Lag Synchronization Research Articles

Cluster lag synchronization in fractional-order community networks with nondelay and delay coupling

Lag synchronization is a special synchronization manner and has wide applications. For community network, in view of the differences among communities, the synchronization lags in different communities may be nonidentical. This paper investigates the cluster lag synchronization in fractional-order community networks with nondelay and delay coupling. The node dynamics in different communities are nonidentical and even have nonidentical dimensions. Based on the Lyapunov stability theory, effective feedback controllers are designed for achieving cluster lag synchronization and several synchronization criteria are derived. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

Dynamics of coupled erbium-doped fiber lasers: Modulation effects and synchronization patterns

Studying the dynamics of coupled Erbium-Doped Fiber Lasers helps in optimizing the performance of these systems in different applications. An important factor in these systems is the modulation signal which can affect the dynamics of systems, leading to complex behaviors including diverse periodic and chaotic dynamics. This paper investigates the dynamics of a ring network of Erbium-Doped Fiber Lasers and compares its behaviors in the presence and absence of the modulation. The results reveal that although complete synchronization is not reachable, certain synchronization patterns exist during the periodic oscillations. In the non-modulated network, two distinct clusters are formed which can achieve lag synchronization under specific coupling intensities. While in the coupled modulated systems, the chimera state may form. These findings represent the complex relationship among modulation, coupling intensity, and network dynamics in EDFL systems.

Deep brain stimulation and lag synchronization in a memristive two-neuron network

In the pursuit of potential treatments for neurological disorders and the alleviation of patient suffering, deep brain stimulation (DBS) has been utilized to intervene or investigate pathological neural activities. To explore the exact mechanism of how DBS works, a memristive two-neuron network considering DBS is newly proposed in this work. This network is implemented by coupling two-dimensional Morris–Lecar neuron models and using a memristor synaptic synapse to mimic synaptic plasticity. The complex bursting activities and dynamical effects are revealed numerically through dynamical analysis. By examining the synchronous behavior, the desynchronization mechanism of the memristor synapse is uncovered. The study demonstrates that synaptic connections lead to the appearance of time-lagged or asynchrony in completely synchronized firing activities. Additionally, the memristive two-neuron network is implemented in hardware based on FPGA, and experimental results confirm the abundant neuronal electrical activities and chaotic dynamical behaviors. This work offers insights into the potential mechanisms of DBS intervention in neural networks.

Multistability and synchronicity of memristor coupled adaptive synaptic neuronal network

Memristor coupled neuronal networks can simulate the complex interactions between neurons in biological neuronal networks. These capture the current and synaptic transmission between neurons through mathematical equations, thus reflecting the signal transmission and integration in biological neuronal networks. This paper presents a five-dimensional isomorphic memristor coupled adaptive synaptic neuron (mCASN) network using a non-ideal memristor to couple two-dimensional adaptive synaptic neurons. The theoretical analysis of equilibrium points shows that the mCASN network has many different stability types. The complex parameters-dependent bifurcation behaviors are studied using various numerical methods, and the initial state-dependent coexistence behaviors and the riddled-like basins of attraction sensitive to initial states are further revealed, which proves that the coupled network has multistability. In addition, using the normalized average synchronization error method, we reveal that the mCASN network has synchronization characteristics controlled by parameters and initial states. The complete synchronization and lag synchronization induced by the network parameters, the internal variable of the coupled memristor, and the state variable of the sub-neuron are numerically analyzed. Finally, the mCASN network is implemented using an MCU-based digital hardware platform, and the numerical results are verified.

Auditory discrimination learning differentially modulates neural representation in auditory cortex subregions and inter-areal connectivity

Changes in sound-evoked responses in the auditory cortex (ACtx) occur during learning, but how learning alters neural responses in different ACtx subregions and changes their interactions is unclear. To address these questions, we developed an automated training and widefield imaging system to longitudinally track the neural activity of all mouse ACtx subregions during a tone discrimination task. We find that responses in primary ACtx are highly informative of learned stimuli and behavioral outcomes throughout training. In contrast, representations of behavioral outcomes in the dorsal posterior auditory field, learned stimuli in the dorsal anterior auditory field, and inter-regional correlations between primary and higher-order areas are enhanced with training. Moreover, ACtx response changes vary between stimuli, and such differences display lag synchronization with the learning rate. These results indicate that learning alters functional connections between ACtx subregions, inducing region-specific modulations by propagating behavioral information from primary to higher-order areas.

