Time Delay Parameter Research Articles

A study of the 3-phase lag model to a two-dimensional isotropic micro-polar thermoelastic medium with memory-dependent properties

This article enlightens the two-dimensional (2D) isotropic micro-polar thermoelastic problem of the three-phase-lag (3PHL) model and heat conduction equation is formulated in the context of memory-dependent derivative (MDD). The equations are converted into the domain of the Laplace transform vector matrix differential equation form and solved by using the eigenvalue technique. To obtain an analytical solution of displacement, temperature, and stress components Silicon material properties are used. Inversion of the Laplace transform with Fourier series expansion technique is used to obtain the numerical solution. For obtaining graphical results Mathematica software is used. For the purpose of exhibiting the beauty of MDD in the present model comparisons are made between the time delay parameters and kernel functions (constant, linear, and non-linear kernels), respectively, over the micro-polar panel. The results obtained have a valuable impact on structural analysis, especially in the design of rotating machinery structures using accurate material properties.

Analysis of vibration characteristics of face gear powering-split transmission system

A nonlinear dynamic model of the face gear powering-split transmission system was established, and the nonlinear dynamic characteristics of the face gear powering-split transmission system were studied by considering various factors such as support stiffness, time-varying meshing stiffness, lateral clearance of teeth, comprehensive transmission error and bearing stiffness. The Runge–Kutta integral method is used to solve the differential dynamics of the system. The nonlinear behavior of the system is described by the phase plane diagram, time history diagram, frequency domain diagram, and Poincare section diagram. The influence of external excitation frequency on the nonlinear behavior of the system is described by the bifurcation diagram. In addition, the multi-scale method is used to analyze the superharmonic resonance of the system and determine the stability conditions of the superharmonic resonance of the system. The influence of meshing damping, time-varying meshing stiffness, and time-delay control parameters on the amplitude-frequency characteristics of the system is studied by numerical analysis of the superharmonic resonance. The results show that the system will show periodic chaotic alternating motion characteristics under external excitation. Selecting meshing damping, meshing stiffness, and time delay control parameters in a reasonable range can effectively reduce the superharmonic co-amplitude and keep the system in a stable state.

Dynamical behavior of fractional order SEIR epidemic model with multiple time delays and its stability analysis

With multiple time delays, we investigated a Caputo fractional order dynamical system involving susceptible, exposed, infected, and recovered individuals. Positivity and boundedness are also theoretically demonstrated using Laplace transform and Mittag-Leffler function. The stability of the disease-free and epidemic equilibrium points has been studied for both delayed and non-delayed model. For generating numerical solutions to the model system, we used the Adam-Bashforth-Moulton predictor-corrector technique. With the help of MATLAB (2018a), we were able to conduct graphical demonstrations and numerical simulations. The system displays Hopf bifurcation and the solutions are no longer periodic beyond a certain threshold value of the time delay parameters.

Stochastic dynamics of a semiconductor laser with delayed optoelectronic feedback and noise

Semiconductor lasers(SLs), versatile tools in communication, medicine, and scientific research, demand close examination of their dynamic behavior. With their unique geometric forms and diminutive sizes, these lasers possess a heightened sensitivity to noise. In this paper, we delve into time-delay semiconductor laser systems, noise included, honing in on time-delays’ effects on noisy laser equations. Carrier density (N) and laser intensity (I) constitute the core parameters that define the performance of these lasers, and we scrutinize their dynamic trajectories. A cutting-edge method fusing stochastic center manifold theory with the stochastic averaging method enables us to probe the stochastic dynamical attributes of semiconductor laser equations. We uncover that the time-delay parameter (τ 1) produces varied consequences on the laser system’s stability under both positive and negative optical feedback conditions. The negative feedback typically bolsters laser performance, fostering increased stability, whereas the positive counterpart could incite instability. By deftly managing the time-delay parameter, one can fine-tune the dynamic performance of semiconductor lasers, mitigating output power fluctuations and tightening linewidths, thereby augmenting stability and spectral purity. Moreover, in the realm of positive optical feedback scenarios, adroitly modifying the time-delay parameter can quell instability to a degree, paving the way for a novel regulatory approach to optimize laser performance. This lays the groundwork for further enhancement of semiconductor laser performance, as well as curbing the detrimental effects of noise on their operation.

