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.

Dynamics and synchronization of neural models with memristive membranes under energy coupling

Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical mechanisms.The electrophysiological environment inside and outside of the nerve cell is different.Due to the continuous and periodical properties of electromagnetic fields in the cell during its operation,electronic components involving two capacitors and a memristor are effective in mimicking these physical features.In this paper,a neural circuit is reconstructed by two capacitors connected by a memristor with periodical mem-conductance.It is found that the memristive neural circuit can present abundant firing patterns without stimulus.The Hamilton energy function is deduced using the Helmholtz theorem.Further,a neuronal network consisting of memristive neurons is proposed by introducing energy coupling.The controllability and flexibility of parameters give the model the ability to describe the dynamics and synchronization behavior of the system.

Quantum synchronization with correlated baths

We study quantum synchronization under the nonequilibrium reservoirs.We consider a two-qubit XXZ chain coupled independently to their own reservoirs modeled by the collisional model.Two reservoir particles,initially prepared in a thermal state or a state with coherence,are correlated through a unitary transformation and afterward interact locally with the two quantum subsystems.We study the quantum effect of reservoir on synchronous dynamics of system.By preparing different reservoir initial states or manipulating the reservoir particles coupling and the temperature gradient,we find that quantum entanglement of reservoir is the key to control quantum synchronization of system qubits.

Synchronization and firing mode transition of two neurons in a bilateral auditory system driven by a high–low frequency signal

The FitzHugh–Nagumo neuron circuit integrates a piezoelectric ceramic to form a piezoelectric sensing neuron,which can capture external sound signals and simulate the auditory neuron system.Two piezoelectric sensing neurons are coupled by a parallel circuit consisting of a Josephson junction and a linear resistor,and a binaural auditory system is established.Considering the non-singleness of external sound sources,the high–low frequency signal is used as the input signal to study the firing mode transition and synchronization of this system.It is found that the angular frequency of the high–low frequency signal is a key factor in determining whether the dynamic behaviors of two coupled neurons are synchronous.When they are in synchronization at a specific angular frequency,the changes in physical parameters of the input signal and the coupling strength between them will not destroy their synchronization.In addition,the firing mode of two coupled auditory neurons in synchronization is affected by the characteristic parameters of the high–low frequency signal rather than the coupling strength.The asynchronous dynamic behavior and variations in firing modes will harm the auditory system.These findings could help determine the causes of hearing loss and devise functional assistive devices for patients.

RL and AHP-Based Multi-Timescale Multi-Clock Source Time Synchronization for Distribution Power Internet of Things

Time synchronization(TS)is crucial for ensuring the secure and reliable functioning of the distribution power Internet of Things(IoT).Multi-clock source time synchronization(MTS)has significant advantages of high reliability and accuracy but still faces challenges such as optimization of the multi-clock source selection and the clock source weight calculation at different timescales,and the coupling of synchronization latency jitter and pulse phase difference.In this paper,the multi-timescale MTS model is conducted,and the reinforcement learning(RL)and analytic hierarchy process(AHP)-based multi-timescale MTS algorithm is designed to improve the weighted summation of synchronization latency jitter standard deviation and average pulse phase difference.Specifically,the multi-clock source selection is optimized based on Softmax in the large timescale,and the clock source weight calculation is optimized based on lower confidence bound-assisted AHP in the small timescale.Simulation shows that the proposed algorithm can effectively reduce time synchronization delay standard deviation and average pulse phase difference.

A Synchronization Acquisition Algorithm Based on the Frequency Hopping Pulses Combining

As modern electromagnetic environments are more and more complex,the anti-interference performance of the synchronization acquisition is becoming vital in wireless communications.With the rapid development of the digital signal processing technologies,some synchronization acquisition algorithms for hybrid direct-sequence(DS)/frequency hopping(FH)spread spectrum communications have been proposed.However,these algorithms do not focus on the analysis and the design of the synchronization acquisition under typical interferences.In this paper,a synchronization acquisition algorithm based on the frequency hopping pulses combining(FHPC)is proposed.Specifically,the proposed algorithm is composed of two modules:an adaptive interference suppression(IS)module and an adaptive combining decision module.The adaptive IS module mitigates the effect of the interfered samples in the time-domain or the frequencydomain,and the adaptive combining decision module can utilize each frequency hopping pulse to construct an anti-interference decision metric and generate an adaptive acquisition decision threshold to complete the acquisition.Theory and simulation demonstrate that the proposed algorithm significantly enhances the antiinterference and anti-noise performances of the synchronization acquisition for hybrid DS/FH communications.