Lag synchronization for coupled neural networks with multistate or multiderivative couplings

In this paper, two kinds of lag synchronization for coupled neural networks (CNNs) are addressed, that is, the cases with multiple state or derivative couplings. Firstly, several lag synchronization criteria for these two CNNs are derived by selecting proper state feedback controllers. Furthermore, since external disturbances in neural network implementation should not be ignored, the impact of external disturbances on the lag synchronization for CNNs are also further investigated. Lastly, the obtained criteria are verified through two illustrative examples.

Conflict-free joint decision by lag and zero-lag synchronization in laser network

With the end of Moore’s Law and the increasing demand for computing, photonic accelerators are garnering considerable attention. This is due to the physical characteristics of light, such as high bandwidth and multiplicity, and the various synchronization phenomena that emerge in the realm of laser physics. These factors come into play as computer performance approaches its limits. In this study, we explore the application of a laser network, acting as a photonic accelerator, to the competitive multi-armed bandit problem. In this context, conflict avoidance is key to maximizing environmental rewards. We experimentally demonstrate cooperative decision-making using zero-lag and lag synchronization within a network of four semiconductor lasers. Lag synchronization of chaos realizes effective decision-making and zero-lag synchronization is responsible for the realization of the collision avoidance function. We experimentally verified a low collision rate and high reward in a fundamental 2-player, 2-slot scenario, and showed the scalability of this system. This system architecture opens up new possibilities for intelligent functionalities in laser dynamics.

Lag Synchronization in Mean Square of Stochastic Complex Networks with Multiple Mixed Delays via Impulsive Control

Lag Synchronization in Mean Square of Stochastic Complex Networks with Multiple Mixed Delays via Impulsive Control

Finite-time lag synchronization for two-layer complex networks with impulsive effects

<abstract><p>This paper mainly considered the finite-time lag synchronization for two-layer complex networks with impulsive effects. Different types of controllers were designed to achieve the lag synchronization of two-layer complex networks. Several sufficient conditions on lag synchronization in the sense of finite time were derived. The time for synchronization was also estimated. It is important to note that synchronization time was influenced by the initial value, as well as the impulses and impulse sequence. This implied that different impulse effects result in varying synchronization times. Additionally, desynchronizing impulses can extend the synchronization time, whereas synchronizing impulses have the opposite effect. Finally, a numerical example was presented to showcase the practicality and validity of the proposed theoretical criteria.</p></abstract>

Delayed Impulsive Control for Lag Synchronization of Delayed Neural Networks Involving Partial Unmeasurable States.

In the framework of impulsive control, this article deals with the lag synchronization problem of neural networks involving partially unmeasurable states, where the time delay in impulses is fully addressed. Since the complexity of external environment and uncertainty of networks, which may lead to a result that the information of partial states is unmeasurable, the key problem for lag synchronization control is how to utilize the information of measurable states to design suitable impulsive control. By using linear matrix inequality (LMI) and transition matrix method coupled with dimension expansion technique, some sufficient conditions are derived to guarantee lag synchronization, where the requirement for information of all states is needless. Moreover, our proposed conditions not only allow the existence of unmeasurable states but also reduce the restrictions on the number of measurable states, which shows the generality of our results and wide-application in practice. Finally, two illustrative examples and their numerical simulations are presented to demonstrate the effectiveness of main results.

The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters

<p>This research presents an adaptive synchronization approach crafted to facilitate exact lag synchronization between a pair of unidirectionally linked Hindmarsh-Rose (HR) neurons, taking into account both explicit propagation delays and the existence of uncertain parameters. The precise condition for lag synchronization is deduced analytically, utilizing the Laplace transform and convolution theorem, alongside the iterative approach within the framework of Volterra integral equations theory. The established criterion guarantees robust stability irrespective of the propagation delay's magnitude, facilitating the realization of approximate lag and anticipating synchronization in a pair of HR neurons. The approximate synchronizations are realized in the absence of direct time-delay coupling, with the Taylor series expansion serving as an alternative to the precise time-delay component. Numerical simulations are executed to validate the effectiveness of the suggested approximate synchronization approach. The research demonstrates that employing the current state of an HR neuron, despite having uncertain parameters, enables the accurate prediction of future states and the reconstruction of past states. This study provides a novel perspective for comprehending neural processes and the advantageous attributes inherent in nonlinear and chaotic systems.</p>

