Influence Of Time Delay Research Articles

Stability and bifurcation analysis of $ SIQR $ for the COVID-19 epidemic model with time delay

<abstract> Based on the $ SIQR $ model, we consider the influence of time delay from infection to isolation and present a delayed differential equation (DDE) according to the characteristics of the COVID-19 epidemic phenomenon. First, we consider the existence and stability of equilibria in the above delayed $ SIQR $ model. Second, we analyze the existence of Hopf bifurcations associated with two equilibria, and we verify that Hopf bifurcations occur as delays crossing some critical values. Then, we derive the normal form for Hopf bifurcation by using the multiple time scales method for determining the stability and direction of bifurcation periodic solutions. Finally, numerical simulations are carried out to verify the analytic results. </abstract>

Switching Time Delay Optimization for “SiC+Si” Hybrid Device in a Phase-Leg Configuration

Compared to SiC MOSFET, the switching loss of Si IGBT is much higher due to its slow switching speed and tail current. Si IGBT/SiC MOSFET hybrid switch device can reach to optimal performance with low static and dynamic loss, which can improve the current capacity of SiC devices and reduce the power loss of Si IGBT based converters. With the separated gate control signals, the switching moments of the two devices can be controlled independently to ensure Si IGBT under zero-voltage switching (ZVS) conditions. This measurement tends to reduce the switching loss of Si IGBT. However, the switching time delay between these two devices has significant impacts on its power loss. In this paper, the switching time delay optimization method is proposed to minimize the power loss of the hybrid switch. The static and dynamic characteristics of Si IGBT/SiC MOSFET hybrid-paralleled switch are studied, and a generalized power loss model for hybrid switch is developed. The influence of switching time delay on the characteristics of hybrid switch is analyzed and verified through double pulse tests in a phase-leg configuration. The experimental results show that the optimal turn-on delay time is that the two devices turn on at the same time and the turn-on loss can be reduced by about 73% compared with the solely Si IGBT and by about 52% compared with the solely SiC MOSFET. While the optimal turn-off sequence is that the Si IGBT turns off ahead of the SiC MOSFET. Under the proposed optimal turn-off delay time of the hybrid switch, the turn-off loss is reduced by about 61.4%. This optimization strategy is used in a Buck converter to verify the superiority of the SiC/Si hybrid switch and the optimal switching sequence. Simulation results show that the optimal switching sequence is consistent with theoretical analysis, and the efficiency is improved by 2.5% compared with Buck converter using solely Si IGBT.

Influence of demographic parameters and time delays among patients with ACS and OHCA in non-urban areas

Out-of-hospital cardiac arrest (OHCA) represents a major public health. Acute coronary syndrome (ACS) is the leading precipitant of collapse. Predictors of survival have been described in the literature. However, most studies have been conducted in city areas. Less is known about resuscitation performance of mobile medical team (MMT) in non-urban areas. Established in 1903, our institution was initially founded to treat patients suffering from tuberculosis. Built at the top of a hill, the location of the ancient sanatorium consists of rural areas with a low population density. To perform a quality control assessment on the management of OHCA after ACS in non-urban areas. To identify quantitative variables influencing 30-day outcome. Retrospective single-center study including 40 patients resuscitated from OHCA after ACS. Baseline characteristics, resuscitation settings, time delays, blood samples, cardiac findings and clinical outcomes were analyzed. 30-day mortality was more likely associated with the following parameters: age, no-bystander CPR, no use of AED, non-convertible rhythm, recurrent cardiac arrest, epinephrine dose, shock, lactate level, LVEF, culprit lesion, no-flow & low-flow duration, kilometres and time delays (MMT arrival, ER - CathLab - ICU admission). Particularly, high lactate, long duration of RCP, remoteness from hospital and prolonged pre-hospital management (MMT arrival, ER admission) were predictors of early mortality (see bold type in Table 1 ). Beyond the usual prognostic factors, it would appear that demographic parameters and time delays represent major determinants of mortality after OHCA in non-urban areas. Therefore, shortening response times and prompt delivery to hospital facilities may help to improve the prognosis, rather than prolonged pre-hospital care. Further RCTs are needed to assess the effect of the ‘scoop & run’ approach vs the ‘stay & play’ approach in this setting.

