Multiple Coherence Resonance Research Articles

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance.

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

Binocular rivalry subjected to noises and time delay

Neural systems are inherently noisy and time-delay, and these effects influence our perception from time to time. This is particularly apparent in binocular rivalry, where our perception alternates between competing stimuli shown to the two eyes. Here, we investigated the binocular rivalry behavior under the action of time delay and two noise sources. Our numerical results find that (i) the time delay and additive noise make the stationary probability distribution function of the binocular rivalry jump among two, three and four stabilities, breaking or maintaining balance of the binocular rivalry; (ii) the dependence of mean first passage time on multiplicative noise intensity shows a maximum, i.e., noise enhance perceptual stability, while the stability can be enhanced many times by the time delay; (iii) the characteristic correlation time not only exhibits a underdamped oscillation behavior as a function of delay time (i.e., multiple coherence resonances), but also shows a nonmonotonic behavior with the additive noise intensity. These findings have the significant implication for understanding and controlling perception alteration from a new perspective.

Multiple coherence resonances evoked from bursting and the underlying bifurcation mechanism

Coherence resonance (CR), which is typical nonlinear phenomenon that noise plays construct roles, has been widely investigated in single neurons at resting state instead of bursting behavior when noise free. In the present paper, multiple CRs evoked from bursting instead of resting state and the underlying bifurcation mechanism are studied in a theoretical neuron model composed of fast subsystem and slow variable, which is very important for the bursting neurons receiving strong synaptic noise in the central nervous system. With increasing noise intensity within a range, the bursting period decreases to induce the burst number increases firstly and then becomes irregular, which results in the increase firstly and then decrease in the corresponding peak of the power spectrum of membrane potentials, i.e., CR is evoked from bursting instead of resting state. With further increasing noise intensity, two other peaks exhibit CR phenomenon, one at middle frequency and middle noise intensity and the other at large frequency and strong noise intensity, which shows that multiple CRs are evoked from bursting. Furthermore, the bifurcation mechanism of the latter two resonant peaks is acquired with fast–slow variable dissection method. With increasing the value of slow variable, the fast subsystem exhibits a fold bifurcation of limit cycle and a subcritical Hopf bifurcation to a stable focus, and the imaginary part of the characteristic value of the focus increases, which implies that spikes evoked from the focus exhibit increasing frequency. The trajectory of the deterministic bursting in phase space locates between the two bifurcations and alternates between the coexisting limit cycle and focus of the fast subsystem. With increasing noise intensity, the value of slow variable of the stochastic bursting increases and moves to a range of the focus of the fast subsystem, and the spikes of the stochastic bursting are evoked from the focus by noise. Therefore, the stronger the noise intensity, the larger the value of slow variable, and the higher frequency the spikes, due to the changes of characteristic values, which is the cause that the peaks with middle and high frequency appear at middle and strong noise intensity, respectively. The results of the present paper extend the concept of CR to multiple CRs evoked from bursting, provide the bifurcation mechanism underlying the multiple CRs, and imply multiple chances to utilize noise to enhance information of bursting neurons.

Electric activities of time-delay memristive neuron disturbed by Gaussian white noise.

To study the effect of electromagnetic induction on the electric activities of neuron, memristive neuron models have been proposed by coupling membrane potential with magnetic flux. In this paper, on the basis of memristive Hindmarsh-Rose neuron model, time-delay memristive Hindmarsh-Rose neuron model is described and the responses of neuron in electrical activities are detected. The effect of time-delay on the dynamical behaviors of the neuron is discussed and the transition of electrical activities of the neuron is investigated with the change of noise intensity. It is found that, both the time-delay and the noise have effect on the electrical activities of the neuron. Especially, by selecting appropriate parameters, the noise not only can excite neuron from quiescent state to bursting state, but also can suppress the electrical activities in neuron during certain discharge period. Results mean that multiple modes and coherence resonance can be observed by changing the size of time-delay or the noise intensity, which could be associated with memory effect and self-adaption in neurons.

Coherence resonance in a modified FHN neuron with autapse and phase noise

The influences of phase noise together with autapse on the resonance dynamics in a modified FitzHugh–Nagumo (FHN) neuron are investigated by numerical simulation, where the neuronal model is in the environment of electromagnetic induction. First, it is found that phase noise can induce double coherence resonances, which is further confirmed to be robust to the feedback gain of induction current. Surprisingly, by individually changing the period of phase noise and the feedback gain, a resonance-like behavior also appears. Subsequently, the significant phenomenon of autapse-induced multiple coherence resonances is discovered. Moreover, the phenomenon of multiple coherence resonances can emerge at a broad parameter range of autaptic strength and autaptic delay.