Novel Results on Fixed-Time Complex Projective Lag Synchronization for Fuzzy Complex-Valued Neural Networks With Inertial Item

Novel Results on Fixed-Time Complex Projective Lag Synchronization for Fuzzy Complex-Valued Neural Networks With Inertial Item

Synchronization, Desynchronization, and Intermediate Regime of Breathing Solitons and Soliton Molecules in a Laser Cavity.

We report on the experimental and numerical observations of synchronization and desynchronization of bound states of multiple breathing solitons (breathing soliton molecules) in an ultrafast fiber laser. In the desynchronization regime, although the breather molecules as wholes are not synchronized to the cavity, the individual breathers within a molecule are synchronized to each other with a delay (lag synchronization). An intermediate regime between the synchronization and desynchronization phases is also observed, featuring self-modulation of the synchronized state. This regime may also occur in other systems displaying synchronization. Breathing soliton molecules in a laser cavity open new avenues for the study of nonlinear synchronization dynamics.

Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling

The problem of successive lag synchronization (SLS) for heterogeneous distributed-order coupled neural networks (HDOCNNs) with unbounded delayed coupling is investigated in this paper. Firstly, a model for HDOCNNs under the framework of distributed order Caputo derivative is proposed which is the generalization of integer order and fractional order cases. Secondly, a new Razumikhin-type stability theorem for distributed order systems is proposed. On this basis, the well-known Halanay type inequality is generalized to analyze the convergence of solutions for a class of distributed order dynamical systems. Thirdly, the SLS criteria for HDOCNNs with delayed coupling by designing a novel adaptive controller and a valid feedback controller are presented herein, respectively. Finally, a numerical example is presented to illustrate the reliability of the proposed scheme.

Analytical Studies on Approximate Lag and Anticipating Synchronization in Two Unidirectionally Coupled Hyperchaotic Chen Systems without Time Delay

In this paper, approximate lag synchronization (LS) and anticipating synchronization (AS) between two unidirectionally coupled hyperchaotic Chen systems without time-delay coupling are analytically investigated. Firstly, the synchronization condition for exact LS in two unidirectionally coupled hyperchaotic Chen systems with time delay in signal transmission is analytically obtained. Under such conditions, approximate LS and AS are discussed by replacing the true time-delay terms with their Taylor expansions up to the third order.Differently from other research studies, the condition for exact LS is derived by regarding LS as a special type of generalized synchronization (GS), which has nothing to do with the value of the time delay. It is convenient to individually change the value of the lag and anticipation time of approximate LS and AS without considering the synchronization condition. Our study shows the power of a new method for recreating the past signals or predicting the future signals of a hyperchaotic Chen system by using its current signals. The results provide a simple way to eliminate the negative effects of time delay in the signal transmission between two hyperchaotic systems.

Multi-stable states and synchronicity of a cellular neural network with memristive activation function

The cellular neural network (CNN) is an implementable solution for fully connected neural networks. Using nanoscale memristor to realize its nonlinear activation function can simplify the circuit implementation of CNN effectively. This paper presents a paradigm of the basic CNN cell by introducing a voltage-controlled memristor as the activating module of its output circuit. A three-cell memristor-based CNN (mCNN) is constructed to demonstrate the parameter- and initial condition-influenced dynamical behaviors induced by the activating memristor. Furtherly, two identical three-cell mCNNs are chosen as the subnets to construct a memristor-coupled mCNN, based on which the multi-stable states and the synchronous behaviors are investigated. Numerical results show that the multi-stable states of the memristor-coupled mCNN are flexibly switched by adjusting the coupling strength and initial conditions. Under the control of the memristor coupler, the two subnets can achieve complete synchronization, lag synchronization and phase synchronization. Finally, the FPGA-based hardware experiments are executed to verify the numerical results.