An Improved Prony Prediction Compensation‐Based Wide‐Area Damping Control Approach for Power System Low‐Frequency Oscillation Suppression

Currently, wide‐area damping control has been considered one of the most effective and promising methods to solve the problem of interval low‐frequency oscillation in power systems. In order to reduce adverse affection caused by time delay in acquisition and transmission of wide‐area signals, an improved Prony prediction compensation‐based wide‐area damping control approach for power system low‐frequency oscillation suppression is proposed in this paper. Firstly, the influence of communication time delay on power system stability is analyzed by a small disturbance stability analysis method. An algorithm based on the improved Prony prediction algorithm is designed to predict the acquired signals with time delay. A second derivative‐based order determination algorithm is used to obtain the best effective order of the prediction model, and the parameter prediction step size of the prediction model is determined by the actual situation of time delay change. Finally, design of a wide‐area damping controller based on the improved Prony prediction compensation is presented in detail. The proposed control approach is conducted in a four‐machine and two‐zone power system, and the experiment results show that the proposed approach can effectively compensate for the signal under the conditions of fixed time delay and variable time delay and has better adaptability advantages than the traditional Prony prediction compensation method.

A Deformation Measurement Algorithm Based on Adaptive Variable Parameter Multiple Model for Large Ships

Accurate measurement of ship deformation angle is of great significance for building a unified space attitude reference and improving the combat performance of the entire ship. However, many problems existing in the actual sailing process restrict its measurement accuracy severely, such as the time delay between measurement equipment, the unknown characteristics of measurement noise, and the unknown model parameters of the dynamic deformation. This article proposes an adaptive variable parameter multiple model (AVPMM) algorithm that can simultaneously solve these problems. First, a time delay compensation algorithm is derived to suppress the influence of time delay on measurement accuracy; then an adaptive cubature Kalman filter is designed based on the idea of adaptive filtering to suppress the influence of unknown characteristics of measurement noise; and finally, an AVPMM algorithm is designed by combining the above ideas to reduce the impact of unknown model parameters of dynamic deformation. The results of the simulation and turntable experiment show that this algorithm has good measurement accuracy and the error is less than $0.15^\prime$ .

On a stage-structured population model in discrete periodic habitat: III. unimodal growth and delay effect

For a stage-structured population model in periodic discrete habitat, with periodic initial values it reduces to a system of two differential equations with time delay. Assuming the birth rate is of unimodal type, we obtain the influence of time delay on the local and global dynamics. In particular, large delay leads to population vanishing. As delay decreases, we found three critical values of delay for the emergence of different dynamics, by appealing to a combination of monotone dynamical system theory, Hopf bifurcation theory and the fluctuation method. Numerical simulations are also performed to illustrate the results.

A Network Selection Strategy Based on Joint Optimization of User Satisfaction and Transmission Efficiency in Internet of Vehicle

Network selection in the Internet of Vehicles has become a popular topic of research. Unlike existing algorithms for heterogeneous network environments that rarely consider user satisfaction, in this paper, we propose a network selection strategy that takes into account both user satisfaction and transmission efficiency. We employ the effective capacity concept, which describes the maximum throughput a system can achieve under a specific statistical Quality-of-Service (QoS) delay violation probability constraint. This strategy first analyzes the influence of different utility function weight coefficients, transmission power, and time delay on each network utility satisfaction function. It is evident that the weight coefficient is proportional to the value of the utility function. Within a constrained transmission power range, the rate of increase of the function gradually slows down until it approaches a fixed value. When the delay factor value is larger, the function value is smaller, which indicates that the pursuit of lower delay will sacrifice other network performance aspects. In order to determine the maximum value of each network utility satisfaction function, a convex optimization theory is introduced for the joint optimization of user satisfaction and transmission efficiency. Finally, simulation experiments carried out under three representative network environments show that the proposed strategy is efficient and reliable.

