Constant Time Delay Research Articles

Novel criteria for global robust stability of dynamical neural networks with multiple time delays

This research article considers the problem regarding global robust asymptotic stability of the general type of dynamical neural networks involving multiple constant time delays. Some new sufficient criteria are proposed for the existence, uniqueness and global asymptotic stability of the equilibrium point of this neural network model whose network parameters possess uncertainties. This paper will first address the existence and uniqueness problem for equilibrium points by utilizing the Homomorphic transformation theory. Secondly, by exploiting a novel Lyapunov functional candidate, the sufficient conditions for asymptotic stability of equilibrium points of this class of delayed neural networks will be established. The derived robust stability conditions are expressed independently of the constant time delay parameters and define some novel relationships among network parameters of the considered neural network. Thus, the applicability and validity of the obtained robust stability conditions for delayed-type neural networks can be easily tested. The comprehensive comparisons among the results of the current article and some of previously derived corresponding results will also be made by giving an illustrative numerical example.

Optimized dosage control of the ozonation process in drinking water treatment

Ozonation is an important process in drinking water treatment. Determination of optimal ozonation dose is of significant importance for enhancing the quality of treated water and reducing the energy cost. It is known that keeping the dissolved ozone residual constant is an effective and reliable dosage control scheme. However, some external disturbances, such as large changes in raw water quality and water flow rate, always exist in the ozonation process. Meanwhile, the ozonation is a nonlinear process with large time constant and long time delay. Thus, it has been always a challenge for dosage control to maintain the dissolved ozone residual constant. The traditional control strategies such as PID and MPC merely utilize feedback regulation to suppress disturbances. This will degrade the control performance when strong disturbances occur. In this work, an effective control method integrating MPC method with disturbance observer (DO) is put forward to improve disturbance suppression performance. DO is utilized to estimate the disturbances and uncertainties, and then the estimated values are employed to conduct feed-forward compensation. The test results indicate that significant disturbance suppression improvements can be accomplished under the proposed method in comparison with the conventional MPC method in the ozonation process.

Numerical bifurcation analysis for a prey-predator type interactions with a time lag and habitat complexity

In this paper, a two-component generic prey-predator system incorporated with habitat complexity in predator functional response, and with constant time delay in predator gestation is considered. Although the role of time delay on the system dynamics is widely studied in the literature, only a few researchers have addressed the effect of habitat complexity in the prey-predator type interactions. In the first part of the paper the equilibria and stability analysis of the mathematical model is mentioned. In the second part, particular attention is paid on the numerical bifurcation analysis of the prey and predator densities based on two system parameters:(i) the strength of homogeneous habitat complexity and (ii) predator attack rate with and without time delay. It is found that dynamics with time delay in predator gestation are found to be much richer compared to that without time delay. The system stability may change from stable to unstable through a Hopf bifurcation and the solution branches emanating from these Hopf points are usually stable and supercritical. However, delay driven system may lead unstable orbits arising from Hopf bifurcations. It is also found that increasing the strength of habitat complexity may lead the stability change from unstable to stable.

Massed versus Embedded Trial Arrangements: Teaching Community Signs to Children with Autism Spectrum Disorder

The aim of this study is to compare the effectiveness and efficiency of teaching the meaning of community signs with massed trial arrangements (MTA) and embedded trial arrangements (ETA) using constant time delay intervention. The constant time delay intervention was used two different arrangements; MTA versus ETA. The study was conduct with four boys with Autism Spectrum Disorder, aged between 44-64 months. An adapted alternating design was used. The two arrangements were equally effective in terms of the number of sessions required for participants to learn the meaning of the signs. However, MTA sessions were much shorter. The study asked participants’ preferred arrangement; two chose MTA and two chose ETA.

Modulated Time Delays, Synchronized Josephson Junctions in High-Temperature Superconductors and Chaotic Terahertz Waves

We make the first report on chaos synchronization between Josephson junctions governed by a central junction, when the coupling time between the driving junction and driven junctions is modulated. The results are compared with the case of constant coupling time delays between the junctions. We establish that synchronization is quite robust to the modulation of the coupling time delays, including chaotically modulated delay times. Synchronized Josephson junctions can serve as a terahertz wave generators with enough power for practical applications in diverse scientific fields.

