Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh–Rose and FitzHugh–Nagumo neurons with two time delays

A memristor-coupled heterogenous neural network consisting of two-dimensional(2D)FitzHugh–Nagumo(FHN)and Hindmarsh–Rose(HR)neurons with two time delays is established.Taking the time delays as the control parameters,the existence of Hopf bifurcation near the stable equilibrium point in four cases is derived theoretically,and the validity of the Hopf bifurcation condition is verified by numerical analysis.The results show that the two time delays can make the stable equilibrium point unstable,thus leading to periodic oscillations induced by Hopf bifurcation.Furthermore,the time delays in FHN and HR neurons have different effects on the firing activity of neural network.Complex firing patterns,such as quiescent state,chaotic spiking,and periodic spiking can be induced by the time delay in FHN neuron,while the neural network only exhibits quiescent state and periodic spiking with the change of the time delay in HR neuron.Especially,phase synchronization between the heterogeneous neurons is explored,and the results show that the time delay in HR neurons has a greater effect on blocking the synchronization than the time delay in FHN neuron.Finally,the theoretical analysis is verified by circuit simulations.

Discrimination of Motor Imagery Patterns by Electroencephalogram Phase Synchronization Combined With Frequency Band Energy

Central nerve signal evoked by thoughts can be directly used to control a robot or prosthetic devices without the involvement of the peripheral nerve and muscles.This is a new strategy of human-computer interaction.A method of electroencephalogram(EEG) phase synchronization combined with band energy was proposed to construct a feature vector for pattern recognition of brain-computer interaction based on EEG induced by motor imagery in this paper,rhythm and beta rhythm were first extracted from EEG by band pass filter and then the frequency band energy was calculated by the sliding time window;the instantaneous phase values were obtained using Hilbert transform and then the phase synchronization feature was calculated by the phase locking value(PLV) and the best time interval for extracting the phase synchronization feature was searched by the distribution of the PLV value in the time domain.Finally,discrimination of motor imagery patterns was performed by the support vector machine(SVM).The results showed that the phase synchronization feature more effective in4s-7s and the correct classification rate was 91.4%.Compared with the results achieved by a single EEG feature related to motor imagery,the correct classification rate was improved by 3.5 and4.3 percentage points by combining phase synchronization with band energy.These indicate that the proposed method is effective and it is expected that the study provides a way to improve the performance of the online real-time brain-computer interaction control system based on EEG related to motor imagery.

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.

Time and phase synchronization using clutter observations in airborne distributed coherent aperture radars

Airborne Distributed Coherent Aperture Radar(ADCAR)is one of the most promising next-generation radars to significantly improve target detection and discrimination abilities.However,time and phase synchronization among unit radars should be done before an ADCAR is intended to cohere on a potential target.To address this problem,a time and phase synchronization technique using clutter observations is proposed in this paper.Clutter returns from different azimuths and elevations on the surface of the earth are employed to calibrate system uncertainties.Two stages are mainly considered:a scene registration among range-Doppler units from different transmit/receive pairs is performed to enhance the clutter coherence in the first stage,followed by a joint estimation of those synchronization errors in the second stage.To relieve the computational burden,a novel Separable and Sequential Estimation(SSE)method is provided to separate the unknowns at the sacrifice of a range-Doppler unit.Moreover,performance analyses including the clutter coherence ability,estimation lower bound,and signal coherence loss are also performed.Finally,simulation results indicate that ADCAR time and phase synchronization is realized by using our methods.

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Synaptic crosstalk is a prevalent phenomenon among neuronal synapses,playing a crucial role in the transmission of neural signals.Therefore,considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks are highly necessary.In this paper,we propose a heterogeneous discrete neural network(HDNN)consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron.These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered.The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents.It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths.Furthermore,the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated,revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.