The role of delay in vaccination rate on Covid-19

The role of vaccination in tackling Covid-19 and the potential consequences of a time delay in vaccination rate are discussed. This study presents a mathematical model that incorporates the rate of vaccination and parameters related to the presence and absence of time delay in the context of Covid-19. We conducted a study on the global dynamics of a Covid-19 outbreak model, which incorporates a vaccinated population and a time delay parameter. Our findings demonstrate the global stability of these models. Our observation indicates that lower vaccination rates are associated with an increase in the overall number of infected individuals. The stability of the corresponding time delay model is determined by the value of the time delay parameter. If the time delay parameter is less than the critical value at which the Hopf bifurcation occurs, the model is stable. The results are supported by numerical illustrations that have epidemiological relevance.

Optimizing the Imaging Scheme of Small-Dose Contrast Agent in 4D-CT Localization Enhancement Scan for Radiotherapy of Liver Cancer

The primary liver cancer radiation therapy 4D-CT-enhanced (CE-4DCT) scan can accurately reflect the state of the liver as it moves with respiration, and enables clear visualization of the tumor, providing a precise range for target area outlining. However, the CE-4DCT scan localization time of primary liver cancer is long, and the fixed delay time of diagnostic CT cannot obtain high-quality 4DCT images. To this end, we designed a randomized controlled study to investigate the ideal localization scan delay time parameters for primary liver cancer CE-4DCT. Patients with primary hepatocellular carcinoma who presented to our department for radiotherapy CT localization from January to December 2022 participated in this study. All subjects were randomly divided into two groups in a 1:1 ratio. CE-4DCT scans were performed using a high concentration of iodomepril (400 mg/ml) contrast agent with a contrast volume equal to the patient's body weight. The scanning parameters were set according to scheme A (flow rate 2.0 ml/s, delay time 30s) and B (2.0 ml/s, 35s) respectively. Before the CE-4D CT scan, CT plain scan was routinely performed, physicians measured the CT value (HU) of abdominal aorta, portal vein, left hepatic vein, middle hepatic vein, right hepatic vein, liver parenchyma and tumor lesion on CT40 time item and plain scan images respectively. The image quality was subjectively and qualitatively assessed. The image enhancement effect is divided into excellent, good, relatively poor and poor. A total of 18 patients were included in this study. Patient characteristics were well-balanced in both groups. There were statistical differences between the two groups (A vs B) in the abdominal aorta (226.66 ± 45.59 vs. 176.66 ± 32.84, p = 0.017), left hepatic vein (142.77 ± 24.41 vs. 164.88 ± 19.02, p = 0.048); in the portal vein, middle hepatic vein, right hepatic vein, liver parenchyma, and tumor lesions CT values were not statistically different. The comparison of all flat-scan images between the two groups was statistically significant. The comparison of all flat-scan images in both groups was statistically significant. The subjective qualitative assessment of the developing effect was excellent in 44.4% (33.3% vs. 11.1%), good in 16.7% (5.6% vs. 11.1%), and poor in 38.9% (16.7% vs. 22.2%) in both groups. image quality was slightly higher in group A than in group B, but did not reach statistical significance (χ2 = 1.088, p = 0.698). In patients with primary hepatocellular carcinoma with portal vein carcinoma thrombosis 83.33% subjectively evaluated poor results. Qualitatively acceptable enhanced images were obtained for primary hepatocellular carcinoma (CE-4DCT) localization scans with a delay time controlled at 30s when using the least amount of contrast agent and the same flow rate.

An investigation of seismic anisotropy in the crust beneath the western part of the North Anatolian Fault Zone

The North Anatolian Fault (NAF) is one of the most well-known continental strike slip faults, however, the details related to the geodynamic processes and the extent of deformation in the crust remain poorly understood. Within the context of the Dense Array for North Anatolia (DANA) project, a comprehensive data set was gathered from a dense temporary seismic network consisting of 70 stations that were deployed in early May 2012 and operated for 18 months in the Sakarya region and the surroundings. With the aim of further exploring the crustal deformation near the fault mainly caused by the strike slip motion also resulting in the alignment of minerals, the crustal seismic anisotropy beneath the western segment of NAF was investigated by local shear wave splitting analysis. Out of 1371 events, 90 well located earthquakes were extracted with magnitudes >1.4 corresponding to a total of 645 splitting measurements. This method makes use of earthquakes nearby or directly below each station benefiting from the fast polarization direction and the relevant delay time parameters as the main output. Despite the scattered patterns, the fast orientations are dominantly E-W parallel to the fault strike. Delay times between the fast and slow components of the shear wave vary between 0.01 and 0.3 s clearly revealing the existence of crustal anisotropy. In particular, measurements at each station exhibits spatial variations across the fault where it splays into two main branches beneath the study area separating different geologic units. A strong correlation could not be established between small scale faults and azimuthal anisotropy. The measurements presented here constrain crustal anisotropy above the deepest earthquakes at approximately 15 km depth.