Spectral Line Asymmetries of Hot Fe Lines in Multiloop Models

Abstract Extreme ultraviolet emission line profiles often show asymmetries, in the form of wing enhancements, during solar flares. Various explanations, ranging from magnetic disturbances to non-Maxwellian electron distributions to plasma turbulence have been proposed to explain these features. Plasma dynamics in a single loop can also satisfactorily explain line asymmetry. However, the presence of sub-resolution structures, confirmed by increasingly high-resolution observations, and observational difficulties in isolating a monolithic loop from nearby loops, necessitate detailed modeling efforts to investigate the effect of superposed dynamics on some line asymmetries. In the present work, we design multiloop models, representative of three possible loop configurations, to study how the resultant Fe xxiii spectral line profiles differ in each case and examine the differences between these multiloop models and the single loop model. We also briefly explore the role of a constant time delay in heating successive sub-loops on the spectral line shape. We find that for a multiloop model with sub-loops of the same length, heating time delay is an important factor that alters the line profile shape from the single loop case. Whereas, multiloop models with sub-loops of varied lengths predict significantly different line profiles, such as asymmetric lines for longer durations and with large blueshifts, without the necessity of introducing time delays.

Pilot Study to Characterize Middle Cerebral Artery Dynamic Response to an Acute Bout of Moderate Intensity Exercise at 3- and 6-Months Poststroke.

BackgroundThe primary aim of this study was to characterize the middle cerebral artery blood velocity (MCAv) dynamic response to an acute bout of exercise in humans at 3‐ and 6‐months poststroke. As a secondary objective, we grouped individuals according to the MCAv dynamic response to the exercise bout as responder or nonresponder. We tested whether physical activity, aerobic fitness, and exercise mean arterial blood pressure differed between groups.Methods and ResultsTranscranial Doppler ultrasound measured MCAv during a 90‐second baseline followed by a 6‐minute moderate intensity exercise bout. Heart rate, mean arterial blood pressure, and end‐tidal CO2 were additional variables of interest. The MCAv dynamic response variables included the following: baseline, time delay, amplitude, and time constant. Linear mixed model revealed no significant differences in our selected outcomes between 3‐ and 6‐months poststroke. Individuals characterized as responders demonstrated a faster time delay, higher amplitude, and reported higher levels of physical activity and aerobic fitness when compared with the nonresponders. No between‐group differences were identified for baseline, time constant, or exercise mean arterial blood pressure. In the nonresponders, we observed an immediate rise in MCAv following exercise onset followed by an immediate decline to near baseline values, while the responders showed an exponential rise until steady state was reached.ConclusionsThe MCAv dynamic response profile has the potential to provide valuable information during an acute exercise bout following stroke. Individuals with a greater MCAv response to the exercise stimulus reported statin use and regular participation in exercise.

The investigation of pre-service special education teachers’ treatment integrity in the use of response prompting strategies

ABSTRACT The purpose of this study was to examine pre-service teachers’ treatment integrity (TI) in the use of constant time delay (CTD) and simultaneous prompting (SP) while teaching discrete and chained behaviours. A descriptive research design was used. A total of 28 pre-service special education teachers (16 females and 12 males), whose ages ranged from 20 to35 years, participated in the study. The data were collected by applying four different observation and self-assessment checklists to video recordings. A descriptive analysis was conducted. The findings reveal that pre-service teachers implemented CTD and SP in discrete behaviours with higher TI than the CTD and SP in chained behaviours. Recommendations for future research and practice are provided.