A 5M Synchronization Mechanism for Digital Twin Shop-Floor

In recent years,as a promising way to realize digital transformation,digital twin shop-floor(DTS)plays an impor-tant role in smart manufacturing.The core feature of DTS is the synchronization.How to implement and maintain the synchronization is critical for DTS.However,there is still a lack of a common definition for synchronization in DTS.Besides,a systematic synchronization mechanism for DTS is strongly needed.This paper first summarizes the defi-nition and requirements of synchronization in DTS,to clarify the understanding of synchronization in DTS.Then,a 5M synchronization mechanism for DTS is proposed,where 5M refers to multi-system data,multi-fidelity model,multi-resource state,multi-level state,and multi-stage operation.As a bottom-up synchronization mechanism,5M synchronization mechanism for DTS has the potential to support DTS to achieve and maintain physical-virtual state synchronization,and to realize operation synchronization of DTS.The implementation methods of 5M synchronization mechanism for DTS are also introduced.Finally,the proposed synchronization mechanism is validated in a digital twin satellite assembly shop-floor,which proves the effectiveness and feasibility of the mechanism.

FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH

The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical results.

A master-slave generalized predictive synchronization control for preheating process of multi-cavity hot runner system

As a key component of injection molding,multi-cavity hot runner(MCHR)system faces the crucial problem of polymer melt filling imbalance among the cavities.The thermal imbalance in the system has been considered as the leading cause.Hence,the solution may rest with the synchronization of those heating processes in MCHR system.This paper proposes a’Master-Slave’generalized predictive synchronization control(MS-GPSC)method with’Mr.Slowest’strategy for preheating stage of MCHR system.The core of the proposed method is choosing the heating process with slowest dynamics as the’Master’to track the setpoint,while the other heating processes are treated as‘Slaves’tracking the output of’Master’.This proposed method is shown to have the good ability of temperature synchronization.The corresponding analysis is conducted on parameters tuning and stability,simulations and experiments show the strategy is effective.

Generalized projective synchronization for the chaotic Lorenz system and the chaotic Chen system

Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called ＂generalized projective synchronization＂, is reported in the chaotic Lorenz system and the chaotic Chen one.

Robust synchronization of uncertain chaotic systems

This paper investigates robust unified （lag, anticipated, and complete） synchronization of two coupled chaotic systems, By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.

Diffusive field coupling-induced synchronization between neural circuits under energy balance

When charged bodies come up close to each other,the field energy is diffused and their states are regulated under bidirectional field coupling.For biological neurons,the diversity in intrinsic electric and magnetic field energy can create synaptic connection for fast energy balance and synaptic current is passed across the synapse channel;as a result,energy is pumped and exchanged to induce synchronous firing modes.In this paper,a capacitor is used to connect two neural circuits and energy propagation is activated along the coupling channel.The intrinsic field energy in the two neural circuits is exchanged and the coupling intensity is controlled adaptively using the Heaviside function.Some field energy is saved in the coupling channel and is then sent back to the coupled neural circuits to reach energy balance.Therefore the circuits can reach possible energy balance and complete synchronization.It is possible that the diffusive energy of the coupled neurons inspires the synaptic connections to grow stronger for possible energy balance.

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.

Synchronization–desynchronization transitions in networks of circle maps with sinusoidal coupling

Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention has been focused on coupled time-continuous oscillators described by differential equations. In this paper, we study the synchronization dynamics of networks of coupled circle maps as the discrete version of the Kuramoto model. Despite of its simplicity in mathematical form, it is found that discreteness may induce many interesting synchronization behaviors. Multiple synchronization and desynchronization transitions of both phases and frequencies are found with varying the coupling among circle-map oscillators. The mechanisms of these transitions are interpreted in terms of the mean-field approach, where collective bifurcation cascades are revealed for coupled circle-map oscillators.