Potential field-based modeling and stability analysis of heterogeneous traffic flow

Car-following behavior is influenced by multiple factors. Utilizing the potential field theory, previously determined as a comprehensive representation of these influencing factors, this study introduces a unified potential field-based car-following model tailored for mixed traffic flow. Considering the diverse information receptivity of various vehicle types, the model is shaped to encapsulate both Human Driven Vehicles and Connected and Automated Vehicles. Using the characteristic equation-based method, the stability conditions of the model are delineated. Subsequently, a detailed examination of mixed traffic flow stability was conducted across varying Connected and Automated Vehicles penetration rates. Leveraging a dataset of 300 real-world trajectories, the results were benchmarked against classical models such as the Intelligent Driver Model. Notably, our proposed model exhibited an 18.67 % improvement in safety metrics and a 1.36 % improvement in fuel economy over the Intelligent Driver Model when representing Connected and Automated Vehicles. The stability of the mixed traffic flow was found to correlate strongly with vehicular time delay and acceleration parameter weights. Furthermore, augmenting the Connected and Automated Vehicles penetration rate surfaced as a promising strategy to bolster traffic flow stability. Collectively, these findings furnish substantial enhancements to the existing body of knowledge on mixed traffic flow stability, offering pragmatic insights for future research and real-world applications, including traffic management, urban planning, and the development of Intelligent Transport Systems.

New results for dynamical analysis of fractional-order gene regulatory networks with time delay and uncertain parameters

In this paper, a novel class of networks named fractional-order gene regulatory networks with time delay and uncertain parameters (FGRNTDUP) are formulated, and some new results are obtained for the dynamics of FGRNTDUP. Firstly, a general fractional-order differential equality is built to supply a new viewpoint about the study of finite-time stability, stabilization, and synchronization for many fractional systems. Secondly, based on contraction mapping principle, the existence and uniqueness of the equilibrium point are strictly proved for the FGRNTDUP. Meanwhile, by virtue of fractional Lyapunov method and inequality techniques, some sufficient conditions are derived to guarantee the global Mittag–Leffler stability of FGRNTDUP. Moreover, based on a newly developed inequality, some novel criteria are yielded to realize the finite-time synchronization of FGRNTDUP by designing a suitable adaptive controller. Finally, two numerical examples are provided to verify the effectiveness of the obtained results.

Desynchronizing oscillators coupled in multi-cluster networks through adaptively controlling partial networks.

This article introduces an adaptive control scheme with a feedback delay, specifically designed for controlling partial networks, to achieve desynchronization in a coupled network with two or multiple clusters. The proposed scheme's effectiveness is validated through several representative examples of coupled neuronal networks with two interconnected clusters. The efficacy of this scheme is attributed to the rigorous and numerical analyses on the corresponding transcendental characteristic equation, which includes time delay and other network parameters. In addition to investigating the impact of time delay and inter-connectivity on the stability of an incoherent state, we also rigorously find that controlling only one cluster cannot realize the desynchronization in the coupled oscillators within three or more clusters. All these, we believe, can deepen the understanding of the deep brain stimulation techniques presently used in the clinical treatment of neurodegenerative diseases and suggest future avenues for enhancing these clinical techniques through adaptive feedback settings.

Mechanism of time-delay feedback control of suspension damping with an annular vibration-absorbing structure

With the aim of enhancing both the ride comfort and the safety of the vehicle, we propose a new type of suspension with an annular vibration-absorbing structure, and establish a 3-DOF 1/4 vehicle model. The structure parameters and time-delay feedback control parameters are determined by particle swarm optimization algorithms, which take the root mean values of body acceleration, suspension dynamic deflection, and tire dynamic displacement as their optimization objectives. We analyze the stability of the suspension control system to ensure the stability of the time-delay control system through the Routh-Hurwitz stability criterion, characteristic root method, and stability switching method. Then, we compare and analyze the response characteristics of conventional suspension, new suspension without time-delay feedback control, and new suspension with time-delay feedback control under simple harmonic excitation and random excitation. The results show that the new suspension with time-delay feedback control has a significant damping effect on the body under the premise of ensuring the stability of the system.