Two-step feedback preparation of entanglement for qubit systems with time delay

Quantum entanglement plays a fundamental role in quantum computation and quantum communication. Feedback control has been widely used in stochastic quantum systems to generate given entangled states since it has good robustness, where the time required to compute filter states and conduct filter-based control usually cannot be ignored in many practical applications. This paper designed two control strategies based on the Lyapunov method to prepare a class of entangled states for qubit systems with a constant delay time. The first one is bang–bang-like control strategy, which has a simple form with switching between a constant value and zero, the stability of which is proved. Another control strategy is switching Lyapunov control, where a constant delay time is introduced in the filter-based feedback control law to compensate for the computation time. Numerical results on a two-qubit system illustrate the effectiveness of these two proposed control strategies.

A Minimum Action Method for Dynamical Systems with Constant Time Delays

In this work, we construct a minimum action method for dynamical systems with constant time delays. The minimum action method (MAM) plays an important role in seeking the most probable transition pathway induced by small noise. There exist two formulations of the minimum action method: one is the geometric formulation based on the Maupertuis principle, and the other one is the temporal formulation. The geometric formulation relies on the conservation of Hamiltonian corresponding to the Freidlin--Wentzell action functional. For systems with time delays, the Hamiltonian does not conserve due to the explicit dependence on the time delay, which implies that the geometric MAM is not applicable. We work with the temporal formulation of MAM for problems with time delays. By defining an auxiliary path, we remove the optimization with respect to time through the optimal linear time scaling. The pointwise correspondence between the auxiliary path and the delayed transition path is dealt with by a penalty term included into the action functional. The action functional is then discretized by the finite element method, and strategies for $h$-adaptive mesh refinement have been developed. Numerical examples have been presented to demonstrate the effectiveness of our algorithm.

Complex Dynamics and Periodic Oscillation Mechanism in Two Novel Gene Expression Models with State-Dependent Delays

The reaction time delay in the transcription process depends on the concentration of the protein because the transportation of mRNA from the nucleus to the cytoplasm becomes saturated. Thus the gene regulatory network is a state-dependent delayed model. This study aims to provide some mathematical explanations for the dynamics of the system, such as the linear stability and periodic oscillation, using mathematical techniques, such as formal linearization, linear stability analysis, the method of multiple scale (MMS), and the normal form. First, Hopf bifurcation of the state-dependent delayed gene regulatory networks model in the gene expression is analyzed by the method of multiple scales (MMS). Mechanism of periodic oscillations is obtained by Hopf bifurcation. The findings show that when degradation effects of the mRNA and protein are very strong, the oscillatory gene expression disappears. Then, a more realistic version of the aforementioned model with both constant and state-dependent time delays is established due to the existence of the constant time delay in the protein degradation process. Its nonresonant double Hopf bifurcation is found and analyzed using MMS. Interesting complex dynamic phenomena, such as periodic, quasi-periodic, and global period-[Formula: see text] solutions, are also discovered. These observations indicate that both state-dependent delay and constant delay could induce richer dynamics of the system, and the modified model may potentially describe the real dynamical mechanism (both the transcription process and the degradation process) more accurately in the gene expression. The findings may provide important guidance or hints to understand the real dynamic mechanism of the gene expression process.

Gain Scheduling MPC Controller Design for Tankless Gas Water Heaters with Time-Varying Delay

One of the most significant drawbacks of tankless gas water heaters is the difficulty of controlling the outlet hot water temperature as changes in water demand cannot be predicted. These sudden changes of hot water flow rate, associated with the system inhered delays, origins temperature overshoots and undershoots that severely affect the comfort perception by the user. In the present work, a linear MPC design is employed for the stabilization of a constrained nonlinear process with time-varying delay, however, control performance degrades significantly when operating far from the linearization operating point. The idea is to design multiple linear MPC controllers, each with its linear state-space model and constant time delay, describing process dynamics at a specific level of operation. Gain scheduling MPC presents improved performance when compared with classic PID and combined feedforward-feedback controllers, reducing the settling time up to two thirds.

Using a Technology-based Instructional Package to Teach Students with ASD to Construct Sentences

In the current study, we investigated the effects of a technology-based instructional package on accurate sentence construction of three middle school students with autism spectrum disorder and complex communication needs. The autonomous package used constant time delay to teach students to select words to construct sentence frames. We evaluated the effectiveness of the package using a single case multiple probe research design. Data indicated that two of the participants increased accurate sentence construction.