Successive Lag Synchronization for Multilayer Complex Networks With Multiple Weights

Successive Lag Synchronization for Multilayer Complex Networks With Multiple Weights

Transcranial alternating current stimulation over multiple brain areas with non-zero phase delays other than 180 degrees modulates visuospatial working memory performance

While zero-phase lag synchronization between multiple brain regions has been widely observed, relatively recent reports indicate that systematic phase delays between cortical regions reflect the direction of communications between cortical regions. For example, it has been suggested that a non-zero phase delay of electroencephalography (EEG) signals at the gamma frequency band between the bilateral parietal areas may reflect the direction of communication between these areas. We hypothesized that the direction of communication between distant brain areas might be modulated by multi-site transcranial alternating current stimulation (tACS) with specific phase delays other than 0° and 180°. In this study, a new noninvasive brain stimulation (NIBS) method called multi-site multi-phase tACS (msmp-tACS) was proposed. The efficacy of the proposed method was tested in a case study using a visuospatial working memory (VWM) paradigm in which the optimal stimulation conditions including amplitudes and phases of multiple scalp electrodes were determined using finite element analysis adopting phasor representation. msmp-tACS was applied over the bilateral intraparietal sulci (IPS) and showed that 80 Hz tACS with the phase for the right IPS leading that for the left IPS by 90° (= 3.125 ms) partialized VWM performance toward the right visual hemifield. The three stimulation conditions were synchronized, RL, and LR, which refers to stimulation condition with no phase lag, stimulation phase of right IPS (rIPS) leading left IPS (lIPS) by 90° and the stimulation of lIPS leading rIPS by 90°, respectively. The lateralization of VWM significantly shifted towards right visual hemifield under the RL condition compared to the synchronized and LR conditions. The shift in VWM was the result of the stimulation affecting both left and right visual hemifield trials to certain degrees, rather than significantly increasing or decreasing VWM capacity of a specific visual hemifield. Altered brain dynamics caused by msmp-tACS partialized VWM performance, likely due to modulation of effective connectivity between the rIPS and lIPS. Our results suggest that msmp-tACS is a promising NBS method that can effectively modulate cortical networks that cannot be readily modulated with conventional multi-site stimulation methods.

Further results on fixed/preassigned-time projective lag synchronization control of hybrid inertial neural networks with time delays

This article aims to study fixed-time projective lag synchronization(FXPLS) and preassigned-time projective lag synchronization(PTPLS) of hybrid inertial neural networks(HINNs) with state-switched and discontinuous activation functions(DAFs). By constructing new hybrid fixed-time control and based on theory of non-smooth analysis, we achieve novel results on FXPLS for such HINNs. Through designing novel hybrid preassigned-time control, new criteria on PTPLS of the HINNs is also taken into account. And as distinct from recent works, the FXPLS and PTPLS results are established via non-variable substitution and in a more generalized framework than common synchronization, which also has more extensive practical applications. Finally, example simulations are displayed to set forth the validity of the acquired FXPLS and PTPLS.

Multistability and synchronization of discrete maps via memristive coupling

Due to its internal state, the memristive nonlinearity has different dynamic characteristics from the traditional resistive nonlinearity. It has been proved that the memristive nonlinearity used as a nonlinear coupler to connect two dynamical systems has rich multi-stability phenomena and complex synchronous behaviors. However, few reports have extended memristive couplers and dynamical systems from continuous-time domain to discrete-time domain. To this end, this article proposes a simple memristor-coupled Logistic map (MCLM) model by coupling two identical Logistic maps through a memristive coupler. The MCLM model owns two line fixed point sets related to memristor initial condition and their stability distributions are discussed based on three eigenvalues. The chaotic/hyperchaotic attractors with outstanding performance indicators are revealed using numerical methods, and the initial-related heterogeneous multistability and memristor initial-boosting homogeneous multistability are demonstrated by basins of attraction that have complex and fractal evolutions. Afterwards, by inspecting the synchronous behaviors of the two Logistic maps in the MCLM model, the lag and complete synchronization behaviors dependent on the coupling strength and memristor initial condition, especially the homogeneous synchronization behavior boosted by the memristor initial condition, are disclosed in succession. In addition, an MCU-based hardware platform is fabricated to experimentally validate the numerical results. Of particular interest, to the best knowledge of the authors, the initial-boosting synchronization has not been reported in the literature.