Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Research on discrete memristor-based neural networks has received much attention.However,current research mainly focuses on memristor–based discrete homogeneous neuron networks,while memristor-coupled discrete heterogeneous neuron networks are rarely reported.In this study,a new four-stable discrete locally active memristor is proposed and its nonvolatile and locally active properties are verified by its power-off plot and DC V–I diagram.Based on two-dimensional(2D)discrete Izhikevich neuron and 2D discrete Chialvo neuron,a heterogeneous discrete neuron network is constructed by using the proposed discrete memristor as a coupling synapse connecting the two heterogeneous neurons.Considering the coupling strength as the control parameter,chaotic firing,periodic firing,and hyperchaotic firing patterns are revealed.In particular,multiple coexisting firing patterns are observed,which are induced by different initial values of the memristor.Phase synchronization between the two heterogeneous neurons is discussed and it is found that they can achieve perfect synchronous at large coupling strength.Furthermore,the effect of Gaussian white noise on synchronization behaviors is also explored.We demonstrate that the presence of noise not only leads to the transition of firing patterns,but also achieves the phase synchronization between two heterogeneous neurons under low coupling strength.

Improving Dendritic Neuron Model With Dynamic Scale-Free Network-Based Differential Evolution

Some recent research reports that a dendritic neuron model(DNM)can achieve better performance than traditional artificial neuron networks(ANNs)on classification,prediction,and other problems when its parameters are well-tuned by a learning algorithm.However,the back-propagation algorithm(BP),as a mostly used learning algorithm,intrinsically suffers from defects of slow convergence and easily dropping into local minima.Therefore,more and more research adopts non-BP learning algorithms to train ANNs.In this paper,a dynamic scale-free network-based differential evolution(DSNDE)is developed by considering the demands of convergent speed and the ability to jump out of local minima.The performance of a DSNDE trained DNM is tested on 14 benchmark datasets and a photovoltaic power forecasting problem.Nine meta-heuristic algorithms are applied into comparison,including the champion of the 2017 IEEE Congress on Evolutionary Computation(CEC2017)benchmark competition effective butterfly optimizer with covariance matrix adapted retreat phase(EBOwithCMAR).The experimental results reveal that DSNDE achieves better performance than its peers.

Recognition system of leaf images based on neuronal network

In forest variety registration, visual traits of the plants appearance are widely used to discern different tree species. The new recognition system of leaf image strategy which based on neural network established to administrate a hierarchical list of leaf images, some sorts of edge detection can be performed to identify the individual tokens of every image and the frame of the leaf can be got to differentiate the tree species. An approach based on back-propagation neuronal network is proposed and the programming language for the implementation is also Riven by using Java. The numerical simulations results have shown that the proposed leaf strategt is effective and feasible.

Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.

Delay-aided stochastic multiresonances on scale-free FitzHugh-Nagumo neuronal networks

The stochastic resonance in paced time-delayed scale-free FitzHugh--Nagumo （FHN） neuronal networks is investigated. We show that an intermediate intensity of additive noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble. Furthermore, we reveal that appropriately tuned delays can induce stochastic multiresonances, appearing at every integer multiple of the pacemaker＇s oscillation period. We conclude that fine-tuned delay lengths and locally acting pacemakers are vital for ensuring optimal conditions for stochastic resonance on complex neuronal networks.

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency （wave number） of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.

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.

Plasticity-induced characteristic changes of pattern dynamics and the related phase transitions in small-world neuronal networks

Phase transitions widely exist in nature and occur when some control parameters are changed. In neural systems, their macroscopic states are represented by the activity states of neuron populations, and phase transitions between different activity states are closely related to corresponding functions in the brain. In particular, phase transitions to some rhythmic synchronous firing states play significant roles on diverse brain functions and disfunctions, such as encoding rhythmical external stimuli, epileptic seizure, etc. However, in previous studies, phase transitions in neuronal networks are almost driven by network parameters （e.g., external stimuli）, and there has been no investigation about the transitions between typical activity states of neuronal networks in a self-organized way by applying plastic connection weights. In this paper, we discuss phase transitions in electrically coupled and lattice-based small-world neuronal networks （LBSW networks） under spike-timing-dependent plasticity （STDP）. By applying STDP on all electrical synapses, various known and novel phase transitions could emerge in LBSW networks, particularly, the phenomenon of self-organized phase transitions （SOPTs）： repeated transitions between synchronous and asynchronous firing states. We further explore the mechanics generating SOPTs on the basis of synaptic weight dynamics.