Effect of Channel Block on Multiple Coherence Resonance Induced by Time Delay in Adaptive Neuronal Networks with Spike-Timing-Dependent Plasticity

In this paper, we study effect of channel block (CB) on multiple coherence resonance (MCR) in adaptive scale-free Hodgkin–Huxley neuronal networks with spike-timing-dependent plasticity (STDP). It is found that potassium CB suppresses MCR, but sodium CB can enhance MCR, and there is optimal sodium CB level by which MCR becomes most pronounced. In addition, STDP has a significant influence on the effect of CB on MCR. As adjusting rate [Formula: see text] of STDP increases, for potassium CB there is proper [Formula: see text] by which MCR is most pronounced; however, for sodium CB MCR is reduced. These findings could provide a new insight into effect of CB on information processing in neural systems.

Spike-timing-dependent plasticity optimized coherence resonance and synchronization transitions by autaptic delay in adaptive scale-free neuronal networks

In this paper, we numerically study the effect of spike-timing-dependent plasticity on multiple coherence resonance and synchronization transitions induced by autaptic time delay in adaptive scale-free Hodgkin–Huxley neuron networks. As the adjusting rate Ap of spike-timing-dependent plasticity increases, multiple coherence resonance and synchronization transitions enhance and become strongest at an intermediate Ap value, indicating that there is optimal spike-timing-dependent plasticity that can most strongly enhance the multiple coherence resonance and synchronization transitions. As Ap increases, increasing network average degree has a small effect on multiple coherence resonance, but its effect on synchronization transitions changes from suppressing to enhancing it. As network size is varied, multiple coherence resonance and synchronization transitions nearly do not change. These results show that spike-timing-dependent plasticity can simultaneously optimize multiple coherence resonance and synchronization transitions by autaptic delay in the adaptive scale-free neuronal networks. These findings provide a new insight into spike-timing-dependent plasticity and autaptic delay for the information processing and transmission in neural systems.

Inducement and enhancement of multiple coherence resonances in unidirectionally coupled neural systems: Random and time-periodic coupling strength

The effect of cooperative coupling strength (CCS), i.e., random coupling strength and time-periodic coupling strength, on multiple coherence resonances in unidirectionally coupled neural system has been investigated. Results show that noise, frequency and amplitude play efficient roles for the enhancement of various coherent behaviours. There exist an optimal frequency and an optimal amplitude which make the system to display the best coherent behaviours. Furthermore, the novel coherence biresonance (CBR) induced by frequency of CCS and coherence multiresonances (CMR) induced by amplitude of CCS, are found.

Influences of autapse and channel blockage on multiple coherence resonance in a single neuron

We study how the spiking regularity of a single stochastic Hodgkin–Huxley neuron is effected in the presence of ion channel blocking and autaptic connection. In this study, we consider a chemical autapse expressed by its coupling strength and delay time. It is found that the neuron exhibits multiple coherence resonance (MCR) behavior induced by autaptic time delay at an appropriate level of ion channel blocking and autaptic coupling strength. This MCR behavior increases with the decrement of working potassium ion channels, whereas it decreases or completely disappears with the increment of a fraction of sodium ion channels blocking, regardless of autaptic coupling strength. Furthermore, this behavior is more explicit at intermediate autaptic coupling strength regardless of the ion channel blocking type. We briefly discuss the obtained results with the underlying reasons in terms of ion channel blocking type and autapse parameters. We also showed that ion channel noise, thus membrane patch size, should be at an optimal level to obtain MCR behavior otherwise, this behavior would be destroyed. The obtained results also showed that autaptic time delay is more operative on regularity than its coupling strength regardless of ion channel blocking. Considering the importance of spiking regularity on neuronal information processing, our results may help to understand the intersection of ion channel blocking and autaptic connections of a single neuron.

Formation of Ligno-Polyols: Fact or Fiction

The physical and chemical characteristics of several lignin-polyol blends were investigated by qualitative and quantitative methods from the view of biobased polyurethane applications. Four differently isolated biomass lignins from forestry and agricultural residues were blended with polyester polyol, and one was blended with polyethylene glycol. The isolated products were examined thoroughly to elucidate the subsequent lignin and polyol interactions during the premixing stage of biobased polyurethane formulation. Polyol was detected in lignin even after vigorous washings with several organic solvents and Soxhlet extraction. The experimental data coupled with two-dimensional heteronuclear multiple quantum coherence (HMQC) and nuclear magnetic resonance (NMR) spectroscopy confirmed the formation of ligno-polyols via strong intermolecular attractions, as well as some linkages between several lignin hydroxyl and polyol functional groups.

