Single Time Delay Research Articles

Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model

Noise and time delay are ubiquitous in various physical and biological systems. In this paper, we studied the phase synchronization and mode transition of oscillation mode induced by time delays and noises in a coupled FitzHugh–Nagumo (FHN) neural system. In the case of coupled neurons with single time delay, it is found that the mode oscillation of neurons induced by the noise and time delay undergoes a successive transitions from the synchronization, the out-of phase, the alternating phase-drift and anti-phase state, to the anti-phase state. In the case of coupled neurons with two time delays, when the two delays are comparable, the large amplitude oscillation of potential is in alternating synchronous and asynchronous state in the absence of noises, and the small amplitude oscillation of potential is always synchronized. The oscillation behaviors of coupled neurons with two time delays are similar to the cases with a single time delay in the presence of noises. When one of two time delays is largely dominant over the other, the neurons show completely different dynamic behaviors.

Modeling and Formulation of Delayed Cyber-Physical Power System for Small-Signal Stability Analysis and Control

Modeling and formulation of a delayed cyber-physical power system (DCPPS) are the basis of small-signal stability analysis and control synthesis of the system. First, a logic describing the interconnections between various systems of delayed differential algebraic equations (DDAEs) and delayed differential equations (DDEs) is established. It clearly shows the transformation of the most general DDAEs of the non-index-1 Hessenberg form to the widely used DDEs with finite terms of actual delays. Second, the DDAE model of the index-1 Hessenberg form is formulated in detail for DCPPS, which features in preserving the inherent sparsity in system's augmented state matrix. Exploiting the sparsity guarantees the scalability in stability analysis and controller design of a large DCPPS. Third, three delay merge properties are presented with complete proofs, which indicate that the feedback and control delays in one control loop can be treated as one single time delay. The properties facilitate modeling and formulating DCPPS. Last, numerical studies are carried out on a real-life large DCPPS with wide-area damping controllers embedded. Test results validate the correctness of the presented theoretical backgrounds.

Enhanced bifurcation results for a delayed fractional neural network with heterogeneous orders

This paper addresses the stability and bifurcation of a delayed fractional neural network(FNN) with different orders. Firstly, system parameter acts as a bifurcation parameter, and bifurcation criterion are educed for such system. It discovers that the stability performance of the proposed system can be exalted by selecting modest system parameter. Secondly, the bifurcation diagrams are fully illustrated for checking the exactness of the procured bifurcation results. Thirdly, in terms of discreet calculation, it perceives that the onset of bifurcation can be advanced by single order or time delay if as they decrease. Finally, two numerical examples are exploited to validate the efficiency of the theoretical results.

Topological time-series analysis with delay-variant embedding.

Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a high-dimensional space using a time-delay parameter and subsequently extract topological features describing the shape of the data from the embedded points. However, the essential topological features that are extracted using a single time delay are considered to be insufficient for evaluating the aforementioned qualitative changes, even when a well-selected time delay is used. We therefore propose a delay-variant embedding method that constructs the extended topological features by considering the time delay as a variable parameter instead of considering it as a single fixed value. This delay-variant embedding method reveals multiple-timescale patterns in a time series by allowing the observation of the variations in topological features, with the time delay serving as an additional dimension in the topological feature space. We theoretically prove that the constructed topological features are robust when the time series is perturbed by noise. Furthermore, we combine these features with the kernel technique in machine learning algorithms to classify the general time-series data. We demonstrate the effectiveness of our method for classifying the synthetic noisy biological and real time-series data. Our method outperforms a method that is based on a single time delay and, surprisingly, achieves the highest classification accuracy on an average among the standard time-series analysis techniques.

Reconstruction of the complex angle-dependent photoionization transition dipole from a laser-dressed streaking experiment

We study the retrieval of the angular dependence of the photoionization transition dipole phase of an attosecond XUV pulse in order to reconstruct the whole photoelectron wave packet after the photoemission process. Using a one-electron model Ar atom, we show that the full electron wave packet can be reconstructed from IR-free photoelectron angular distributions and the streaking electron spectra in an IR-dressed XUV photoionization, with photoelectrons along the common polarization direction of the two pulses. The method relies on the validity of the strong-field approximation so it is valid only for higher energy photoelectrons. We also point out that a single photoionization group time delay is not enough to represent a photoemission process; instead, a complete characterization of the electron wave packet requires the retrieval of the spectral phase over the whole bandwidth of the wave packet.