PHASE DIFFERENCE BETWEEN LOW-FREQUENCY OSCILLATIONS OF CEREBRAL DEOXY-AND OXY-HEMOGLOBIN CONCENTRATIONS DURING A MENTAL TASK

Hemodynamic low-frequency(~0.1 Hz)spontaneous oscillations as detected in the brain by nearinfrared spectroscopy have potential applications in the study of brain activation,cerebral autoregulation,and functional connectivity.In this work,we have investigated the phase lag between oscillations of cerebral deoxy-and oxy-hemoglobin concentrations in the frequency range 0.05-0.10 Hz in a human subject during a mental workload task.We have obtained a measure of such phase lag using two different methods:(1)phase synchronization analysis as used in the theory of chaotic oscillators and(2)a novel cross-correlation phasor approach.The two methods yielded comparable initial results of a larger phase lag between low-frequency oscillations of deoxy-and oxyhemoglobin concentrations during mental workload with respect to a control,rest condition.

High synchronization absolute distance measurement using a heterodyne and superheterodyne combined interferometer

We propose an absolute distance measurement method that employs heterodyne and superheterodyne combined interferometers to achieve synchronous detection and demodulation of multiwavelengths.Coarse and fine synthetic wavelengths are generated by a dual-longitudinal-mode He-Ne laser and four acoustic optical frequency shifters.Further,to improve phase synchronization measurement for multiwavelengths,we analyze the demodulation characteristics of coarse and fine measurement signals and adopt a demodulation method suitable for both signals.Experimental results demonstrate that the proposed method can achieve high-precision synchronous demodulation of multiwavelengths,and standard deviation is 1.7×10^(-5)m in a range of 2 m.

The meaning of “coherent” and its quantication in coherent hemodynamics spectroscopy

We have recently introduced a new technique,coherent hemodynamics spectroscopy(CHS),which aims at characterizing a specic kind of tissue hemodynamics that feature a high level of covariation with a given physiological quantity.In this study,we carry out a detailed analysis of the signicance of coherence and phase synchronization between oscillations of arterial blood pressure(ABP)and total hemoglobin concentration([Hbt]),measured with near-infrared spectroscopy(NIRS)during a typical protocol for CHS,based on a cyclic thigh cuffocclusion and release.Even though CHS is based on a linear time invariant model between ABP(input)and NIRS measurands(outputs),for practical reasons in a typical CHS protocol,we inducenite“groups”of ABP oscillations,in which each group is characterized by a different frequency.For this reason,ABP(input)and NIRS measurands(output)are not stationary processes,and we have used wavelet coherence and phase synchronization index(PSI),as a metric of coherence and phase synchronization,respectively.PSI was calculated by using both the wavelet cross spectrum and the Hilbert transform.We have also used linear coherence(which requires stationary process)for comparison with wavelet coherence.Themethod of surrogate data is used tond critical values for the signicance of covariation between ABP and[Hbt].Because we have found similar critical values for wavelet coherence and PSI by usingve of the most used methods of surrogate data,we propose to use the data-independent Gaussian random numbers(GRNs),for CHS.By using wavelet coherence and wavelet cross spectrum,and GRNs as surrogate data,we have found the same results for the signicance of coherence and phase synchronization between ABP and[Hbt]:on a total set of 20 periods of cuffoscillations,we have found 17 coherent oscillations and 17 phase synchronous oscillations.Phase synchronization assessed with Hilbert transform yielded similar results with 14 phase synchronous oscillations.Linear coherence and wavelet coherence overall yielded similar number of signicant values.We discuss possible reasons for this result.Despite the similarity of linear and wavelet coherence,we argue that wavelet coherence is preferable,especially if one wants to use baseline spontaneous oscillations,in which phase locking and coherence between signals might be only temporary.