Engrafted newborn neurons could functionally integrate into the host neuronal network

The limited capability to regenerate new neurons following injuries of the central neural system（CNS）still remains a major challenge for basic and clinical neuroscience.Neural stem cells（NSCs）could nearly have the potential to differentiate into all kinds of neural cells in vitro.

Coherence resonance and bi-resonance by time-periodic coupling strength in Hodgkin-Huxley neuron networks

We study the effect of time-periodic coupling strength on the spiking coherence of Newman-Watts networks of Hodgkin-Huxley(HH) neurons with non-Gaussian noise.It is found that the spiking can exhibit coherence resonance(CR) when the extent of deviation of non-Gaussian noise from Gaussian noise and the amplitude of the coupling strength are varied.In particular,coherence bi-resonance(CBR) is observed when the frequency of the coupling strength is varied,and the CBR is always observed when the frequency is equal to,or a multiple of,the spiking period,manifesting as the locking between the frequencies of the spiking and the coupling strength.The results show that a time-periodic coupling strength may play a more constructive and efficient role in enhancing the spiking coherence of the neuronal networks than a constant coupling strength.These findings provide insight into the role of time-periodic coupling strength for enhancing the time precision of information processing in neuronal networks.

Neuronal networks in mental diseases and neuropathic pain:Beyond brain derived neurotrophic factor and collapsin response mediator proteins

The brain is a complex network system that has the capacity to support emotion, thought, action, learning and memory, and is characterized by constant activity, constant structural remodeling, and constant attempt to compensate for this remodeling. The basic insight that emerges from complex network organization is that substantively different networks can share common key organizational principles. Moreover, the interdependence of network organization and behavior has been successfully demonstrated for several specific tasks. From this viewpoint, increasing experimental/clinical observations suggest that mental disorders are neural network disorders. On one hand, single psychiatric disorders arise from multiple, multifactorial molecular and cellular structural/functional alterations spreading throughout local/global circuits leading to multifaceted and heterogeneous clinical symptoms. On the other hand, various mental diseases may share functional deficits across the same neural circuit as reflected in the overlap of symptoms throughout clinical diagnoses. An integrated framework including experimental measures and clinical observations will be necessary to formulate a coherent and comprehensive understanding of how neural connectivity mediates and constraints the phenotypic expression of psychiatric disorders.

Bursting synchronization in clustered neuronal networks

Neuronal networks in the brain exhibit the modular （clustered） property, i.e., they are composed of certain subnetworks with differential internal and external connectivity. We investigate bursting synchronization in a clustered neuronal network. A transition to mutual-phase synchronization takes place on the bursting time scale of coupled neurons, while on the spiking time scale, they behave asynchronously. This synchronization transition can be induced by the variations of inter- and intra coupling strengths, as well as the probability of random links between different subnetworks. Considering that some pathological conditions are related with the synchronization of bursting neurons in the brain, we analyze the control of bursting synchronization by using a time-periodic external signal in the clustered neuronal network, Simulation results show a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even in the presence of external driving. Hence, effective synchronization suppression can be realized with the driving parameters outside the frequency locking region.

Quantitative evaluation of extrinsic factors influencing electrical excitability in neuronal networks： Voltage Threshold Measurement Method(VTMM)

The electrical excitability of neural networks is influenced by different environmental factors. Effective and simple methods are required to objectively and quantitatively evaluate the influence of such factors, including variations in temperature and pharmaceutical dosage. The aim of this paper was to introduce ‘the voltage threshold measurement method＇, which is a new method using microelectrode arrays that can quantitatively evaluate the influence of different factors on the electrical excitability of neural networks. We sought to verify the feasibility and efficacy of the method by studying the effects of acetylcholine, ethanol, and temperature on hippocampal neuronal networks and hippocampal brain slices. First, we determined the voltage of the stimulation pulse signal that elicited action potentials in the two types of neural networks under normal conditions. Second, we obtained the voltage thresholds for the two types of neural networks under different concentrations of acetylcholine, ethanol, and different temperatures. Finally, we obtained the relationship between voltage threshold and the three influential factors. Our results indicated that the normal voltage thresholds of the hippocampal neuronal network and hippocampal slice preparation were 56 and 31 m V, respectively. The voltage thresholds of the two types of neural networks were inversely proportional to acetylcholine concentration, and had an exponential dependency on ethanol concentration. The curves of the voltage threshold and the temperature of the medium for the two types of neural networks were U-shaped. The hippocampal neuronal network and hippocampal slice preparations lost their excitability when the temperature of the medium decreased below 34 and 33°C or increased above 42 and 43°C, respectively. These results demonstrate that the voltage threshold measurement method is effective and simple for examining the performance/excitability of neuronal networks.