Partial pole assignment with time delays for asymmetric systems

Considering both single and multiple time delays, partial pole assignment for stabilising asymmetric systems is exemplified by friction-induced vibration and aerodynamic flutter. The control strategy is a single-input state feedback including constant time delays in the feedback loop. An unobservability condition is considered to assign some poles while keeping others unchanged. The receptance method is applied to avoid modelling errors from evaluating mass, damping and stiffness matrices by the finite element method. The solution is formulated in linear equations which allow determination of control gains. The stability of the closed-loop system is analysed by evaluating the first few dominant poles and determining a critical time delay. The numerical study shows that the proposed method is capable of making partial pole assignment with time delays. Since many structures and systems with non-conservative forces can be represented by asymmetric systems, this approach is widely applicable for vibration control of engineering structures.

Stability of fractional-order prey–predator system with time-delay and Monod–Haldane functional response

In this paper, we study the dynamics of a fractional-order delayed prey–predator system with Monod–Haldane response function. The model describes the interaction between prey and two populations of predator species: immature or juvenile and mature or adult predator. A single time delay is incorporated in the model to justify the gestation period of adult predator. The existence of solutions, steady states, and sufficient conditions to ensure the asymptotic stability of the steady states are investigated. Global stability around the interior equilibrium point by constructing the suitable Lyapunov functional is also investigated. The system displays Hopf bifurcation depending on the conversion coefficient (prey to immature predator) and time delay. The fractional-order derivatives in the model develop the stability results of solutions and improve the model behaviors. Finally, some numerical simulations are given to verify the success of derived theoretical results.

Sliding Mode Control for a Class of Nonlinear Multi-agent System With Time Delay and Uncertainties

In this paper, a type of multi-agent system is adopted in the practical project with time delay, uncertainties, and linear feedback. In addition, sliding mode control is used to ensure the robust stability of the system since it is insensitive to parameter change and interference. For the system in three different conditions, namely fixed structure, every agent being only influenced by single time delay and each agent being affected by multiple time delay, the corresponding sliding surface and the control law are improved. The reaction factors are proven by Lyapunov functions and the linear matrix inequality approach is taken to guarantee the robust stability of the sliding surface. To prove the effectiveness of the conclusion, experiments on each condition are conducted. Besides, in the last part, a simple application is applied and proved to be effective.

A new convolution approach for the time-delay identification of systems with arbitrary entries

In this paper, an online delay identification approach of continuous-time linear systems with unstructured entries is achieved via a new algebraic technique. The arbitrary input and output trajectories are chosen with close and abundant crossing zero. Initial conditions and static disturbances are taken into account in the design of the identification approach. The proposed method is based on a distributional algebraic technique and a convolution approach. A proposed theorem is hence enounced to identify a single time-delay of such systems. The effectiveness of the proposed approach is demonstrated by an illustrative example. The obtained results show the high performances of the proposed time-delay identification approach in severe operation conditions of the considered system.

Event-triggered containment control for multi-agent systems with constant time delays

The paper investigates containment control for the first-order and second-order multi-agent systems with constant time delays under event-triggered conditions, respectively. By applying existing sum of square method to stability analysis of containment control for multi-agent systems, sufficient containment conditions for multi-agent systems are obtained. First, we discussed the case of containment control for multi-agent system with single time delay, and event-triggered conditions are proposed. Then, we extend the results of containment control for multi-agent systems with single time delay to the case with multiple time delays. Finally, simulation examples are given to illustrate the effectiveness of our theoretical results.

A Chaotic Time-Delay System with Saturation Nonlinearity

Complex dynamics are observed in time-delay systems because the presence of time delay could induce unexpected oscillations. Therefore, time-delay systems are effective for constructing chaotic signal generators which have used in various engineering applications. In this paper, a new system with a single scalar time delay and a saturation nonlinearity is introduced. Dynamics of such time-delay system are investigated by using phase planes, bifurcation diagrams and the maximum Lyapunov exponent with the variance of system parameters. It is interesting that the time-delay system can generate double-scroll chaotic attractors despite its elegant model. Circuitry of the system is also presented to show the feasibility of the theoretical model.