Numerical simulation of square shaped particle sedimentation

Direct numerical simulations of square particle sedimentation in a viscous incompressible fluid are presented to examine the effects of sharp edges for various particle-to-fluid density ratios and different initial inclination angles.The settling process exhibits four different motion regimes;non-oscillatory,non-uniform centered oscillatory,uniform off-centered oscillatory,and non-uniform off-centered(irregular)oscillatory.At moderate density ratios,we observe that the rotational motion of settling square particle varies with the initial inclination angle.We employ Dynamic Time Warping and Fast Fourier Transform to analyze translational and angular velocities.Oscillating systems are described using phase-space plots,and a chaotic phenomenon is observed at a higher density ratio.

Dynamics and synchronization of a complex-valued star network

Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.

The effect of oxygen concentration on the coupled neurons:Rich spiking patterns and synchronization

The dynamical microenvironments play a crucial role in neuronal spiking patterns.In this paper,we investigated the effect of oxygen concentration on different synchronous spiking patterns of two coupled neuron models by including dynamical ion concentration.Two coupling modes of electrical diffusive coupling and potassium diffusive coupling were considered.In these two cases,oxygen concentration exhibited an important role in the synchronous spiking patterns between two coupled neurons,and extremely rich electrical activities were observed.For the potassium diffusive coupling,differential synchronous patterns of oscillation state(OS),synchronous epileptic seizure state(SSZ)and synchronous spreading depression state(SSD)as well as SZ and SD bursting states were generated.For the electrical diffusive coupling,differential synchronous patterns of resting state(RS),SSZ and SSD were observed.

Bunch-length measurement at a bunch-by-bunch rate based on time–frequency-domain joint analysis techniques and its application

This paper presents a new technique for measuring the bunch length of a high-energy electron beam at a bunch-by-bunch rate in storage rings.This technique uses the time–frequency-domain joint analysis of the bunch signal to obtain bunch-by-bunch and turn-by-turn longitudinal parameters,such as bunch length and synchronous phase.The bunch signal is obtained using a button electrode with a bandwidth of several gigahertz.The data acquisition device was a high-speed digital oscilloscope with a sampling rate of more than 10 GS/s,and the single-shot sampling data buffer covered thousands of turns.The bunch-length and synchronous phase information were extracted via offline calculations using Python scripts.The calibration coefficient of the system was determined using a commercial streak camera.Moreover,this technique was tested on two different storage rings and successfully captured various longitudinal transient processes during the harmonic cavity debugging process at the Shanghai Synchrotron Radiation Facility(SSRF),and longitudinal instabilities were observed during the single-bunch accumulation process at Hefei Light Source(HLS).For Gaussian-distribution bunches,the uncertainty of the bunch phase obtained using this technique was better than 0.2 ps,and the bunch-length uncertainty was better than 1 ps.The dynamic range exceeded 10 ms.This technology is a powerful and versatile beam diagnostic tool that can be conveniently deployed in high-energy electron storage rings.

PARALLEL SIMULATION OF LARGE-SCALE ARTIFICIAL SOCIETY WITH GPU AS COPROCESSOR

Large-scale artificial societies with millions or billions of agents call for high-performance parallel simulation.Prevailing supercomputers with thousands of CPUs and GPUs make it possible to carry out such simulation.The key is to distribute large-scale agents to massive cores of CPUs and GPUs properly for parallel computing with efficient communication and synchronization.For simplicity and efficiency,a modified discrete event system specification(DEVS)is proposed for large-scale artificial society modeling and parallelism is exploited in agent models because similar agents usually share similar behaviors.Through phased synchronization,a two-tier parallel simulation engine is designed with support of MPI and OpenCL where GPU is used as coprocessor.One-sided communication is used for reflection of remote simulation objects and message passing between processes.A general kernel function prototype is elaborately designed and conditionally compiled for execution on both CPU and GPU.An artificial society for epidemic study is used to test the performance on a supercomputer with 1024 CPU cores and 1792 GPU cores.The speedup reaches 3512 for even 2 billion agents with GPU acceleration which is far over 701 when only CPUs are used.It turns out feasible for parallel simulation of large-scale artificial society with GPU as coprocessor.