Time Delay Response Research Articles

Normal Form of Saddle-Node-Hopf Bifurcation in Retarded Functional Differential Equations and Applications

In this paper, we firstly employ the normal form theory of delayed differential equations according to Faria and Magalhães to derive the normal form of saddle-node-Hopf bifurcation for the general retarded functional differential equations. Then, the dynamical behaviors of a Leslie–Gower predator–prey model with time delay and nonmonotonic functional response are considered. Specially, the dynamical classification near the saddle-node-Hopf bifurcation point is investigated by using the normal form and the center manifold approaches. Finally, the numerical simulations are employed to support the theoretical results.

Research on Maritime Radio Wave Multipath Propagation Based on Stochastic Ray Method

Multipath effect in vessel communication is caused by a combination of reflections from the sea surface and vessels. This paper proposes employing stochastic ray method to analyze maritime multipath propagation properties. The paper begins by modeling maritime propagation environment of radio waves as random lattice grid, by utilizing maximum entropy principle to calculate the probability of stochastic ray undergoingktime(s) reflection(s), and by using stochastic process to produce the basic random variables. Then, the paper constructs the multipath channel characteristic parameters, including amplitude gain, time delay, and impulse response, based on the basic random variables. Finally, the paper carries out a digital simulation in two-dimensional specific fishery fleet model environment. The statistical properties of parameters, including amplitude response, probability delay distribution, and power delay profiles, are obtained. Using these parameters, the paper calculates the root-mean-squared (rms) delay spread value with the amount of 9.64 μs. It is a good reference for the research of maritime wireless transmission rate of the vessels. It contributes to a better understanding of the causes and effects of multipath effect in vessel communication.

A Printed UWB Vivaldi Antenna Using Stepped Connection Structure Between Slotline and Tapered Patches

In this letter, a new stepped connection structure between slotline and tapered patches is adopted in a planar printed Vivaldi antenna. By using the stepped connection structure, the impedance matching is significantly improved and a wide bandwidth is achieved. In order to illustrate the effectiveness of this design, a prototype of the modified Vivaldi antenna is fabricated and tested. Experimental results show that the impedance matching is significantly improved in the band from 3 to 15.1 GHz. In addition, a measured gain, which is better than 5 dBi, is obtained with a compact size. Compared to other techniques, the presented technique effectively improves the impedance matching and enlarges the bandwidth without changing the overall dimensions. Moreover, a relatively flat group time delay response is achieved within the band of 3-15.1 GHz.

Influence of coupling conditions on the time delay characteristics of parallel-cascaded optical waveguide ring resonators

The influence of coupling conditions of parallel-cascaded waveguide ring resonators on the time delay application in the optically phased array antennas is analyzed. Two kinds of coupling conditions, over-coupling and restriction free are considered to achieve a certain target delay time by parallel-cascaded three ring resonators. The results show that the restriction free coupling condition is better than the over-coupling one to obtain a flat time delay response in the target delay bandwidth especially for the small target delay time, which is the advantage of ring-resonator-based tunable true time delay line. The influence of round-trip loss on the time delay response and the transmission amplitude response is also investigated, which indicates that ring resonators with low optical round-trip loss are preferred to achieve a high performance true time delay line.

Accuracy of estimation of parameters with LISA

We present the results of the estimation of parameters with LISA for nearly monochromatic gravitational waves in the low and high frequency regimes for the time-delay interferometry response. Angular resolution of the detector and the estimation errors of the signal's parameters in the high frequency regimes are calculated as functions of the position in the sky and as functions of the frequency. For the long-wavelength domain we give compact formulas for the estimation errors valid on a wide range of the parameter space.

CALIBRATION OF TIME DOMAIN REFLECTOMETRY (TDR) SOIL MOISTURE POINT PROBE FOR TWO SOILS

Maintaining adequate soil moisture in the root zone is crucial in achieving good plant growth. Accurate measurement of soil moisture is essential to keep the right level of soil moisture. Many studies have reported the successful application of Time Domain Reflectometry (TDR) for soil moisture measurement. This study was initiated to obtain calibration curves for soil water content determinations by TDR for two soil types. Measurements were taken in the laboratory for a silt loam and a sandy loam soils, using TDR Soil Moisture Measurement Instrument, Moisture PointTM Model MP-917, and Moisture Point Probe type-K. TDR probe calibration was performed for two soil types contained in wooden boxes (100 cm x 100 cm x 80 cm). The calibration was accomplished by comparing the volumetric moisture content (qTDR) and time delay (tTDR) response of TDR probe to that of the gravimetric volumetric moisture content (qgrav). The TDR measurements were taken, in triplicates, at four depths (0-15 cm, 15-30 cm, 30-45 cm, and 45-60 cm) for 38 days after wetting the soil. Soil samples for the gravimetric moisture content measurements were collected from the same locations from where TDR readings were taken. The study has demonstrated that the TDR technique is a reliable alternative method for measuring soil moisture content. The moisture content measurements obtained with TDR were comparable to that of the gravimetric method and showed a good relationship to gravimetric determinations (r 2 =0.85 for silt loam and 0.89 for sandy loam).