Mean attractors of stochastic delay lattice [formula omitted]-Laplacian equations driven by superlinear noise in high-order product Bochner spaces

This paper is concerned with the existence and uniqueness of mean random attractors of a class non-autonomous stochastic delay p-Laplacian lattice systems defined on a high-dimensional integer set Zd driven by a family infinite-dimensional superlinear noise. We first establish the global-in-time existence and uniqueness of the solutions in C([τ,∞),L2k(Ω,ℓ2(Zd)))∩Lq(Ω,Llocq((τ,∞),ℓq(Zd))) for any k⩾1 when the draft term has an arbitrary polynomial growth rate q>2 and the coefficient of the noise admits a superlinear growth order q̃∈[2,q). We then show that the mean random dynamical system generated by the solution operators has a unique weakly compact and weakly attracting mean random attractor in the high-order product Bochner space L2k(Ω,F;ℓ2(Zd))×L2k(Ω,F;L2k((−ϱ,0),ℓ2(Zd))), where ϱ is the time delay parameter. The dissipative property of the draft term is employed to carefully controlling the superlinear growth diffusion term. When k=1, our results are new even in the product Hilbert space L2(Ω,F;ℓ2(Zd))×L2(Ω,F;L2((−ϱ,0),ℓ2(Zd))). This work can be regard as a further study of mean attractors of stochastic p-Laplacian lattice systems in the works of Wang and Wang (2020) and Chen et al. (2023).

Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations

We consider a system of fractional delayed differential equations. The ordinary differential version of the system without delay is introduced in the Lengyel-Epstein reaction-diffusion system. We evaluate the system with and without delay and explore the stability of the unique positive equilibrium. We also prove the existence of Hopf bifurcation for both cases. Furthermore, the impacts of Caputo fractional order parameter and time delay parameter on the dynamics of the system are investigated with numerical simulations. It is also concluded that for different values of time delay parameter, the decreament of the Caputo fractional order parameter has opposite effects on the system in terms of stability.

Investigation of memory influences on bio-heat responses of skin tissue due to various thermal conditions.

Advancement of new technologies such as laser, focused ultrasound, microwave and radio frequency for thermal therapy of skin tissue has increased numerous challenging situations in medical treatment. In this article, a new meticulous bio-heat transfer model based on memory-dependent derivative with dual-phase-lag has been developed under different thermal conditions such as thermal shock and harmonic-type heating. Laplace transform method is acquired to perceive the analytical consequences. Quantitative results are evaluated for displacement, strain and temperature along with stress distributions in time domain by adopting the technique of inverse Laplace transform. Impacts of the constituents of memory-dependent derivatives-kernel functions along with time-delay parameter are analysed on the studied fields (temperature, displacement, strain and stress) for both thermal conditions separately using computational results. It has been found that the insertion of the memory effect proves itself a unified model, and therefore, this model can better predict temperature field data for thermal treatment processes.

A Computationally Efficient Estimator for the Target Angle, Delay, and Doppler Parameters in Passive Radar

The azimuth, elevation, time delay (TD), and Doppler shift (DS) of the target echo signal are important parameters for target localization in passive radar. In this paper, for the problem of joint estimation of target azimuth, elevation, TD, and DS parameters in passive radar, a computationally efficient estimator is proposed based on segmented coherent integration and uniform circular array (UCA) interferometer direction finding. First, according to the parameters of the target motion and illuminators of opportunity, the reference and surveillance signals are divided into segments, with fast time within a segment and slow time across the segments; then, matching filtering along the fast time and fast Fourier transform (FFT) along the slow time are performed to accumulate the target echo energy to the same delay-Doppler cell; finally, the UCA interferometer two-dimensional direction finding is performed at the delay-Doppler cell where the target echo is located, to achieve the target azimuth and elevation estimate. Simulation results demonstrate that the proposed algorithm has low computational complexity, high real-time processing capability, and can achieve efficient and real-time estimation of the azimuth, elevation, TD, and DS parameters of weak target echoes in passive radar.