Solar oscillation time delay measurement assisted celestial navigation method

Solar oscillation, which causes the sunlight intensity and spectrum frequency change, has been studied in great detail, both observationally and theoretically. In this paper, owing to the existence of solar oscillation, the time delay between the sunlight coming from the Sun directly and the sunlight reflected by the other celestial body such as the satellite of planet or asteroid can be obtained with two optical power meters. Because the solar oscillation time delay is determined by the relative positions of the spacecraft, reflective celestial body and the Sun, it can be adopted as the navigation measurement to estimate the spacecraft's position. The navigation accuracy of single solar oscillation time delay navigation system depends on the time delay measurement accuracy, and is influenced by the distance between spacecraft and reflective celestial body. In this paper, we combine it with the star angle measurement and propose a solar oscillation time delay measurement assisted celestial navigation method for deep space exploration. Since the measurement model of time delay is an implicit function, the Implicit Unscented Kalman Filter (IUKF) is applied. Simulations demonstrate the effectiveness and superiority of this method.

Optimal Time Delay Extraction for Transmission Line Modeling

The frequency-dependent transmission line modeling by the traveling wave method requires approximating the propagation function with a delayed rational function. Some approaches are based on modal decomposition where scalar functions are fitted with a rational model plus a single time delay. The delay is calculated from the modal velocity and the minimum-phase-shift angle that can be reconstructed from the magnitude function. This paper shows that the accuracy in the phase reconstruction as calculated by Bode's magnitude-phase integral relation can be greatly improved by removal of a singularity in the integrand and by prediction of out-of-band samples for the magnitude derivative. It is further shown that the time delay giving the smallest rms-error in the final rational approximation is often substantially larger than the mps induced delay. An improved estimation is calculated via an auxiliary magnitude function and used for determining a bracketing interval for the true optimum that is identified by searching.

Maximum Likelihood Time Delay Estimation Based on Monte Carlo Importance Sampling in Multipath Environment

In multipath environment, the computation complexity of single snapshot maximum likelihood for time delay estimation is huge. In particular, the computational complexity of grid search method increases exponentially with the increase of dimension. For this reason, this paper presents a maximum likelihood estimation algorithm based on Monte Carlo importance sampling technique. Firstly, the algorithm takes advantage of the channel frequency response in order to build the likelihood function of time delay in multipath environment. The pseudoprobability density function is constructed by using exponential likelihood function. Then, it is crucial to choose the importance function. According to the characteristic of the Vandermonde matrix in likelihood function, the product of the conjugate transpose Vandermonde matrix and itself is approximated by the product of a constant and an identity matrix. The pseudoprobability density function can be decomposed into product of many probability density functions of single path time delay. The importance function is constructed. Finally, according to probability density function of multipath time delay decomposed by importance function, the time delay of the multipath is sampled by Monte Carlo method. The time delay is estimated via calculating weighted mean of sample. Simulation results show that the performance of proposed algorithm approaches the Cramér-Rao bound with reduced complexity.

Small-Signal Analysis of the Microgrid Secondary Control Considering a Communication Time Delay

This paper presents a small-signal analysis of an islanded microgrid composed of two or more voltage-source inverters connected in parallel. The primary control of each inverter is integrated through an internal current and voltage loops using proportional resonant compensators, a virtual impedance, and an external power controller based on frequency and voltage droops. The frequency restoration function is implemented at the secondary control level, which executes a consensus algorithm that consists of a load-frequency control and a single time delay communication network. The consensus network consists of a time-invariant directed graph and the output power of each inverter is the information shared among the units, which is affected by the time delay. The proposed small-signal model is validated through simulation results and experimental results. A root locus analysis is presented that shows the behavior of the system considering control parameters and time delay variation.