STABILITY ANALYSIS OF A RATIO-DEPENDENT CHEMOSTAT MODEL WITH TIME DELAY AND VARIABLE YIELD

A chemostat model with time delay, variable yield and ratio-dependent functional response is investigated. By analyzing the corresponding characteristic equations, the local stability of a boundary equilibrium and a positive equilibrium is discussed and the existence of Hopf bifurcation is established. By using the comparison arguments, sufficient conditions are obtained for the global stability of the boundary equilibrium. By constructing a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive equilibrium. Finally, numerical simulations are carried out to illustrate the theoretical results.

New spectrophotometric measurement method for process control of miniaturized intensified systems

Since the introduction of miniaturized intensified systems, it has been recognized that one of the most crucial challenges is the establishment of appropriate control strategies for the systems. The unavailability of a suitable measurement system imposes several limitations in controlling the miniaturized systems. The present research proposes a spectrophotometric measurement system for controlling miniaturized intensified systems which can be used for a wide range of measurement objectives such as micro total analysis systems (μTAS) or micro chemical plant systems (MCPs). The spectrophotometric pH measurement is selected as the case study in order to demonstrate the high performance of the proposed measurement system. An embedded PID controller in the MATLAB ® environment is used as a controller which is interfaced with LabVIEW ® in order to facilitate communication with the rig components. The results obtained from the experimental study showed that using a spectrophotometric measurement can dramatically reduce process time delay and measurement response time.

A Stage-Structured Predator-Prey System with Time Delay and Beddington-DeAngelis Functional Response

A stage-structured predator-prey system with time delay and Beddington- DeAngelis functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.

OL-052 A mathematical model with time-delay immune response for adefovir treatment

OL-052 A mathematical model with time-delay immune response for adefovir treatment

STABILITY AND HOPF BIFURCATION OF A PREDATOR–PREY SYSTEM WITH TIME DELAY AND HOLLING TYPE-II FUNCTIONAL RESPONSE

A predator–prey model with time delay and Holling type-II functional response is investigated. By choosing time delay as the bifurcation parameter and analyzing the associated characteristic equation of the linearized system, the local stability of the system is investigated and Hopf bifurcations are established. The formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.

基于8×8 MOEMS光开关的7-Bit光真延时系统

We demonstrate a 7-bit photonic true-time-delay (TTD) system which uses an 8\times8 micro-optical-electro-mechanical system (MOEMS) optical switch for phased array antennas (PAAs) beamforming applications. The switch controls the optical signal to pass by the fiber delay lines (FDLs) of different lengths. Different time delays between adjacent channels are obtained due to the chromatic dispersion of FDLs. Therefore, the system cannot be disturbed by the environment. The measured time delay responses are nearly linear with the wavelength spacing between optical carriers as well as the lengths of FDLs, which agrees well with the theoretical analysis.

Improved Photonic True Time Delay Unit for a Ku-Band Phased Array Antenna Demonstration

In this letter, a Photonic True Time Delay (PTTD) unit for phased array antennas is experimentally demon- strated. The PTTD unit, employing a single wavelength laser source, exploits the distributed photonic bandgap offered by a Linearly Chirped Fiber Bragg Grating (LCFBG) to attain different time delays by properly actuating the physical and geometrical features of the LCFBG through temperature changes. The time delay response of the TTD unit has been measured experimentally revealing multiband operation capability (S, C, X and Ku bands) with ps time delay resolution and a maximum dynamic range of 250ps. The time steering demonstration has been performed by characterizing in the Ku band an array prototype within a Near Field range.