A Picosecond Delay Generator Optimized by Layout and Routing Based on FPGA

A delay generator is a timing control device that can generate a delay for the input signal according to the actual requirements. A delay generator with a combination of rough delay and precise delay is implemented on a Xilinx Kintex-7 series FPGA with a design scheme based on carry delay chain. The delay generator uses the delay time parameters sent by the upper monitor to work and to reflect the current working state to the upper monitor. In this article, a theoretical model of the delay generator is designed, and a delay compensation scheme is proposed to make the working state of the theoretical model closer to the actual circuit. Through simulation experiments, the time resolution of the delay generator is 54 ps, and the time accuracy is less than 50 ps. The delay scheme adopted in this article is highly scalable, and the time resolution and time accuracy can be further improved. Finally, a theoretical model of the delay generator with relatively high time resolution is implemented through low resource occupancy rate and little workload.

Simultaneous identification of time-delay parameter and fractional order in nonlinear fractional delay differential equation

In this paper, we propose a novel algorithm for simultaneously identifying the time-delay parameter and fractional order in nonlinear fractional delay differential equations. Building upon the optimal perturbation method, we introduce an important perturbation function and develop a modified optimal perturbation method to identify the unknown parameters. Our proposed algorithm overcomes the issue of the optimal perturbation method being prone to local optimal values and requires relatively fewer iterations. Numerical examples are presented to confirm the validity of our algorithm.

Trade-Off Between Positioning and Communication for Millimeter Wave Systems With Ziv-Zakai Bound

In this paper, we investigate the trade-off between positioning and communication for an integrated positioning and communication (IPAC) millimeter wave system. First, in terms of the positioning in the IPAC system, the Cramér-Rao bound (CRB) is commonly used as a performance metric. Unfortunately, the CRB is only tight in a certain region for the high signal-to-noise ratio (SNR). To compensate for this deficiency, we derive the Ziv-Zakai bound (ZZB) for the IPAC system by exploiting the a priori delay information extracted from both the time delay parameter and the channel amplitude attenuation. Further, we derive the expected CRB (ECRB) and the weighted CRB (WCRB) of the system for comparisons. Second, we analyze the trade-off between positioning and communication for this IPAC system based on the derived ZZB. Specifically, we aim to optimize the power allocation to maximize the achievable data rate subject to the ZZB and total transmit power constraints. Numerical results show that the ZZB provides a tighter and more reasonable bound for the minimum mean square error (MMSE) estimator over the wide range of SNRs compared to the ECRB and WCRB. Moreover, the trade-off between positioning and communication is revealed via changing critical parameters by simulations.

Bipartite synchronization of multi‐agent systems under deception attacks via pinning delayed‐impulsive control

AbstractThis article aims to investigate the bipartite synchronization problem of multi‐agent systems (MASs) under deception attacks. A pinning delayed‐impulsive control scheme is proposed to solve the synchronization of MASs under deception attacks that modify the transmitted data information and destroy the data integrity. The time delay can have a gain effect on the stability of the system by using time delay utilization technology. By selecting the appropriate time delay parameters, the convergence speed of the system is effectively improved. Furthermore, cooperative and competitive interactions between agents are considered. Sufficient conditions of the bipartite mean‐square bounded synchronization of MASs under deception attacks are theoretically obtained. Finally, the designed numerical simulations illustrate the correctness and effectiveness of our results.

Time delay feedbacks enhanced bifurcation in the birhythmic fractional self-sustained system subjected to correlated noise

The response of the birhythmic fractional Van der Pol (VdP) self-sustained oscillator driven both by time delay feedbacks and correlated noise is considered. We mainly focus on the effects of time-delay feedback parameter and fractional damping on stochastic properties of the birhytmic system, such as P-bifurcation. The minimum mean-square error is used to reduce the system to its equivalent integer-order nonlinear stochastic equation. An analytical approximation is adopted to obtain the system behavior and it is compared with numerical simulation. The delay self-control feedbacks are transformed into state variables without delay by means of the harmonic approximation. The maximum extension of the control parameters to have a birhythmic solution can be thus determined by an appropriated choice of the fractional order and delay time parameters. In particular, when the fractional damping is lowered below 2, the birhythmic region disappears. However, the influence of the fractional damping changes as a function of the correlation noise parameter. Instead, the delay feedback and the fractional derivative are not so effective on the transition. The input delay and fractional derivative can be greatly enhanced by the nonlinear interaction. Specifically, the amplitude of the induced oscillations can be much larger than that of the input fractional with the cooperation of an appropriated time delay and nonlinear terms. It is then shown that the time delay feedback parameters and the fractional damping also act as bifurcation parameters.