Time-delayed Coupling Research Articles

Unraveling coupling delays through a transfer entropy analysis in stochastic processes and non-linear systems

Abstract In this work we propose a transfer entropy approach to discern time-delay couplings within non-linear and stochastic coupled systems. We introduce the concept of “time-wise transfer entropy”, which quantifies the reduction in future uncertainty for a process Y by considering the values of processes X and Y at a specific past moment. The key advantage of our approach is a reduction in the number of parameters required for estimation when compared to other transfer entropy methodologies. Our proposed time-wise transfer entropy not only lends itself to effective estimation from actual data but also enhances our understanding of the origins of seemingly “spurious” couplings observed in some transfer entropy approaches. To validate our method, we apply it to determine coupling delays in minimal stochastic models where the time-wise transfer entropy can be precisely derived in terms of the Shannon entropy. We further assess the technique performance in coupled non-linear systems with delays, demonstrating its capacity to accurately reproduce the corresponding coupling delays. The developed technique may be useful in the analysis of multifactor nonlinear physical systems where complex causal relationships may exist.

Space-climatic feedback of the magnetic solar cycle through the interplanetary space

The relationship between solar magnetic activity and solar wind parameters, with observed time-delayed mutual coupling, is an outstanding challenge in space physics. In this study, drawing inspiration from recent observations, we propose a reconciliation framework whose fundamentals stand in the Parker model for solar wind expansion. We investigate the effects on fluctuations in solar wind speed when linearly sustained by an oscillating magnetic solar dynamo described via a modified Van der Pol nonlinear oscillator mimicking the magnetic activity at different timescales. Our findings reveal the presence of a “space-climatic feedback” that, in absence of the driving magnetic activity, slows down solar wind velocity fluctuations. The combined action of the slowing down of fluctuations and a periodic driving is the responsible for the time-delay between solar magnetic activity and solar wind dynamics. Furthermore, we also demonstrate how the space-climatic feedback controls the value of the time-delay which depends on the different periodicities of the driving magnetic activity. This holistic approach provides a formal link at the interplay between solar magnetic activity and solar wind dynamics through the interplanetary space which can advance our understanding of long-term effects of solar activity on solar wind variations, and consequently on interactions with planetary environments.

Spatiotemporal discoordination of brain spontaneous activity in major depressive disorder

BackgroundMajor depressive disorder (MDD) is a widespread mental health issue, impacting spatial and temporal aspects of brain activity. The neural mechanisms behind MDD remain unclear. To address this gap, we introduce a novel measure, spatiotemporal topology (SPT), capturing both the hierarchy and dynamic attributes of brain activity in depressive disorder patients. MethodsWe analyzed fMRI data from 285 MDD inpatients and 141 healthy controls (HC). SPT was assessed by coupling brain gradient measurement and time delay estimation. A nested machine learning process distinguished between MDD and HC using SPT. Person's correlation tested the link between SPT's and symptom severity, and another machine learning method predicted the gap between patients' chronological and brain age. ResultsSPT demonstrated significant differences between patients and healthy controls (F = 2.944, p < 0.001). Machine learning approaches revealed SPT's ability to discriminate between patients and healthy controls (Accuracy = 0.65, Sensitivity = 0.67, Specificity = 0.64). Moreover, SPT correlated with the severity of depression symptom (r = 0.32. pFDR = 0.045) and predicted the gap between patients' chronological age and brain age (r = 0.756, p < 0.001). LimitationsEvaluation of brain dynamics was constrained by MRI temporal resolution. ConclusionsOur study introduces SPT as a promising metric to characterize the spatiotemporal signature of brain function, providing insights into deviant brain activity associated with depressive disorders and advancing our understanding of their psychopathological mechanisms.

Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations

In this study, we propose coupled time-delayed fractional oscillators with dichotomous fluctuating frequencies and investigate the collective resonant behavior. Firstly, we obtain the condition of complete synchronization between the average behavior of the two oscillators. Subsequently, we derive the precise analytical expression of the output amplitude gain. Based on the analytical results, we observe the collective resonant behavior of the coupled time-delayed system and further study its dependence on various system parameters. The observed results underscore that the coupling strength, fractional order, and time delay play significant roles in controlling the collective resonant behavior by facilitating the occurrence and optimizing the intensity. Finally, numerical simulations are also conducted and verify the accuracy of the analytical results.

Novel f-CaO soft sensor for cement clinker based on integrated model of dual-parallel structure.

Aiming at the problem that the cement production process is inherently affected by uncertainty, time delay, and strong coupling among variables, this paper proposed a novel soft sensor of free calcium oxide in a cement clinker. The model utilizes a dual-parallel integrated structure with an optimized integration of one-dimensional convolutional neural networks, long and short-term memory networks, graphical neural networks, and extreme gradient boosting. The proposed model can mitigate the risks associated with overfitting while incorporating the strengths of each individual model and excels in extracting both local and global features as well as temporal and spatial characteristics from the original time series data, ensuring its stability. The experimental results demonstrate that this dual-parallel integrated model exhibits superior robustness, predictive accuracy, and generalization capabilities when compared to single models or enhancements made to other deep learning algorithms.

A New Grey Wolf Optimizer Tuned Extended Generalized Predictive Control for Distillation Process.

The distillation process plays an essential role in the petrochemical industry. However, the high-purity distillation column has complicated dynamic characteristics such as strong coupling and large time delay. To control the distillation column accurately, we proposed an extended generalized predictive control (EGPC) method inspired by the principles of extended state observer and proportional-integral-type generalized predictive control method; the proposed EGPC can adaptively compensate the system for the effects of coupling and model mismatch online and performs well in controlling time-delay systems. The strong coupling of the distillation column needs fast control, and the large time delay requires soft control. To balance the requirement for fast and soft control at the same time, a grey wolf optimizer with reverse learning and adaptive leaders number strategies (RAGWO) was proposed to tune the parameters of EGPC, and these strategies enable RAGWO to have a better initial population and improve its exploitation and exploration ability. The benchmark test results indicate that the RAGWO outperforms the existing optimizers for most of the selected benchmark functions. Extensive simulations show that the proposed method in terms of fluctuation and response time is superior to other methods for controlling the distillation process.

TDITI: A time-delay information transfer index algorithm for corticomuscular coupling

Time delay (TD) across corticomuscular coupling (CMC) is a significant index to assess the information transmission between brain and muscle during movement execution. Larger methods have been widely used to calculate the time delay by estimating phase information, but fail to account for both linear and nonlinear characteristics in the bidirectional coupled systems. For this, this study proposed a novel time-delay estimation method, defined as time-delay information transfer index (TDITI), to explore the TD characteristics between two signal deriving from one system with time-delay coupling. To verify this, we introduced two models to generate a series of simulation signal with linearly unidirectional/ bidirectional coupling or nonlinearly unidirectional/ bidirectional coupling. Simulation results manifested that the TDITI method, compared with the information transfer index (ITI) and coherence methods, can not only describe the TD in the linearly or nonlinearly unidirectional systems, but was also suitable for the bidirectional coupled systems. We also found its robustness to data length, coupling strength and signal-noise ratio. After that, we applied it to explore the TD of CMC by synchronizing the electroencephalogram (EEG) and electromyogram (EMG) signal during steady-state task. Experimental results showed that the CMC between cortex and muscle were direction-dependent, and the average delay time from EEG to EMG (∼25 ms) was shorter than that in the opposition (∼30 ms). Both simulation and experimental data expound the effectiveness of the TDITI method to describe the time delay in the unidirectional or bidirectional coupled systems, and this study extends our perspective to the mechanism of motor control.

Multi-index control strategy from cement calcination denitration system: a model predictive control method for combined control of nitrogen oxide and ammonia escape.