Multiple coherence resonances and synchronization transitions by time delay in adaptive scale-free neuronal networks with spike-timing-dependent plasticity

In this paper, we numerically study the effect of spike-timing-dependent plasticity (STDP) on multiple coherence resonances (MCR) and synchronization transitions (ST) induced by time delay in adaptive scale-free Hodgkin–Huxley neuronal networks. It is found that STDP has a big influence on MCR and ST induced by time delay and on the effect of network average degree on the MCR and ST. MCR is enhanced or suppressed as the adjusting rate Ap of STDP decreases or increases, and there is optimal Ap by which ST becomes strongest. As network average degree 〈k〉 increases, ST is enhanced and there is optimal 〈k〉 at which MCR becomes strongest. Moreover, for a larger Ap value, ST is enhanced more rapidly with increasing 〈k〉 and the optimal 〈k〉 for MCR increases. These results show that STDP can either enhance or suppress MCR, and there is optimal STDP that can most strongly enhance ST induced by time delay in the adaptive neuronal networks. These findings could find potential implication for the information processing and transmission in neural systems.

Autapse-induced multiple coherence resonance in single neurons and neuronal networks.

We study the effects of electrical and chemical autapse on the temporal coherence or firing regularity of single stochastic Hodgkin-Huxley neurons and scale-free neuronal networks. Also, we study the effects of chemical autapse on the occurrence of spatial synchronization in scale-free neuronal networks. Irrespective of the type of autapse, we observe autaptic time delay induced multiple coherence resonance for appropriately tuned autaptic conductance levels in single neurons. More precisely, we show that in the presence of an electrical autapse, there is an optimal intensity of channel noise inducing the multiple coherence resonance, whereas in the presence of chemical autapse the occurrence of multiple coherence resonance is less sensitive to the channel noise intensity. At the network level, we find autaptic time delay induced multiple coherence resonance and synchronization transitions, occurring at approximately the same delay lengths. We show that these two phenomena can arise only at a specific range of the coupling strength, and that they can be observed independently of the average degree of the network.

Effect of spike-timing-dependent plasticity on coherence resonance and synchronization transitions by time delay in adaptive neuronal networks

In this paper, we numerically study how time delay induces multiple coherence resonance (MCR) and synchronization transitions (ST) in adaptive Hodgkin-Huxley neuronal networks with spike-timing dependent plasticity (STDP). It is found that MCR induced by time delay STDP can be either enhanced or suppressed as the adjusting rate A p of STDP changes, and ST by time delay varies with the increase of A p , and there is optimal A p by which the ST becomes strongest. It is also found that there are optimal network randomness and network size by which ST by time delay becomes strongest, and when A p increases, the optimal network randomness and optimal network size increase and related ST is enhanced. These results show that STDP can either enhance or suppress MCR and optimal STDP can enhance ST induced by time delay in the adaptive neuronal networks. These findings provide a new insight into STDP’s role for the information processing and transmission in neural systems.

Multiple coherence resonance and synchronization transitions induced by autaptic delay in Newman–Watts neuron networks

In this paper, we study the effect of delayed autaptic self-feedback activity on the spiking temporal coherence and spatial synchronization of Newman–Watts networks of stochastic Hodgkin–Huxley neurons. As autaptic delay is varied, the spiking behaviors of the neurons intermittently become synchronous and non-synchronous, and meanwhile they are ordered and disordered, exhibiting both synchronization transitions (ST) and multiple coherence resonance (MCR). Moreover, the autaptic delays for CR and synchronization are close. When coupling strength or network randomness increases, or when channel noise intensity decreases, MCR is enhanced, but ST becomes strongest at optimal coupling strength, network randomness, or channel noise intensity. These results show that autaptic activity can induce both MCR and ST in the neuronal networks. This implies that autaptic activity can simultaneously enhance or reduce the temporal coherence and synchronization of the neuronal network. These findings could find potential implications for the information processing and transmission in neural systems.

