Time-delay Behavior Research Articles

Hopf bifurcation of a delayed predator–prey model with Allee effect and anti-predator behavior

This paper proposes a diffusive predator–prey model with Allee effect, time delay and anti-predator behavior. First, the existence and stability of all equilibria are analyzed and the conditions for the appearance of the Hopf bifurcation are studied. Using the normal form and center manifold theory, the formulas which can determine the direction, period and stability of Hopf bifurcation are obtained. Numerical simulations show that the Allee effect can determine the survival abundance of the prey and predator populations, and anti-predator behavior can greatly improve the stability of the coexisting equilibrium.

Parameter Uncertainty Analysis in Precise Pointing Control of Flexible Spacecraft

This article focuses on the validation of a classical PID controller scheme for flexible spacecraft with regards to the effect of parameter uncertainty on system stability and pointing precision. A high-fidelity simulation environment with external disturbances was built in Simulink using a control-oriented model of an Earth-observing satellite with a flexible appendage and on-board microvibration sources in orbit around the planet. Then, a PID control loop was designed with sensor dynamics, time delay behaviour, and a smooth trajectory generator. After declaring the natural frequencies, damping ratio, and rotation angle of the appendage, as well as the propellant tank mass to be uncertain, two worst-case scenarios were identified. Comparing the response of worst-case systems with nominal settings, only a minor drop has been found in the phase margins, with little to no difference in the pointing errors (smaller than ±2 arcsec for both roll and pitch).

Time-Delay Identification and Validation of a Liquid Film Transport Model based on Pilot Plant Experiments

Abstract The paper presents an identification strategy to obtain relations between time delays of a transport model for an evaporating liquid film and corresponding flow/liquid properties. To this end, step-response based pilot plant experiments referring to the falling film evaporator process are conducted. In this context, the time-delay relations are identified offline by minimizing the output error between the model and experiment. In subsequent validation experiments, we observe that modeled and measured outputs are in good accordance. Within this framework, we conclude that the influence of evaporation on the liquid’s time-delay behavior can be neglected.

Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation

When dealing with real control experimentation, the designer has to take into account several uncertainties, such as: time variation of the system parameters, exogenous perturbation and the presence of time delay in the feedback line. In the later case, this time delay behaviour may be random, or chaotic. Hence, the control block has to be robust. In this work, a robust delay-dependent controller based on H∞ theory is presented by employing the linear matrix inequalities techniques to design an efficient output feedback control. This approach is carefully tuned to face with random time-varying measurement feedback and applied to the Furuta pendulum subject to an exogenous ground perturbation. Therefore, a recent experimental platform is described. Here, the ground perturbation is realised using an Hexapod robotic system. According to experimental data, the proposed control approach is robust and the control objective is completely satisfied.

Bursting dynamics in parametrically driven memristive Jerk system

Compared with general nonlinear systems, multi-time scale system has complex bursting dynamics and has received widespread attention. A memristor-based Jerk system with parametric excitation is proposed in this study. As the selected excitation frequency is far less than the natural frequency, implying the existence of an order gap between the excitation frequency and the natural one, the system can be considered as a classic fast-slow system with two timescales. In our system, when the slow-varying parameters periodically pass through the critical pitchfork bifurcation point periodically, a distinct time delay behavior can be observed. Complex bursting oscillations induced by the delayed pitchfork are revealed with different excitation amplitudes. By virtue of the fast-slow analysis method, the corresponding generation mechanisms are discussed by the transformed phase portraits, the time series, and the phase portraits. As the delay time interval induced by the pitchfork bifurcation is dependant not only on the excitation amplitude, but also on the excitation frequency, some excitation frequency related bursting patterns are also considered in our study. Finally, numerical simulations are provided to verify the validity of the study.

Time delay in slow electron elastic scattering by potentials with arising levels

SynopsisWe study Wigner time delay of slow electrons by spherically symmetric square potential well as a function of the well parameters. We show that the electron interaction with scattering center qualitatively depends on presence of discrete levels in the well. Electron retention mode by a potential well with no discrete level is replaced by the mode at which after level appears the incident electron hardly enters the scatterer. This behavior of time delay is universal since it is typical not only for the first but also for following arising s-levels.

Time delays in ultracold atomic and molecular collisions

We study the behavior of the Eisenbud-Wigner collisional time delay around Feshbach resonances in cold and ultracold atomic and molecular collisions. We carry out coupled-channels scattering calculations on ultracold Rb and Cs collisions. In the low-energy limit, the time delay is proportional to the scattering length, so exhibits a pole as a function of applied field. At high energy, it exhibits a Lorentzian peak as a function of either energy or field. For narrow resonances, the crossover between these two regimes occurs at an energy proportional to the square of the resonance strength parameter $s_\textrm{res}$. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.