The cement industry is one of the main sources of NOx emissions, and automated denitration systems enable precise control of NOx emission concentration. With non-linearity, time delay and strong coupling data in cement production process, making it difficult to maintain stable control of the denitration system. However, excessive pursuit of denitration efficiency is often prone to large ammonia escape, causing environmental pollution. A multi-objective prediction model combining time series and a bi-directional long short-term memory network (MT-BiLSTM) is proposed to solve the data problem of the denitration system and achieve simultaneous prediction of NOx emission concentration and ammonia escape value. Based on this model, a model predictive control framework is proposed and a control strategy of denitration system with multi-index model predictive control (MI-MPC) is built based on neural networks. In addition, the differential evolution (DE) algorithm is used for rolling optimization to find the optimal solution and to obtain the best control variable parameters. The control method proposed has significant advantages over the traditional PID (proportional integral derivative) controller, with a 3.84% reduction in overshoot and a 3.04% reduction in regulation time. Experiments prove that the predictive control framework proposed in this paper has better stability and higher accuracy, with practical research significance.

Low-order modeling of collective dynamics of four ring-coupled turbulent thermoacoustic oscillators

We investigate the low-order modeling of collective dynamics in a can-annular combustor consisting of four ring-coupled turbulent lean-premixed combustors. Each combustor is treated as an individual thermoacoustic oscillator, and the entire combustion system is modeled using four Van der Pol oscillators ring-coupled with dissipative, time-delay, and reactive coupling terms. We show that this model, despite its simplicity, can reproduce many collective dynamics observed in experiments under various combinations of equivalence ratios and combustor lengths, such as 2-can anti-phase synchronization, alternating anti-phase synchronization, pairwise anti-phase synchronization, spinning azimuthal mode, and 4 steady thermoacoustic oscillators. The phase relationship in the majority of cases can be quantitatively modeled. Moreover, by incorporating a reactive coupling term, the model is able to reproduce the frequency shift observed experimentally. This study demonstrates the feasibility of using a simple low-order model to reproduce collective dynamics in complex turbulent combustion systems. This suggests that this model could be used (i) to facilitate the interpretation of experimental data within the synchronization framework, (ii) to identify potential parameter regimes leading to amplitude death, and (iii) to serve as a basis for modeling the collective dynamics observed in more complicated multi-combustors.

Double Hopf bifurcation analysis of time delay coupled active control system

In this paper, the stability analysis of double Hopf bifurcation is carried out based on the time delay coupled active control system by using the related theory of bifurcation analysis. We got the stability switching region of the system with respect to time delay. The time delay and coupling strength are selected as the bifurcation parameters, then the normal form of the coupled time delay active control system is obtained by using the multi-scale method, and the dynamic behavior near the bifurcation point is obtained. So the parameter region of the stable periodic solution and the stable quasi-periodic solution are obtained. The analytical solution of the system is then solved by using the multi-frequency homotopy analysis method (MFHAM) to verify the existence of the unstable periodic solution. Finally, numerical simulation is executed to verify the theoretical results.

Finite-time synchronization for coupled neural networks with time-delay jumping coupling

The finite-time synchronization problem is studied for coupled neural networks (CNNs) with time-delay jumping coupling. Markovian switching topologies, imprecise delay models, uncertain parameters and the unavailable of topology modes are considered in this work. A mode-dependent delay with pre-known conditional probability is built to handle the imprecise delay model problem. A hidden Markov model with uncertain parameters is introduced to describe the mode mismatch problem, and an asynchronous controller is designed. Besides, a set of Bernoulli processes models the random packet dropouts during data communication. Based on Markovian switching topologies, mode-dependent delays, uncertain probabilities and packet dropout, a sufficient condition that guarantees the CNNs reach finite-time synchronization (FTS) is derived. Finally, a numerical example is derived to demonstrate the efficiency of the proposed synchronous technique.