Multiple Spatial Coherence Resonances and Spatial Patterns in a Noise-Driven Heterogeneous Neuronal Network

Heterogeneity of the neurons and noise are inevitable in the real neuronal network. In this paper, Gaussian white noise induced spatial patterns including spiral waves and multiple spatial coherence resonances are studied in a network composed of Morris—Lecar neurons with heterogeneity characterized by parameter diversity. The relationship between the resonances and the transitions between ordered spiral waves and disordered spatial patterns are achieved. When parameter diversity is introduced, the maxima of multiple resonances increases first, and then decreases as diversity strength increases, which implies that the coherence degrees induced by noise are enhanced at an intermediate diversity strength. The synchronization degree of spatial patterns including ordered spiral waves and disordered patterns is identified to be a very low level. The results suggest that the nervous system can profit from both heterogeneity and noise, and the multiple spatial coherence resonances are achieved via the emergency of spiral waves instead of synchronization patterns.

Periodic coupling strength-dependent multiple coherence resonance by time delay in Newman–Watts neuronal networks

Recently, multiple coherence resonance induced by time delay has been observed in neuronal networks with constant coupling strength. In this paper, by employing Newman–Watts Hodgkin–Huxley neuron networks with time-periodic coupling strength, we study how the temporal coherence of spiking behavior and coherence resonance by time delay change when the frequency of periodic coupling strength is varied. It is found that delay induced coherence resonance is dependent on periodic coupling strength and increases when the frequency of periodic coupling strength increases. Periodic coupling strength can also induce multiple coherence resonance, and the coherence resonance occurs when the frequency of periodic coupling strength is approximately multiple of the spiking frequency. These results show that for periodic coupling strength time delay can more frequently optimize the temporal coherence of spiking activity, and periodic coupling strength can repetitively optimize the temporal coherence of spiking activity as well. Frequency locking may be the mechanism for multiple coherence resonance induced by periodic coupling strength. These findings imply that periodic coupling strength is more efficient for enhancing the temporal coherence of spiking activity of neuronal networks, and thus it could play a more important role in improving the time precision of information processing and transmission in neural networks.

White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network with type I excitability

White noise-induced pattern formation is studied in a network composed of Morris–Lecar neuronal models with type I excitability and with initial values higher than that of the resting potential. The appearance and disappearance of spiral waves, as well as the transitions between spiral wave patterns with different kinds of complexity characterized by the normalized spatial autocorrelation function, enable changes in the order of the network so as to exhibit a scenario with two or more locally maximal peaks, as can be clearly seen in the signal to noise ratio curves, as the noise intensity is adjusted from small to large in a wide range. A possible physical mechanism of the multiple resonances based on the dynamics of type I excitability and initial values is provided. The potential biological significance of the noise-induced spiral waves is discussed.

Parameter Diversity Induced Multiple Spatial Coherence Resonances and Spiral Waves in Neuronal Network with and Without Noise

Diversity in the neurons and noise are inevitable in the real neuronal network. In this paper, parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated. The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified. The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased. The results suggest that natural nervous system might profit from both parameter diversity and noise, provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.

Multiple firing coherence resonances in excitatory and inhibitory coupled neurons

The impact of inhibitory and excitatory synapses in delay-coupled Hodgkin–Huxley neurons that are driven by noise is studied. If both synaptic types are used for coupling, appropriately tuned delays in the inhibition feedback induce multiple firing coherence resonances at sufficiently strong coupling strengths, thus giving rise to tongues of coherency in the corresponding delay-strength parameter plane. If only inhibitory synapses are used, however, appropriately tuned delays also give rise to multiresonant responses, yet the successive delays warranting an optimal coherence of excitations obey different relations with regards to the inherent time scales of neuronal dynamics. This leads to denser coherence resonance patterns in the delay-strength parameter plane. The robustness of these findings to the introduction of delay in the excitatory feedback, to noise, and to the number of coupled neurons is examined. Mechanisms underlying our observations are revealed, and it is suggested that the regularity of spiking across neuronal networks can be optimized in an unexpectedly rich variety of ways, depending on the type of coupling and the duration of delays.

Spiral Waves and Multiple Spatial Coherence Resonances Induced by Colored Noise in Neuronal Network

Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris—Lecar neurons are studied. Each neuron is at resting state near a saddle-node bifurcation on invariant circle, coupled to its nearest neighbors by electronic coupling. Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity. By calculating spatial structure function and signal-to-noise ratio (SNR), it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered, respectively. SNR manifest multiple local maximal peaks, indicating that the colored noise can induce multiple spatial coherence resonances. The maximal SNR values decrease as the correlation time of the noise increases. These results not only provide an example of multiple resonances, but also show that Gaussian colored noise play constructive roles in neuronal network.