Internal signal transmission in one-way coupled excitable system: noise and coupling effects

Cascade-enhanced transport efficiency of biochemical systems

Recent developments in nonequilibrium thermodynamics, known as thermodynamic uncertainty relations, limit the system's accuracy by the amount of free-energy consumption. A transport efficiency, which can be used to characterize the capacity to control the fluctuation by means of energy cost, is a direct result of the thermodynamic uncertainty relation. According to our previous research, biochemical systems consume much lower energy cost by noise-induced oscillations to keep almost equal efficiency to maintain precise processes than that by normal oscillations. Here, we demonstrate that the performance of noise-induced oscillations propagating can be further improved through a cascade reaction mechanism. It has been discovered that it is possible to considerably enhance the transport efficiency of the biochemical reactions attained at the terminal cell, allowing the cell to use the cascade reaction mechanism to operate more precisely and efficiently. Moreover, an optimal reaction coupling strength has been predicted to maximize the transport efficiency of the terminal cell, uncovering a concrete design strategy for biochemical systems. By using the local mean field approximation, we have presented an analytical framework by extending the stochastic normal form equation to the system perturbed by external signals, providing an explanation of the optimal coupling strength.

Cooperative effect of random and time-periodic coupling strength on synchronization transitions in one-way coupled neural system: mean field approach

The cooperative effect of random coupling strength and time-periodic coupling strengh on synchronization transitions in one-way coupled neural system has been investigated by mean field approach. Results show that cooperative coupling strength (CCS) plays an active role for the enhancement of synchronization transitions. There exist an optimal frequency of CCS which makes the system display the best CCS-induced synchronization transitions, a critical frequency of CCS which can not further affect the CCS-induced synchronization transitions, and a critical amplitude of CCS which can not occur the CCS-induced synchronization transitions. Meanwhile, noise intensity plays a negative role for the CCS-induced synchronization transitions. Furthermore, it is found that the novel CCS amplitude-induced synchronization transitions and CCS frequency-induced synchronization transitions are found.

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.

Propagation of spiking regularity and double coherence resonance in feedforward networks

We investigate the propagation of spiking regularity in noisy feedforward networks (FFNs) based on FitzHugh-Nagumo neuron model systematically. It is found that noise could modulate the transmission of firing rate and spiking regularity. Noise-induced synchronization and synfire-enhanced coherence resonance are also observed when signals propagate in noisy multilayer networks. It is interesting that double coherence resonance (DCR) with the combination of synaptic input correlation and noise intensity is finally attained after the processing layer by layer in FFNs. Furthermore, inhibitory connections also play essential roles in shaping DCR phenomena. Several properties of the neuronal network such as noise intensity, correlation of synaptic inputs, and inhibitory connections can serve as control parameters in modulating both rate coding and the order of temporal coding.

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.

Oscillation propagation in neural networks with different topologies

In light of the issue of oscillation propagation in neural networks, various topologies of FitzHugh-Nagumo neuron populations are investigated. External Gaussian white noise is injected into the first neuron only. Before the oscillation spreads to the other neurons in the network, some of the inherent stochasticity within the noise-induced oscillation of the first neuron is filtered out due to the neuron's nonlinear dynamics. Both the temporal and the spatial coherence of the evoked activity's propagation are analyzed in conjunction with the network topology randomness p, the coupling strength between neurons g, and the noise amplitude D. The temporal periodicity of the global neural network presents a typical coherence biresonance (CBR) characteristic with regard to the noise intensity. The network topology randomness exerts different influences on the resonance effects for different coupling strength regimes. At an intermediate coupling strength, the random shortcuts reinforce the interactions between the neurons, and then more stochasticity in the firings of the first neuron spreads within the network. Consequently, CBR is decreased with the increase of the network topology randomness. At a large coupling strength, the random shortcuts assist the nonlinearity in impairing the stochastic components, and consequently help to enhance the resonance effects, which differed significantly from previous related work. However, the degree of the spatial synchronization of the systems increases monotonically as the network topology randomness increases at any coupling strength.

Effective phase dynamics of noise-induced oscillations in excitable systems

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.

The selectivity of noise and coupling for coherence biresonance and array-enhanced coherence biresonance in coupled neural systems

The selectivity of noise and coupling for coherence biresonance (CBR) and array-enhanced coherence biresonance (AECBR) in coupled neural systems has been investigated. It is shown that, depending on the coupling strength and noise intensity, various coherence behaviors and phenomena are exhibited, including CBR, coherence resonance without tuning, AECBR and undamped signal transmission. There exist optimal coupling and noise regions for the occurrence of CBR and AECBR in the transmission of noise-induced oscillations (NIOs).

Spontaneously periodic wave generation in coupled excitable media

We studied a modified reaction-diffusion model theoretically by coupling two ideal excitable media systems. In the simulated homogeneous system, we observed the propagation of reaction-diffusion wave trains that required no external force after the initial stimulation. We investigated the dependence of the system's oscillation patterns on model parameters, and we discussed the influence of the different dynamic constants of the individual coupled systems on the dynamics of the coupled systems. Some complex two-dimensional patterns generated by our model are shown. We also found similar phenomena in the models for catalytic CO oxidation on Pt(110), and for cardiac tissue.

Spiking regularity in a noisy small-world neuronal network

The regularity of spiking oscillations is studied in the networks with different topological structures. The network is composed of coupled Fitz-Hugh-Nagumo neurons driven by colored noise. The investigation illustrates that the spike train in both the regular and the Watts-Strogatz small-world neuronal networks can show the best regularity at a moderate noise intensity, indicating the existence of coherence resonance. Moreover, the temporal coherence of the spike train in the small-world network is superior to that in a regular network due to the increase of the randomness of the network topology. Besides the noise intensity, the spiking regularity can be optimized by tuning the randomness of the network topological structure or by tuning the correlation time of the colored noise. In particular, under the cooperation of the small-world topology and the correlation time, the spike train with good regularity could sustain a large magnitude of the local noise.