Microvascular PO2 Kinetics in Hindlimb Skeletal Muscle of Obese Diabetic Zucker Rats

Microvascular PO2 (PO2mv) in skeletal muscle reflects the dynamic balance between oxygen delivery and oxygen uptake. PO2mv on-kinetics in the rat spinotrapezius muscle during the rest-contraction transition are faster in both streptozotocin (STZ) and Goto-Kazazaki (GK) diabetic rats. Reduced nitric oxide (NO) availability has been implicated in these diabetic sequelae. PURPOSE: The purpose of this study was to determine the impact of insulin-resistant diabetes on PO2mv kinetics in a hindlimb locomotory muscle, and to assess the role of NO. METHODS: PO2mv (phosphorescence quenching) was measured in the extensor digitorum longus muscle (EDL) of female lean control (LC, n=10, 194 ± 3 g) and obese diabetic (OD, n=9, 356 ± 11 g) Zucker rats. PO2mv was monitored at rest and through the rest-contraction transition. PO2mv on-kinetics were determined using a monoexponential plus time delay model. EDL blood flow (radiolableled microspheres) was measured at the end of the 150 s contraction period. The experimental protocol included; 1) a pre-stimulation, 2) a control stimulation, 3) administration of L-NAME (30 mg/kg), and 4) a post-L-NAME stimulation. RESULTS: OD rats had elevated blood glucose levels (LC, 5.9 ± 0.4; OD, 25.4 ± 1.8 mmol/L). Resting PO2mv was not different in LC and OD rats (LC, 29 ± 2; OD, 23 ± 3 mmHg). During contractions, PO2mv fell to the same level in both groups (LC, 16 ± 2; OD, 17 ± 2 mmHg). OD rats had both a shorter time delay (LC, 9 ± 2; OD, 7 ± 1 s; P<0.05) and shorter mean response time (LC, 24 ± 2; OD, 17 ± 1 s; P<0.05). EDL blood flow during contractions was not different (LC, 70 ± 15; OD, 67 ± 17 ml/ min/100 g). PO2mv was lower after L-NAME in both LC and OD rats. Both time delay and mean response time were shorter in LC and OD rats, but the PO2mv time constant was shorter only in LC rats. Blood flow during contractions was not reduced by L-NAME, but the vascular conductance was reduced. CONCLUSIONS: The faster PO2mv on-kinetics observed in the EDL of OD rats is consistent with previous reports in STZ and GK rats, and may be due to a slower rise in blood flow and oxygen delivery at the onset of contractions. These data also suggest that impaired NO production in OD rats may contribute to the more rapid fall in PO2mv at the onset of muscle contractions. (Supported by the AHA, Heartland Affiliate and the KCOM Graduate Program.)

Effects of multiple-stage membrane process designs on the achievable performance of automatic control

There is limited information from literature on the dynamic operability of membrane processes with multiple stages or loops. Such information is useful for assessing the performance achievable by an automatic controller proposed for a process design before the actual controller is implemented. Based on dynamic modeling of an industrial whey ultrafiltration process with an increasing number of stages up to a maximum of 12, the dynamic responses of the flowrate and concentration of the retentate were obtained. Features of the dynamic responses were used to determine the performance, in terms of quality and speed, that can be achieved by automatic controllers. In particular, limitations on the performance are indicated by features of dynamic responses such as effective time delay and inverse responses. Changes in effective time delay and inverse responses with the number of stages in the whey ultrafiltration process demonstrate a trade-off between process performance and control performance. This trade-off should be considered during process and controller design to maximize the economic return from the production of whey protein concentrates.

Traveling waves connecting equilibrium and periodic orbit for reaction–diffusion equations with time delay and nonlocal response

A class of reaction–diffusion equations with time delay and nonlocal response is considered. Assuming that the corresponding reaction equations have heteroclinic orbits connecting an equilibrium point and a periodic solution, we show the existence of traveling wave solutions of large wave speed joining an equilibrium point and a periodic solution for reaction–diffusion equations. Our approach is based on a transformation of the differential equations to integral equations in a Banach space and the rigorous analysis of the property for a corresponding linear operator. Our approach eventually reduces a singular perturbation problem to a regular perturbation problem. The existence of traveling wave solution therefore is obtained by the application of Liapunov–Schmidt method and the Implicit Function Theorem.

Periodic Traveling Waves for Diffusion Equations with Time Delayed and Non-local Responding Reaction

We develop a singular perturbation technique to study the existence of periodic traveling wave solutions with large wave speed for a class of reaction-diffusion equations with time delay and non-local response. Unlike the classical singular perturbation method, our approach is based on a transformation of the differential equations to integral equations in a Banach space that reduces the singular perturbation problem to a regular perturbation problem. The periodic traveling wave solutions then are obtained by the use of Liapunov-Schmidt method and a generalized implicit function theorem. The general result obtained has been applied to a non-local reaction-diffusion equation derived from an age-structured population model with a logistic type of birth function.

