our results show that when the successive spikes are produced in neuron 1 (N1), the bursting-like spikes (BLSs) occur in two neurons simultaneously during the spikes being transferred to neuron 2 (N2). The existence of the astrocyte and a higher expression level of mGluRs facilitate the occurrence of BLSs, but the rate of occurrence is not sensitive to the parameters. Furthermore, time delay τ occurs during the information transmission, and τ is almost independent of the effect of the astrocyte. Additionally, we found that low coupling strength may result in the distortion of the information, and this distortion is also proven to be almost independent of the astrocyte.