Explosive synchronization of multi-layer complex networks based on star connection between layers with delay

Explosive synchronization(ES)is a kind of first-order jump phenomenon that exists in physical and biological systems.In recent years,researchers have focused on ES between single-layer and multi-layer networks.Most research on complex networks with delay has focused on single-layer or double-layer networks,multi-layer networks are seldom explored.In this paper,we propose a Kuramoto model of frequency weights in multi-layer complex networks with delay and star connections between layers.Through theoretical analysis and numerical verification,the factors affecting the backward critical coupling strength are analyzed.The results show that the interaction between layers and the average node degree has a direct effect on the backward critical coupling strength of each layer network.The location of the delay,the size of the delay,the number of network layers,the number of nodes,and the network topology are revealed to have no direct impact on the backward critical coupling strength of the network.Delay is introduced to explore the influence of delay and other related parameters on ES.

Mixing trait-based corn(Zea mays L.)cultivars increases yield through pollination synchronization and increased cross-fertilization

Abiotic stress such as high temperature at flowering is one of many conditions reducing yield of corn(Zea mays L.).Mixing corn cultivars with diverse functional traits increases within-crop diversity and provides a potential means of mitigating yield losses under stress conditions.We conducted a three-year field study to investigate the effects of cultivar mixtures on kernel setting rate,pollen sources,and yield.This study consisted of six treatments,including two high temperature-tolerant(HTT)monocrops of WK702 and DH701,two high temperature-sensitive(HTS)monocrops of DH605 and DH662,and two HTT–HTS mixtures of WK702-DH605 and DH701-DH662.The anthesis–silking interval(ASI)was 0.9–1.6 days shorter in mixtures than in monocrops.Kernel setting rate was increased in mixtures(86.4%–88.7%)compared with those in monocrops(74.7%–84.1%)as a result of synchrony and complementarity of pollination.Grain yields of the HTT–HTS mixtures increased by 13.3%–18.7%,equivalent to 1169 to1605 kg ha^(-1),in comparison with HTS corn monocrops.The results of SSR markers showed that crossfertilization percentage in corn cultivar mixtures ranged from 29.3%to 47.8%,partially explaining yield improvement.Land equivalent ratio(LER)was 1.12 for corn mixtures and the partial land equivalent ratio(e.g.,>0.5)showed the complementary benefits in corn mixtures.The results indicated that mixing corn cultivars with diverse flowering and drought-tolerance traits increased yields via pollination synchrony.

Stability and multistability of synchronization in networks of coupled phase oscillators

Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state.Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of the synchronized state. Globally the emergence of synchronous state depends on the initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.

Synchronization of stochastic complex networks with time-delayed coupling

Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay,and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability;otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.

Adaptive Fixed-Time Synchronization of Delayed Memristor-Based Neural Networks with Discontinuous Activations

Fixed-time synchronization(FTS)of delayed memristor-based neural networks(MNNs)with discontinuous activations is studied in this paper.Both continuous and discontinuous activations are considered forMNNs.And the mixed delays which are closer to reality are taken into the system.Besides,two kinds of control schemes are proposed,including feedback and adaptive control strategies.Based on some lemmas,mathematical inequalities and the designed controllers,a few synchronization criteria are acquired.Moreover,the upper bound of settling time(ST)which is independent of the initial values is given.Finally,the feasibility of our theory is attested by simulation examples.

A consensus time synchronization protocol in wireless sensor network

Time synchronization is one of the base techniques in wireless sensor networks(WSNs).This paper proposes a novel time synchronization protocol which is a robust consensusbased algorithm in the existence of transmission delay and packet loss.It compensates for transmission delay and packet loss firstly,and then,estimates clock skew and clock offset in two steps.Simulation and experiment results show that the proposed protocol can keep synchronization error below 2μs in the grid network of 10 nodes or the random network of 90 nodes.Moreover,the synchronization accuracy in the proposed protocol can keep constant when the WSN works up to a month.