Stability of coupled Wilson–Cowan systems with distributed delays

Building upon our previous work on the Wilson-Cowan equations with distributed delays (Kaslik et al., 2022), we study the dynamic behavior in a system of two coupled Wilson-Cowan pairs. We focus in particular on understanding the mechanisms that govern the transitions in and out of oscillatory regimes associated with pathological behavior. We investigate these mechanisms under multiple coupling scenarios, and we compare the effects of using discrete delays versus a weak Gamma delay distribution. We found that, in order to trigger and stop oscillations, each kernel emphasizes different critical combinations of coupling weights and time delay, with the weak Gamma kernel restricting oscillations to a tighter locus of coupling strengths, and to a limited range of time delays. We finally illustrate the general analytical results with simulations for two particular applications: generation of beta-rhythms in the basal ganglia, and alpha oscillations in the prefrontal-limbic system.

Finite-Time Topology Identification of Delayed Complex Dynamical Networks and Its Application

To understand the functional behaviors of systems built on networks, it is essential to determine the uncertain topology of these networks. Traditional synchronization-based topology identification methods generally converge asymptotically or exponentially, resulting in their inability to give timely identification results. The finite-time stability theory is adopted in this paper with the aim of addressing the problem of fast identification of uncertain topology in networks. A novel finite-time topology observer is proposed to achieve finite-time topology identification and synchronization of general complex dynamical networks with time delay and second-order dynamical networks with time delay and nonlinear coupling. In addition, the proposed finite-time identification method is applied to power grids to address the problem of fast detection of line outages. Finally, 2 numerical experiments are provided to demonstrate the effectiveness and rapidity of the proposed finite-time identification method.

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

&lt;p&gt;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.&lt;/p&gt;

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.

An effective mathematical model of cardiac electrical activities for Bundle Branch Blocks

In this paper a mathematical model of cardiac induction system is developed. Sinoatrial node (SA), atrioventricular node (AV) and His Purkinje system (HP) are represented by modified Van der Pol-type oscillators (VDP) connected with time-delay coupling. Atrial and ventricular muscles are modeled using modified Aliev-Panfilov equations (AP), with stimulation current from the related pacemakers, to represent the P, QRS, Ta, and T waves. The main aim of this paper is to model bundle branch blocks (BBBs) for right (RBBB) and left (LBBB) branches. In fact, the right and left ventricles are directly affected by these blocks since the HP bundle is composed of right and left bundle branches that provide electrical signals, respectively, to the right and left ventricles. Four VDP oscillators are utilized, one for each of SA, AV, right HP, and left HP. The depolarization of the right and left ventricular muscles are represented by two systems of AP equations to produce right QRS and left QRS waves. The results of the simulation are compared with real normal and pathological electrocardiograms (ECGs) to show the effectiveness and the accuracy of the proposed model. The simulation proves that the model can reproduce the blocks in the HP bundle branches.

Bifurcations and synchrony in a ring of delayed Wilson–Cowan oscillators

Ring structures are crucial in network neuroscience, enabling the integration of neural information through closed loop circuits within feedback systems. Here, we use numerical bifurcation analysis to explore time delay effects on a ring of delay-coupled Wilson–Cowan masses. Investigating a low-dimensional ‘self-coupled’ version of the aforementioned system, we uncover the bifurcation structure of the synchronization manifold, and unveil a diverse array of dynamic synchronization patterns that emerge as a consequence of Hopf branch crossings and subsequent higher-order bifurcations. Analysis of the full system reveals transverse instabilities in the synchronized state for large regions of parameter space, with the ring network architecture promoting various dynamics depending on the balance between coupling strength and delay time. Under weak coupling, emergent oscillations are generally synchronous or anti-phase synchronous, with transitions between them triggered by a torus bifurcation of a periodic orbit. Regions of synchronous and anti-phase synchronous solutions are delineated by weakly chaotic borders due to the breakdown of the torus. As coupling strength increases, the bifurcation diagram displays more overlapped branching structure, resulting in increasingly complicated, multistable dynamics.