Sliding Mode Dynamic Surface Control for Multi-Machine Power Systems with Time Delays and Dead-Zones

This paper presents a sliding mode dynamic surface control strategy for multi-machine power systems with static var compensator (SVC) to design the controller of the generator excitation system. Firstly, compared with the existing control methods, the combination of sliding mode control and dynamic surface control improves the robustness of the system and avoids the “explosion of complexity” problems. Subsequently, the fuzzy logic system is introduced to estimate the unknown continuous function in power system, and the norm of the weight vector is used to replace the estimation of the entire weight vector. In this way, computational burden will be reduced. In addition, the influences of unknown time delays and dead-zones are considered. Finite cover lemma is introduced to deal with unknown time delays, which enables arbitrarily small tracking performance. The unknown dead-zone is converted into the sum of linear dead zone and bounded nonlinear dead zone. Finally, the simulation results are provided to validate the feasibility and effectiveness of the proposed control strategy.

NIMCE: A Gene Regulatory Network Inference Approach Based on Multi Time Delays Causal Entropy.

Gene regulatory networks (GRNs)are involved in various biological processes, such as cell cycle, differentiation and apoptosis. The existing large amount of expression data, especially the time-series expression data, provide a chance to infer GRNs by computational methods. These data can reveal the dynamics of gene expression and imply the regulatory relationships among genes. However, identify the indirect regulatory links is still a big challenge as most studies treat time points as independent observations, while ignoring the influences of time delays. In this study, we propose a GRN inference method based on information-theory measure, called NIMCE. NIMCE incorporates the transfer entropy to measure the regulatory links between each pair of genes, then applies the causation entropy to filter indirect relationships. In addition, NIMCE applies multi time delays to identify indirect regulatory relationships from candidate genes. Experiments on simulated and colorectal cancer data show NIMCE outperforms than other competing methods. All data and codes used in this study are publicly available at https://github.com/CSUBioGroup/NIMCE.

Mathematical analysis of information propagation model in complex networks

In virtue of identifying the influence of nodes, the spatial distance of rumor propagation is defined with the partition and clustering in the network. Considering the temporal and spatial propagation characteristics of rumors in online social networks, we establish a delayed rumor propagation model based on the graph theory and partial functional differential equations. Firstly, the unique existence and uniform boundedness of the nonnegative solution are explored. Secondly, we discuss the existence of positive equilibrium points sufficiently. Thirdly, stabilities of the rumor-free and rumor-spreading equilibrium points are investigated according to the linearization approach and Lyapunov function. Finally, we perform several numerical simulations to validate theoretical results and show the influence of time delay on rumor propagation. Experimental results further illustrate that taking forceful actions such as increasing the time delay in the rumor-spreading process can control rumor propagation due to the timely effectiveness of the information.

Mechanism Analysis and Damping Method for High Frequency Resonance Between VSC-HVDC and the Wind Farm

As of now, the issue of High Frequency Resonance (HFR) in the Doubly Fed Induction Generator (DFIG) with the weak ac grid have been widely investigated. However, due to the influence of time delay in the control of VSC-HVSC, the HFR can occur in the interconnected system where the VSC-HVDC connects to the wind farm as well. Based on impedance model of DFIG system and the deduced impedance model of VSC-HVDC, this paper investigates the occurrence mechanism of the HFR when the VSC-HVDC connects to DFIG based wind farm, and analyzes the mechanism that the control delay influences the stability of VSC-HVDC system. Further, to avoid the HFR, this article proposes a damping control method based on an additional voltage controller, the damping controller can fully counteract the influence of time delay so that the HFR can be damped. Also, the performance of the controller can be maintained when control delay changes. Simulation results of the VSC-HVDC system connects to a wind farm are given in this paper to verify the correctness of the occurrence mechanism and the effectiveness of the proposed damping methods.