Spiking sychronization regulated by noise in three types of Hodgkin-Huxley neuronal networks

In this paper,we study spiking synchronization in three different types of Hodgkin-Huxley neuronal networks,which are the small-world,regular,and random neuronal networks.All the neurons are subjected to subthreshold stimulus and external noise.It is found that in each of all the neuronal networks there is an optimal strength of noise to induce the maximal spiking synchronization.We further demonstrate that in each of the neuronal networks there is a range of synaptic conductance to induce the effect that an optimal strength of noise maximizes the spiking synchronization.Only when the magnitude of the synaptic conductance is moderate,will the effect be considerable.However,if the synaptic conductance is small or large,the effect vanishes.As the connections between neurons increase,the synaptic conductance to maximize the effect decreases.Therefore,we show quantitatively that the noise-induced maximal synchronization in the Hodgkin-Huxley neuronal network is a general effect,regardless of the specific type of neuronal network.

Effects of information transmission delay and channel blocking on synchronization in scale-free Hodgkin-Huxley neuronal networks

In this paper,we investigate the evolution of spatiotemporal patterns and synchronization transitions in dependence on the information transmission delay and ion channel blocking in scale-free neuronal networks.As the underlying model of neuronal dynamics,we use the Hodgkin-Huxley equations incorporating channel blocking and intrinsic noise.It is shown that delays play a significant yet subtle role in shaping the dynamics of neuronal networks.In particular,regions of irregular and regular propagating excitatory fronts related to the synchronization transitions appear intermittently as the delay increases.Moreover,the fraction of working sodium and potassium ion channels can also have a significant impact on the spatiotemporal dynamics of neuronal networks.As the fraction of blocked sodium channels increases,the frequency of excitatory events decreases,which in turn manifests as an increase in the neuronal synchrony that,however,is dysfunctional due to the virtual absence of large-amplitude excitations.Expectedly,we also show that larger coupling strengths improve synchronization irrespective of the information transmission delay and channel blocking.The presented results are also robust against the variation of the network size,thus providing insights that could facilitate understanding of the joint impact of ion channel blocking and information transmission delay on the spatiotemporal dynamics of neuronal networks.

Power-law statistics of synchronous transition in inhibitory neuronal networks

We investigate the relationship between the synchronous transition and the power law behavior in spiking networks which are composed of inhibitory neurons and balanced by dc current. In the region of the synchronous transition, the avalanche size and duration distribution obey a power law distribution. We demonstrate the robustness of the power law for event sizes at different parameters and multiple time scales. Importantly, the exponent of the event size and duration distribution can satisfy the critical scaling relation. By changing the network structure parameters in the parameter region of transition, quasicriticality is observed, that is, critical exponents depart away from the criticality while still hold approximately to a dynamical scaling relation. The results suggest that power law statistics can emerge in networks composed of inhibitory neurons when the networks are balanced by external driving signal.

Coherence resonance in globally coupled neuronal networks with different neuron numbers

Because a brain consists of tremendous neuronal networks with different neuron numbers ranging from tens to tens of thousands, we study the coherence resonance due to ion channel noises in globally coupled neuronal networks with different neuron numbers. We confirm that for all neuronal networks with different neuron numbers there exist the array enhanced coherence resonance and the optimal synaptic conductance to cause the maximal spiking coherence. Furthermoremore, the enhancement effects of coupling on spiking coherence and on optimal synaptic conductance are almost the same, regardless of the neuron numbers in the neuronal networks. Therefore for all the neuronal networks with different neuron numbers in the brain, relative weak synaptic conductance （0.1 mS/cm2） is sufficient to induce the maximal spiking coherence and the best sub-threshold signal encoding.

Effects of internal noise on the spiking regularity of a clustered Hodgkin–Huxley neuronal network

Spiking regularity in a clustered Hodgkin–Huxley（HH） neuronal network has been studied in this letter. A stochastic HH neuronal model with channel blocks has been applied as local neuronal model. Effects of the internal channel noise on the spiking regularity are discussed by changing the membrane patch size. We find that when there is no channel blocks in potassium channels, there exist some intermediate membrane patch sizes at which the spiking regularity could reach to a higher level. Spiking regularity increases with the membrane patch size when sodium channels are not blocked. Namely, depending on different channel blocking states, internal channel noise tuned by membrane patch size could have different influence on the spiking regularity of neuronal networks.