The digitization work of cement plant in China

This article is to introduce the digitization work of smart cement plant in China. To save power and promote the product quality, delicacy management in variety ways of digital transformation is the best tool for the new built, or existing cement plants. New technologies, such as special integrated robots, online equipment, information plant form, cement process digital applicant (SAAS), Artificial Intelligence (AI) and Advanced Process Control (APC) are implemented to approve the traditional ways of operation.This paper introduces the application of intelligent factory technology in China, and focuses on the intelligent optimization control system. The system has self-learning and global optimization functions, with strong adaptability and robustness. In combination with quality prediction, kiln condition identification and quantitative identification of fire watching TV video images, the kiln system is feed-forward controlled to solve the control problem of long time delay, large inertia and strong coupling of the burning system. The system gives the global optimal recommended value of the control target through calculation, with which to ensure the best control and operation of the system.With the application of comprehensive intelligent construction, the cement plant will usually save 2–5 % of energy and 20 % staff simplification, and make the management mode more concise and efficient. Meanwhile, the cement groups are also developing the production information plat form, by merging the Enterprise Resource Planning (ERP) data, sales business to lower down the total cost. This paper tries to introduce the digital efforts that are carried out in the smart cement plants and shows the methodology of implementation.

Design of Hypersonic Vehicle Time-Delay Compensation Controller based on Dynamic Surface Control

vehicles with input delays is described in this paper. Due to high dynamic characteristics of hypersonic vehicle, the strong uncertainties, high nonlinearity, strong coupling and control input time delays are challenging problems in the design of its control system. Therefore, it is necessary to design a control method that can handle input time delays. Finally, in this paper, the mathematical expression of the altitude nonlinear control theory problem of an aircraft with input time delay is given. Secondly, based on the backstepping method, the time delay compensation controller is designed. Thirdly, the backstepping method and dynamic control surface are used to design altitude angle control law. The stability and time delay compensation effect are proved. Finally, simulation results show that the suggested method can improve the stability and disturbance rejection performance for the system effectively, which has certain actual application value.

Multi-modal and multi-model interrogation of large-scale functional brain networks

Existing whole-brain models are generally tailored to the modelling of a particular data modality (e.g., fMRI or MEG/EEG). We propose that despite the differing aspects of neural activity each modality captures, they originate from shared network dynamics. Building on the universal principles of self-organising delay-coupled nonlinear systems, we aim to link distinct features of brain activity - captured across modalities - to the dynamics unfolding on a macroscopic structural connectome.To jointly predict connectivity, spatiotemporal and transient features of distinct signal modalities, we consider two large-scale models - the Stuart Landau and Wilson and Cowan models - which generate short-lived 40 Hz oscillations with varying levels of realism. To this end, we measure features of functional connectivity and metastable oscillatory modes (MOMs) in fMRI and MEG signals - and compare them against simulated data.We show that both models can represent MEG functional connectivity (FC), functional connectivity dynamics (FCD) and generate MOMs to a comparable degree. This is achieved by adjusting the global coupling and mean conduction time delay and, in the WC model, through the inclusion of balance between excitation and inhibition. For both models, the omission of delays dramatically decreased the performance. For fMRI, the SL model performed worse for FCD and MOMs, highlighting the importance of balanced dynamics for the emergence of spatiotemporal and transient patterns of ultra-slow dynamics. Notably, optimal working points varied across modalities and no model was able to achieve a correlation with empirical FC higher than 0.4 across modalities for the same set of parameters. Nonetheless, both displayed the emergence of FC patterns that extended beyond the constraints of the anatomical structure. Finally, we show that both models can generate MOMs with empirical-like properties such as size (number of brain regions engaging in a mode) and duration (continuous time interval during which a mode appears).Our results demonstrate the emergence of static and dynamic properties of neural activity at different timescales from networks of delay-coupled oscillators at 40 Hz. Given the higher dependence of simulated FC on the underlying structural connectivity, we suggest that mesoscale heterogeneities in neural circuitry may be critical for the emergence of parallel cross-modal functional networks and should be accounted for in future modelling endeavours.