Continuously Variable Optical Delay Line Based on a Chirped Fiber Bragg Grating

In this letter, a continuously variable optical delay line (ODL), useful for phased array antennas, is experimentally demonstrated. The ODL operates at a single optical wavelength and it is based on a linearly chirped fiber Bragg grating (LCFBG). Continuous true time delay is achieved by changing the temperature of the LCFBG. In order to limit the actuating temperature range, the grating was bonded to a metallic support and the effect of the thermal apparent strain was considered. The time-delay response of the system is measured with an optical signal modulated with double sideband technique at a frequency of 2 GHz. The experimental results demonstrate a time-delay resolution of 3.1 ps employing a temperature controller with a stability of plusmn0.1 degC and a maximum time delay of 96 ps over a temperature range of 16 degC-40degC. The time-delay-temperature characteristic offers a slope of 3.8 ps/degC with a mean-square deviation from the linearity of 3.5 ps. Such a delay line, by operating at a single optical wavelength and by using a simple actuating system, offers many advantages being low cost, compactness, and reliability. The main limitation to the ODL resolution is due to the amplitude ripple of the LCFBG used and a performance enhancement can be obtained with specifically tailored LCFBG

Effects of Altered Nitric Oxide Availability on Rat Muscle Microvascular Oxygenation During Contractions

Aging, chronic heart failure (CHF) and diabetes are all associated with vascular endothelial dysfunction. Compared with muscles from young healthy individuals, those from old and CHF/diabetic individuals exhibit a reduced muscle microvascular O pressure (POmv) at the onset of contractions that is expected to impair blood-myocyte O2 exchange. PURPOSE: To explore the putative role of nitric oxide (NO) in controlling PO2mv at rest and during contractions, we tested the hypotheses that at the onset of contractions (1 Hz) sodium nitroprusside (SNP, ↑ NO) would raise PO2mv and slow the kinetics of PO mv change whereas L-nitro arginine methyl ester (L-NAME, ↓ NO) would decrease PO2mv and speed its kinetics. This would assess the potential for derangements in NO production to induce the PO2mv and O2 kinetics impairments characteristic of aged and CHF/diabetic individuals. METHODS: Separately, we superfused the spinotrapezius muscle of female Sprague-Dawley rats (n = 7, body mass = 298 ± 10 g) with a NO donor SNP (300 uM) and the NO synthase inhibitor L-NAME (1.5 μM) during muscle contractions. Microvascular PO2 was measured by phosphorescence quenching. RESULTS: SNP decreased mean arterial pressure (92 ± 5 mmHg) below that of control (CON, 124 ± 4 mmHg) and L-NAME (120 ± 4 mmHg) conditions. SNP did not raise PO mv at rest but it did slow the kinetics of PO2mv by lengthening the time delay (TD, 14 ± 5 s), time constant (τ, 24 ± 10 s) and mean response time (MRT, 38 ± 4 s) of the response compared with CON (TD, 8.4 ± 3.3 s; τ, 16 ±4.5 s and MRT, 25 ± 1.5 s, P <: 0.05). In contrast, L-NAME decreased PO2mv at rest and speeded τ (10.1 ±3.8 s, P= 0.05), while TD (8.1 ± 1 s) was not significantly different. However, the MRT (18 ± 1 s) was faster for L-NAME compared to CON. Moreover, L-NAME caused PO2mv to transiently fall below steady-state values. CONCLUSION: These results indicate that NO availability can significantly affect microvascular O2 pressures, and therefore O2 transport, at rest and during contractions and suggests that such derangements in aging and chronic disease conditions may potentially result from impairments in NO availability.

Fault Modeling and Simulation of Power Supply Voltage Transients in Digital Systems on a Chip

This paper addresses the modeling and simulation of power supply voltage transients (? VDD) in digital SoC (Systems on a Chip), namely their impact on SoC core's performance. The goal is to verify, in a cost-effective way, core's fault tolerance to this disturbance, aiming at EMI/EMC standard compliance. The two key parameters are the time slack and the defect size. A top-down approach is used to introduce an innovative fault injection and simulation technique. In fact, fault simulation is carried out either by using faulty delays (defect size as a function of ? VDD magnitude) in the CUT (Core Under Test) and nominal time excitation rate, or by using a fault-free CUT description and faster test application times (speed-up proportional to ? VDD magnitude). A bottom-up approach, using electrical simulation, is extensively used to demonstrate the adequacy of exploiting this duality between time excitation and delay response, for combinational CUT. We refer this duality as the "accordion" effect. For sequential circuits, and for pipeline circuits, it is shown that the tolerance to ? VDD disturbances is significantly lower than the one observed in combinational CUT, due to de-synchronization effects in storage elements. This effect depends on the clock distribution network and is a consequence of differently delayed responses of the CUT and of the clock network. Results are demonstrated using basic infrastructures and ISCAS benchmark circuits.