Adaptive online prediction of operator position in teleoperation with unknown time-varying delay: simulation and experiments

One of the most important problems in teleoperation systems is time delay and packet loss in the communication channel, which can affect transparency and stability. One way to overcome the time delay effects in a teleoperation system is to predict the master-side motion. In this way, when data is received in the slave side, it will be considered as the current position of the master robot and, thus, complete transparency could be achieved. The majority of the previous works regarding operator position prediction have considered known and constant time delay in the system; however, in the real applications, time delay is unknown and variable. In this paper, an adaptive online prediction approach based on artificial neural network (NN) is proposed. The time delay of the communication channel is estimated using an observer based on the dynamics of the master and slave sides. Then an artificial NN predicts the master-side motion based on the current available data of the master robot and the variable time delay estimated by the observer. This adaptive prediction approach is utilized in simulations and experiments on Phantom Omni haptic devices. The simulation results indicate the feasibility of this approach. It is revealed that this approach can predict an alternative human’s hand motion in a teleoperation system with unknown and variable time delay. Finally, the simulation results would be supported by experimental results.

Observer-based adaptive force–position control for nonlinear bilateral teleoperation with time delay

In this paper, a novel observer-based force control scheme is proposed to guarantee the position and force tracking in nonlinear teleoperation systems, subject to constant communication time delay. Stability of the teleoperation system is analytically proved using the Lyapunov stability theorem. Enough condition for asymptotic convergence of the force and position are derived. The transparency is also improved by force tracking capability of the system. The teleoperation controller is then applied to a pair of planar 2-DOF robots, connected via a communication channel with constant time delay. The experimental and simulation results demonstrate the effectiveness of the proposed control algorithm, in force estimation and dealing with time delay.

Predicted rates of merging neutron stars in galaxies

ABSTRACT We compute rates of merging neutron stars (MNS) in different galaxies, as well as the cosmic MNS rate in different cosmological scenarios. Our aim is to provide predictions of kilonova rates for future observations both at low and high redshift. In the adopted galaxy models, the production of r-process elements either by MNS or core-collapse supernovae is taken into account. To compute the MNS rates, we adopt either a constant total time delay for merging (10 Myr) or a distribution function of such delays. We conclude (i) the observed present time MNS rate in our Galaxy is well reproduced either with a constant time delay or a distribution function ∝t−1. (ii) The [Eu/Fe] versus [Fe/H] relation can be well reproduced with only MNS, if the time delay is short and constant. If a distribution function of delays is adopted, core-collapse supernovae are also required. (iii) The present time cosmic MNS rate can be well reproduced in several cosmological scenarios. (iv) Spiral galaxies are the major contributors to the cosmic MNS at all redshifts in hierarchical scenarios. In the pure luminosity evolution scenario, the spirals are the major contributors locally, whereas at high redshift ellipticals dominate. (v) The predicted cosmic MNS rate well agrees with the cosmic rate of short gamma-ray bursts, if the distribution function of delays is adopted in a cosmological hierarchical scenario observationally derived. (vi) Future observations of kilonovae in ellipticals will allow us to disentangle among constant or a distribution of time delays and among different cosmological scenarios.

Optimal I‐PD controller design for setpoint tracking of integrating processes with time delay

Processes including one or more integrators in their transfer functions can frequently be encountered in industry. In this study, integral–proportional–derivative (I-PD) controllers are proposed to control these type of processes. Analytical and optimal tuning rules are derived to tune the I-PD controllers for setpoint tracking of integrating plus first order plus dead time (IFOPDT) processes and double IFOPDT processes. Optimal tuning rules for setpoint tracking are achieved by minimising time moment weighted integral performance criteria. Obtained I-PD tuning formulas are in terms of process’ transfer function parameters, namely the gain, time delay and time constant. Simulation examples are given to demonstrate the use of the proposed method. Comparisons are provided to show the superior closed-loop performance of the proposed approach than existing proportional–integral–derivative and I-PD controller designing methods. In addition, the practical implementation of the proposed designing method is presented by controlling the position of a cart on an experimental setup.