A large time delay of light via two dimensional atom localization in a coupled cavity waveguide

We investigate the time delay behavior of light through a Λ-type atomic system interacting with two orthogonal standing-wave fields in a modified reservoir. Results show that transmission spectra splitting occurs in a coupled cavity waveguide (CCW) and the time delay of light relies remarkably on the strong coupling effect between a localized atom and a CCW. The atom localization can even be larger than λ∕100 in two orthogonal directions, which arises from field-induced interference effect in a modified reservoir. The proposed scheme not only provides a high-precision atom localization but also achieves a large time delay of the probe light.

Peculiarities of Wigner Time Delay in Slow-Electron Elastic Scattering by a Potential Well with Arising Discrete Levels

We generalize here the one-level consideration in our recent paper arXiv:1901.00411 [1] to the case when an electron collides with a potential that have any number of s bound states. We investigate peculiarities in the Wigner time delay behavior for slow electron elastic s-scattering by spherically symmetric square-potential well. We have considered potential wells, the variation of parameters of which (potential depth U and its radius R) lead to arising arbitrary number of s bound states. We demonstrate that while the time delay for potential wells with no discrete s-levels always has a positive value for small electron energies, it changes sign after level arising. We found that at the moments of arising in the well not only of the first but also following s-levels as well, the time delay as a function of U experiences instant jumps from a positive value to a negative one. The amplitudes of these jumps increases with decrease of the electron wave vector k. The times delay for potential well, the variation of the radius of which R leads to the appearance of discrete levels, also change sign at these critical radii.

General on-off damping controller for semi-active tuned liquid column damper

This paper addresses an on-off damping tuned liquid column damper (TLCD) regulated by a general controller. This general controller can represent many conventional controllers such as groundhook, skyhook, bang-bang, or linear clipping controller. Due to the on-off damping and quadratic damping of the TLCD the system is complex nonlinear. To cope with those nonlinearities, this paper presents a simple approximated solution by solving a scalar algebraic equation. Outcomes of numerical simulations verify the proposed approximated solution. Moreover, the approximated solution is useful to clarify the condition of robust controllers, to speed up the optimization of the general controller, and to conduct any parametric study. Based on a parametric study, an empirical formula for the optimized parameters of the general on-off damping controller is derived. In a case study of an earthquake excited five degree-of-freedom shear frame the simplicity, robustness, and effectiveness of the semi-active TLCD with optimized parameters is illustrated, considering limited noisy measurements, time delay, modeling error, and nonlinear TLCD behavior.

Ignition behavior of single coal particle in a fluidized bed under O2/CO2 and O2/N2 atmospheres: A combination of visual image and particle temperature

Single coal particle ignition behavior was studied in a two-dimensional (200mm×20mm×400mm) fluidized bed under O2/N2 and O2/CO2 atmosphere with O2 volume concentration in the range of 0–40%, by a combination of visual observation of the volatile flame and measurement of the particle center temperature. A piece of transparent quartz glass was used as the front wall of the fluidized bed to allow visual observation. The investigated fuel particles were spherical sub-bituminous coal particles with diameter in a range of 6–13mm, which were artificially carved from selected original coal particles. The volatile combustion flame was recorded by a color video camera to analyze its ignition time delay and extinction behavior. The temperature in the particle center was measured by a very thin thermocouple to follow the particle heating process. Results indicate that under O2/CO2 atmosphere the ignition delay time is much longer than in O2/N2 atmosphere. The devolatilization process is controlled by internal and external heat transfer but it is almost unaffected by atmosphere at the same O2 concentration. The effect of volatile combustion on heating and extinction delay time can be neglected for larger coal particles.

Unidirectional open-loop chaotic synchronization communication based on a semiconductor laser with double optical feedback

Using a semiconductor laser with double optical feedback as a chaos transmitter, a unidirectional chaotic synchronization communication system is constructed, and the performances of such a system are investigated numerically. The results show that by selecting reasonable parameters, the time delay behaviour of chaotic carrier generated by the semiconductor laser with double optical feedback can be suppressed efficiently; through the strong injection from transmitter to receiver, the perfect synchronization between transmitter and receiver can be realized, and the synchronization quality has a high tolerance to frequency detuning between transmitted laser and received laser; under the additive chaos modulation encryption scheme, the 500 Mbits/s encoded message can be hidden efficiently in the chaotic carrier and successfully extracted at the receiver.

Effects of group delay ripple on optical beam-formers for pulsed antenna arrays

A semi-analytical formulation is presented to quantify the effects of group delay ripple on the performance of an optical beam-former. For delay elements, implemented with commercially available multi-channel fiber Bragg gratings, an impulse response is introduced and calculated for the group delay ripple. To do this, the transfer function of the fiber Bragg grating is parted into two dispersive and non-dispersive sections. This will also ease the demonstration of the fiber Bragg grating as a true time delay element. The formulation is applied to an ultra-wideband pulsed array of antennas. As an example the array factor and electric field patterns of a four element antenna array is derived, using certain available measured data. The distortion in the temporal-angular radiation patterns due to the non-ideal true time delay behavior may be predicted using the presented work. It also facilitates to distinguish between the effects of long and short ripples. This new mathematical investigation is applicable to any linearly chirped fiber Bragg grating other than multi-channel ones. It also includes corrections to previously published formulations.