Optimal control of an avian influenza model with multiple time delays in state and control variables

In this paper, we consider an optimal control model governed by a class of delay differential equation, which describe the spread of avian influenza virus from the poultry to human. We take three control variables into the optimal control model, namely: slaughtering to the susceptible and infected poultry ( \begin{document}$ u_{1}(t) $\end{document} ), educational campaign to the susceptible human population ( \begin{document}$ u_{2}(t) $\end{document} ) and treatment to infected population ( \begin{document}$ u_{3}(t) $\end{document} ). The model involves two time delays that stand for the incubation periods of avian influenza virus in the infective poultry and human populations. We derive first order necessary conditions for existence of the optimal control and perform several numerical simulations. Numerical results show that different control strategies have different effects on controlling the outbreak of avian influenza. At the same time, we discuss the influence of time delays on objective function and conclude that the spread of avian influenza will slow down as the time delays increase.

Stability and Bifurcation Analysis of Time Delayed Prey-Predator System with Holling Type-III Response Function

Interaction between prey and predator is a recurring event that occurs continuously and the presence of both can mutually affect each other’s population. This paper discusses the stability and bifurcation analysis of time delayed prey-predator system with Holling type-III response function incorporating a prey refuge. Holling type-III response function is used because the availability of the prey in nature is decreasing. Time delay represents the time for predators to find another prey population when the available population is decreasing. Dynamic analysis is used to study the influence of a given response function. The equilibrium point and stability analysis of the model with and without time delay has been calculated and analyzed. Model analysis under the influence of time delay and coefficient of competition among predators shows an indication of Hopf bifurcation in the neighborhood of the co-existing equilibrium point.

Distributed Control of Cooperative Vehicular Platoon With Nonideal Communication Condition

An optimized control approach for the distributed cooperative vehicular platoon was proposed in this paper, considering actuator delay and nonideal communication condition. A hierarchical structure is used to model the vehicular platoon, where the desired acceleration is optimized by CACC controller and the longitudinal tracking controller is proposed to follow it. In the design process of CACC controller, a parameter space approach and linear quadratic regulator (LQR) method are applied to guarantee the string stability and optimized performance. The influence of communication time delay and dropout rate is revealed by the changing of string stable region. Analytical results are verified by numerical simulations of a six-vehicle platoon where the leading vehicle follows the FTP-75 drive cycle speed profile. Furthermore, a Hardware-in-the-Loop (HIL) test is carried out with Carsim to simulate a high-fidelity vehicle dynamic model and dedicated short range communication (DSRC) modems as hardware in the loop as well as the control unit to achieve the inter-vehicle communication. The results show that the designed CACC platooning controller exhibits favorable performance in highway driving scenarios. The platooning vehicles display excellent car-following behavior with high accuracy, driving comfort and safety.

Research on the Influence of Communication Time-Delay on Multi-agent System Based Distributed Energy Dispatching Control Consensus

Multi-agent based distributed control methods are widely applied in distributed energy dispatching control. However, the control processes are highly dependent on the information interaction among the distributed generation units through the communication network. The communication time-delay would affect the performance and stability of the multi-agent based distributed energy dispatching control system. To investigate the effect of communication time-delay on the dispatching control, the incremental cost rate in the economic dispatch model is adopted as consensus variables of multi-agent system, and a multi-agent system with communication time-delay based distributed energy dispatching control consensus algorithm is proposed. Moreover, two cases simulations are implemented and the effects of the time-delay on the consensus convergence are analyzed. This work provides a reference for the optimal design of distributed energy dispatching control.

Comparison of Total Factor Productivity and Total Productivity for Their Relationship Attributes with Profit

This study compares two productivity metrics, Total Factor Productivity (TFP) and Total Productivity (TP), for their associations with one another and two types of profits. Several attributes of the direct productivity-profit relationship, not mediated by any other firm characteristic, are evaluated, such as the existence of bi-directionality in the predictive association between productivity and profit. The influence of productivity on profit is reaffirmed; crucially, the impact of profit on productivity is found to exist as well. The unique contribution of this study is that it demonstrates that TFP outperforms TP considerably in its ability to associate with and predict profits. The influence of seasonal and non-seasonal time delays on the productivity-profit association are found to be important implications for engineering managers.