Global Stability Analysis of Neural Networks with Constant Time Delay via Frobenius Norm

This paper deals with the global asymptotic robust stability (GARS) of neural networks (NNs) with constant time delay via Frobenius norm. The Frobenius norm result has been utilized to find a new sufficient condition for the existence, uniqueness, and GARS of equilibrium point of the NNs. Some suitable Lyapunov functional and the slope bounded functions have been employed to find the new sufficient condition for GARS of NNs. Finally, we give some comparative study of numerical examples for explaining the advantageous of the proposed result along with the existing GARS results in terms of network parameters.

Delay induced nonlinear dynamics of oxygen-plankton interactions

Abstract The present investigation deals with a generic oxygen-plankton model with constant time delays using the combinations of analytical and numerical methods. First, a two-component delayed model: the interaction between the concentration of dissolved oxygen and the density of the phytoplankton is examined in terms of the local stability and Hopf bifurcation analysis around the positive steady state. Then, a three-component model (oxygen-phytoplankton-zooplankton system) is investigated. The prime objective of this trio model is to explore how a constant time delay in growth response of phytoplankton and in the gestation time of zooplankton affects the dynamics of interaction between the concentration of oxygen and the density of plankton. The analytical and numerical investigations reveal that the positive steady states for both models are stable in the absence of time delays for a given hypothetical parameter space. Analysing eigenvalues of the characteristic equation which depends on the delay parameters, the conditions for linear stability and the existence of delay-induced Hopf bifurcation threshold are studied for all possible cases. As the delay rate increases, stability of coexistence state switches from stable to unstable. To support the analytical results, detailed numerical simulations are performed. Our findings show that time delay has a significant impact on the dynamics and may provide useful insights into underlying ecological oxygen-plankton interactions.

Post-swim oxygen consumption: assessment methodologies and kinetics analysis

Objective: This study aimed at comparing different recovery-based methods to assess the highest exercise oxygen uptake value (O2peak) when swimming at low-moderate, heavy and severe intensities. Complementarily, the different recovery curve kinetics were analysed. Approach: Eighteen competitive swimmers performed a 5 × 200 m front crawl intermittent protocol (0.05 m · s−1 increments and 3 min intervals), with respiratory gas exchange being continuously measured breath-by-breath during and post-exercise using a portable gas analyser. The directly determined O2peak (O2dir) was compared with the values obtained by linear and exponential backward extrapolations (of different intervals) and the recovery curve mathematical modelling. Main results: O2dir rose with intensity increase: 41.96 ± 6.22, 46.36 ± 6.89 and 50.97 ± 7.28 ml · kg−1 min−1 for low-moderate, heavy and severe swims. Linear and exponential regressions applied to the first 20 s of recovery presented the O2peak values closest to O2dir at low-moderate (42.80 ± 5.54 vs 42.88 ± 5.58 ml kg−1 min−1), heavy (47.12 ± 4.91 vs 47.48 ± 5.09 ml kg−1 min−1) and severe intensity domains (51.24 ± 6.89 vs 53.60 ± 8.54 ml kg−1 · min−1, respectively; r = 0.5–0.8, p < 0.05). The mono-exponential function was the best fit at low-moderate and heavy intensities, while the bi-exponential function better characterized the severe exercise domain (with a slow component amplitude, time delay and time constant of 6.2 ± 2.3 ml kg−1 min−1, 116.6 ± 24.3 and 39.9 ± 15.2 s, respectively). Significance: The backward extrapolation of the first 20 s of recovery is the best method to assess the O2peak for a large spectrum of swimming intensities. Complementarily, intensity increases imply different recovery curve kinetics, particularly a mono-exponential behaviour for low-moderate and heavy exertions and a bi-exponential dynamics for severe paces.