Experimental Characterization of UWB On-Body Radio Channel in Indoor Environment Considering Different Antennas

An experimental investigation to characterize the transient and spectral behavior of the ultrawideband (UWB) on-body radio propagation channel for body-centric wireless communications is presented. The measurements were performed considering over thirty on-body links in the front of human body in the anechoic chamber, and in indoor environment. Two different pairs of planar antennas have been used, namely, CPW-fed planar inverted cone antennas (PICA), and miniaturized CPW-fed tapered slot antennas (TSA). A path loss model is extracted from measured data, and a statistical study is performed on the time delay parameters. The goodness of different statistical models in fitting the root mean square (RMS) delay has been evaluated. Results demonstrate that the TSA, due to its more directive radiation behavior is less affected from the reflections from body parts and surrounding environment. The antenna shows significant size reduction and improved time delay behavior, and hence is an ideal candidate for UWB body area networks (BAN).

Numerical studies of the interaction of time‐modulated multi‐gigabit sequences with metamaterial structures at millimeter‐wave frequencies

AbstractIt is shown with time domain simulations using the finite integration technique (FIT) that a metamaterial that acts as an artificial magnetic conductor (AMC), i.e. a metamaterial which produces an in‐phase reflection, exhibits a time delay before its intended response can occur. A millimeter‐wave metamaterial AMC is obtained as a generalization of a successfully designed microwave frequency AMC block consisting of an array of capacitively loaded loops (CLLs). It is also shown that while this time delay does distort millimeter‐wave frequency signals composed of time‐modulated multi‐gigabit sequences, it does not have a detrimental impact on the overall system performance when these multi‐gigabit/s signals interact with this CLL‐based AMC. This time delay behaviour is demonstrated for several different but common communication‐based modulation schemes. The presence of peculiar spikes in the output waveforms is tied to the time domain behaviour of the currents on the CLLs in the metamaterial AMC. Copyright © 2006 John Wiley & Sons, Ltd.

Bilateral Teleoperation through Networks

Nowadays haptics (tactile sensation) is receiving much attentions. To transmit a vivid tactile sensation, real-time processing is necessary. In these circumstances, time delay caused in networks or some devices is a very serious problem. Therefore in this paper, influence of time delay on bilateral systems for haptics is examined.At first, the influence is verified by the analysis based on an evaluation index “Transparency. Characteristic behavior of time delay can be found out. Then experimental results via the network between Shinanomachi and Yagami campus (Keio University) are shown. Transmission of vivid tactile sensation of remote environment is realized.

Exhibiting the Behavior of Time-Delayed Systems via an Extension to Qualitative Simulation

This work presents an extension to qualitative simulation that enables a qualitative reasoning system to support variables that exhibit delayed reactions to their constraining functions. Information stored in the previous levels of the behavior tree is retrieved and used to constrain multiple delayed variables and to capture the time-delay behavior of the system. The extension is applicable to qualitative simulators that generate time-stamped behaviors. In particular, this is implemented and integrated with the existing fuzzy qualitative simulation algorithm. Results of an example application of this extended algorithm are provided.

A Model-Based Controller for Interactive Delayed Haptic Feedback Virtual Environments

This paper addresses the stability of time-delayed force-reflecting displays used in virtual reality interactive systems. A novel predictive-like approach is proposed. The developed solution is stable and robust. Neither time delay estimation nor time delay behavior's knowledge are required. The controller applies to constant or time-varying delays without any adaptation. In this research, efforts are devoted towards making results easy to implement in commercial haptic libraries and interface build-in controllers. Moreover, although this study focuses on virtual environments haptics, it can easily spread to force feedback teleoperators.

Lifetime RC time delay of on-chip copper interconnect

Increasing resistance and RC time delay induced by an oxidation in a copper line during its lifetime may limit copper-based metallization for technologies with critical dimension. Based on the mechanisms of resistance, constriction resistance and material diffusion, two dynamic models to access lifetime behavior of resistance and RC time delay were developed and discussed. These models also provide a means to gain insight into the correlation between the resistance and RC time delay of copper interconnect and such key variables as feature dimension, operating condition, and oxidation.

Time-delay at higher genus in high-energy open string scattering

We explore some aspects of causal time-delay in open string scattering studied recently by Seiberg, Susskind and Toumbas. By examining high-energy scattering amplitudes at higher order in perturbation theory, we argue that causal time-delay at Gth order is 1/( G+1) times smaller than the time-delay at tree level. We propose a space–time interpretation of the result by utilizing the picture of the high-energy open string scattering put forward by Gross and Mañes. We argue that the phenomenon of reduced time-delay is attributed to the universal feature of the space–time string trajectory in high-energy scattering that string shape at higher order remains the same as that at tree level but overall scale is reduced. We also discuss implications to the space–time uncertainty principle and make brief comments on causal time-delay behavior in space/time noncommutative field theory.