Active structural control via metaheuristic algorithmsconsidering soil-structure interaction

In this study, multi-story structures are actively controlled using metaheuristic algorithms. The soil conditions such as dense, normal and soft soil are considered under near-fault ground motions consisting of two types of impulsive motions called directivity effect (fault normal component) and the flint step (fault parallel component). In the active tendon-controlled structure, Proportional–Integral–Derivative (PID) type controller optimized by the proposed algorithms was used to achieve a control signal and to produce a corresponding control force. As the novelty of the study, the parameters of PID controller were determined by different metaheuristic algorithms to find the best one for seismic structures. These algorithms are flower pollination algorithm (FPA), teaching learning based optimization (TLBO) and Jaya Algorithm (JA). Furthermore, since the influence of time delay on the structural responses is an important issue for active control systems, it should be considered in the optimization process and time domain analyses. The proposed method was applied for a 15-story structural model and the feasible results were found by limiting the maximum control force for the near-fault records defined in FEMA P-695. Finally, it was determined that the active control using metaheuristic algorithms optimally reduced the structural responses and can be applied for the buildings with the soil-structure interaction (SSI).

Hopf Bifurcation in an Augmented IS-LM Linear Business Cycle Model with Two Time Delays

This paper deals with the amalgamated basic IS-LM business cycle model with Kaldor’s growth model to form an augmented model. Pertaining to substantial evidence, IS-LM model in paradigm with a specific economic extension (Kaldor-Kalecki Business cycle model in our case) provides an adept explanation of a developing but strong economy like that of our country. Occurring in the equation of capital accumulation, the two time delays are a result of the assumption in the investment function being both income and capital stock dependent in past period and maturity period. Investigating a model combined with capital accumulation is both interesting and important. From economist point of view, production without capital is impossible to even imagine. Moreover capital accumulation is impeccable to large-scale production, specialisation and creation of employment opportunities. In our model ‘I’ the investment function, ‘S’ the savings function and ‘L’ the demand for money are depending linearly on their arguments. We adhere to a linear model, contrary to the popular belief of non- linear models being the undisputed style for modern economics. The model is first shown to be mathematically and economically poised. The local stability of boundary and interior equilibrium points has been investigated. Three cases arise, pertaining to two time delays. System dynamics exhibits mutation under the influence of time delays and may clinch or discharge its local stability when subjected to the latter. Hopf bifurcation occurs when the delay parameter crosses a critical value.

Exponential Stability of Mixed Time-Delay Neural Networks Based on Switching Approaches.

Neural networks (NNs) have been deeply studied due to their wide applicability. Since time delays are unavoidable in reality, it is basic and crucial for all applications based on NNs to guarantee system stability under the influence of mixed time delays. To better exploit the variation information of time delay, we introduce the switching idea and approaches into mixed time-delay NNs to solve the stability problem. First, the considered mixed time-delay NNs are modeled as the switched NNs by dividing the two classes of time delays, discrete and distributed time delays, into some variable intervals and combining these intervals as new switching modes. With the help of mode-dependent average dwell-time switching, Lyapunov theory, and mathematical techniques, several exponential stability criteria on the modeled switched systems containing different modes are obtained. Moreover, via introducing the mathematical condition of the unstable subsystem in the switching system, a less conservativeness condition on the exponential stability of the modeled NNs is proposed. We perform three examples for testifying the validity of the proposed methods over existing ones.

Laser processing of dielectrics using spatiotemporally tuned ultrashort pulses

The authors report on the theoretical and experimental studies of laser-induced optical breakdown on the surface of fused silica to elucidate the influence of time delay and spatial separation between two ultrashort pulses on the position and size of the modification. Carriers involved in the damage formation including free electrons in the conduction band and self-trapped excitons (STEs) are investigated. The relationship between damage morphology and time delay shows that the seeding carriers (free electrons and STEs) generated from the first pulse are found to play a significant role for the second pulse—which is temporally and spatially separated from the first pulse—in creating the critical electron density needed for an optical breakdown. Consequently, processing outcomes, such as accuracy (position of the hole) and resolution (size of the hole), depend on the interplay of various laser-induced physics that can be tailored for specific goals. As a demonstration, laser lithography with resolution below the diffraction limit is achieved by exploiting multipulse induced physics. This work is a step toward repeatable laser processing of dielectrics beyond the diffraction limit and provides insights into ultrafast laser-matter interaction under the condition of an extremely high pulse repetition rate.