Stability and Bifurcation Analysis of Arbitrarily High-Dimensional Genetic Regulatory Networks With Hub Structure and Bidirectional Coupling

This paper mainly studies the stability and Hopf bifurcation criteria of hub-based genetic regulatory networks with multiple delays and bidirectional couplings. The hub-structured network is an important motif in complex networks, which provides a new view angle on structure to describe the regulation mechanism between genes (including both mRNAs and proteins). It is well known that hubs play a leading role in characterizing the network dynamical behaviors. However, the dynamics of hubs or star-coupled systems is not well understood. In this paper, we first examine the existence of the positive equilibria in this type of genetic networks. By analyzing the associated characteristic equation, we present sufficient conditions of biochemical parameters for delay-independent local stability in hub-coupled genetic regulatory networks. Then we investigate their Hopf bifurcation when such networks lose their stability. Specific conditions for delay-dependent stability and Hopf bifurcations in genetic networks with hub structure are derived. It is found that the dynamics of hub-structured genetic regulatory networks has no direct relationship with single time delay or individual connection, but instead depends on the sum of all delays among all genes and the product of the connection strengths between all genes. Finally, some simulation examples are provided to substantiate our analysis.

Kernel regression estimates of time delays between gravitationally lensed fluxes

Strongly lensed variable quasars can serve as precise cosmological probes, provided that time delays between the image fluxes can be accurately measured. A number of methods have been proposed to address this problem. In this paper, we explore in detail a new approach based on kernel regression estimates, which is able to estimate a single time delay given several datasets for the same quasar. We develop realistic artificial data sets in order to carry out controlled experiments to test of performance of this new approach. We also test our method on real data from strongly lensed quasar Q0957+561 and compare our estimates against existing results.

Review Study of Detection of Diabetes Models through Delay Differential Equations

Mathematical models based on advanced differential equations are utilized to analyze the glucose-insulin regulatory system, and how it affects the detection of Type I and Type II diabetes. In this paper, we have incorporated several models of prominent mathematicians in this field of work. Three of these models are single time delays, where either there is a time delay of how long it takes insulin produced by the pancreas to take effect, or a delay in the glucose production after the insulin has taken effect on the body. Three other models are two-time delay models, and based on the specific models, the time delay takes place in some sort of insulin production delay or glucose production delay. The intent of this paper is to use these multiple delays to analyze the glucose-insulin regulatory system, and how if it is not properly working at any point, the high risk of diabetes becomes a reality.

Prediction of chatter stability for milling process using Runge-Kutta-based complete discretization method

On the basis of the classical Runge-Kutta method and the complete discretization method, a Runge-Kutta-based complete discretization method (RKCDM) is proposed in the paper to predict the chatter stability of milling process, in which the regenerative effect is taken into consideration. Firstly, the dynamics model of milling process is simplified as a 2-DOF vibration system in the two orthogonal directions, which can be expressed as coefficient-varying periodic differential equations with a single time delay. Then, all parts of the delay differential equation (DDE), including delay term, time-domain term, parameter matrices, and most of all the differential terms are discretized using the classical fourth-order Runge-Kutta iteration method to replace the direct integration scheme used in the classical semi-discretization method (C-SDM) and the classical complete discretization scheme with the Euler method (C-CDSEM), which can simplify the complexity of the discretization iteration formula greatly. Lastly, the Floquet theory is adopted to predict the stability of milling process by judging the eigenvalues of the state transition matrix corresponding to certain cutting conditions. Comparing RKCDM with C-SDM and C-CDSEM, the numerical simulation results show that RKCDM has the highest convergence rate, computation accuracy, and computation efficiency. As dichotomy search rather than sequential search is used in the algorithm, the calculation time for obtaining the stability lobe diagrams (SLDs) is greatly reduced. As a result, it is practical to determine the optimal chatter-free cutting conditions for milling operation in shop floor applications.

A novel approach for the prediction of the milling stability based on the Simpson method

In this paper a new approach is presented for predicting the milling stability based on the Simpson method. Generally the milling dynamic process is described as a linear time-periodic system with a single discrete time delay. By dividing the tooth passing period equally into a finite set of time intervals, the Simpson method is utilized in each time interval to estimate the state items. Then the state transition matrix over one tooth passing period is constructed, and the milling stability could be predicted by the Floquet theory. The convergence rate of the proposed method is discussed, and two benchmark examples are conducted. The results show that the proposed method achieves satisfactory accuracy and efficiency.