Time-delay Case Research Articles

A phase model with large time delayed coupling

We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has an explicit delay and phase shift in the argument of the phases and connection function, respectively. Using the phase model, we prove that for any type of oscillators and any coupling, the in-phase and anti-phase phase-locked solutions always exist and give conditions for their stability. We show that for small delay these solutions are unique, but with large enough delay multiple solutions of each type with different frequencies may occur. We give conditions for the existence and stability of other types of phase-locked solutions. We discuss the various bifurcations that can occur in the phase model as the time delay is varied. The results of the phase model analysis are applied to Morris–Lecar oscillators with diffusive coupling and compared with numerical studies of the full system of delay differential equations. We also consider the case of small time delay and compare the results with the existing ones in the literature.

Detection of sea-surface wind patterns associated with convective systems and their evolution using a combination of Sentinel-1 and Radarsat-2 imagery

ABSTRACTSynthetic Aperture Radar (SAR) can detect wind patterns induced by the Convective Systems (CS) downdraughts hitting the sea surface due to their high spatial resolution and large swath. Additionally, the combination of two successive SAR images (Sentinel-1 and Radarsat-2) with appropriate observation time delays may enable the observation of wind pattern evolution. The corresponding METEOSAT-10/11 infrared images to the SAR ones are used for the detection of deep convective clouds that are potentially associated with wind patterns. The current paper investigates two cases of time delays (1-minute and 5-minute) between two satellites. The estimated wind speeds by CMOD5.N on Sentinel-1 and Radarsat-2 images are almost the same for the background wind areas. However, the intensity of wind patterns on Radarsat-2 images (acquired 1 and 5 minutes later) is decreased, possibly due to a change of downdraught intensity according to observation time. In the 1-minute delay case, the drop of wind intensity is mainly observed for the intense spots (20–25 m s−1), while in the 5-minute delay case, it is noticed for both intense and moderate (10–15 m s−1) convection spots. The intensity of the high-wind convection spots decreases more quickly since the associated convective-scale downdraughts reach the sea surface more rapidly.

Delay-induced synchronization in two coupled chaotic memristive Hopfield neural networks

Abstract This paper is concerned with the synchronization of two coupled hyperbolic-type Hopfield neural networks with a memristive synaptic connection. The results show that the coupling with no time-delay cannot lead to complete synchronization and increasing the coupling strength causes anti-phase synchronization. While adding time-delays to the coupling term not only changes the dynamical behavior of the network but also facilitates reaching the full synchronization manifold. The network is investigated in two different cases of single and multiple time-delays. The calculated average‌ synchronization error indicates that using two time-delays has a better effect on the synchronization of systems. However, the synchronization region is lessened by increasing the time-delay values.

Stability and Hopf bifurcation for a delayed predator–prey model with stage structure for prey and Ivlev-type functional response

In this paper, we mainly investigate a delayed predator–prey model with stage structure for prey and Ivlev-type functional response. Four assumptions about this model are made as follows: (1) there are a single predator and a single prey population in the model; (2) the prey is divided by the age into two stage structures, immature and mature; (3) the trophic transfer from prey to predator is incomplete; (4) there are two time delays due to the time of maturation of prey and the time of gestation of predator. Some properties of equilibria for the model without delays are provided. Further, the stability of equilibria and existence of Hopf bifurcation are studied by discussing the different cases of time delays for the model with delays. We observe that delays can cause a stable equilibrium to become unstable one, even occur Hopf bifurcation when delays pass through their corresponding critical values. Meanwhile, we derive explicit formulae to determine the properties of Hopf bifurcation such as the direction of Hopf bifurcation and the stability of periodic solutions. Numerical simulations of all theoretical analyses are given for verifying our theoretical results. In the present work, we demonstrate that the validity and universality of oscillations induced by the time delays both theoretically and numerically. These results of this paper may be helpful for us to further understand the role of the critical values of time delays in stabilizing the predator–prey model.

Symbolic abstractions for nonlinear control systems via feedback refinement relation

This paper studies the construction of symbolic abstractions for nonlinear control systems via feedback refinement relation. Both the delay-free and time-delay cases are addressed. For the delay-free case, to reduce the computational complexity, we propose a new approximation approach for the state and input sets based on a static quantizer, and then a novel symbolic model is constructed such that the original system and the symbolic model satisfy the feedback refinement relation. For the time-delay case, both static and dynamic quantizers are combined to approximate the state and input sets. This leads to a novel dynamic symbolic model for time-delay control systems, and a feedback refinement relation is established between the original system and the symbolic model. Finally, a numerical example is presented to illustrate the obtained results.

Synchronization of chaotic Hopfield networks with time-varying delay: a resilient DOF control approach**This work was supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Grant Nos. KJ2017A064 and KJ2018ZD007), the Excellent Youth Talent Support Program of Universities in Anhui Province (Grant No. GXYQZD2019021), and the National Natural Science Foundation of China (Grant No. 61503002).

This paper focuses on the issue of resilient dynamic output-feedback (DOF) control for synchronization of chaotic Hopfield networks with time-varying delay. The aim is to determine a DOF controller with gain perturbations ensuring that the norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound. A delay-dependent criterion for the synchronization is derived by employing the Lyapunov functional method together with some recent inequalities. Then, with the help of some decoupling techniques, sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases. Lastly, an example is used to illustrate the applicability of the results obtained.

Discrete-Time Systems With Constrained Time Delays and Delay-Dependent Lyapunov Functions

It is proved in this paper that the existence of a delay-dependent suitable Lyapunov function is a necessary and sufficient condition for a discrete-time fully nonlinear time-delay system, with given delays digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the delays digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions. The case of arbitrary time-varying time delays, with no constraints as long as bounded, is covered as a special case.

The hypothesis of equal wave speeds for stabilization of Timoshenko beam is not necessary anymore: the time delay cases†

AbstractIn the current study, we consider the Bresse–Timoshenko type systems and we prove some stability results for time delay cases into setting of so called simplified Bresse–Timoshenko equations (or truncated version of Bresse–Timoshenko equations) according to contributions of Elishakoff et al. (2010, Advances in Mathematical Modeling and Experimental Methods for Materials and Structures. Solid Mechanics and Its Applications. Springer: Berlin, 249–254.; 2015, Celebrating the Centenary of Timoshenko’s study of effects of shear deformation and rotary inertia. Appl. Mech. Rev.67, 1–11.; 2017, Critical contrasting of three versions of vibrating Bresse-Timoshenko beam with a crack. Int. J. Solids Struct. 109, 143–151.). These equations are free of the so-called ‘second spectrum’ phenomenon, and they have important consequences on stabilization setting. Specifically, following Almeida Júnior and Ramos (2017, On the nature of dissipative Timoshenko systems at light of the second spectrum. Z. Angew. Math. Phys.68, 31.) in a recent contribution that shows that damping effects eliminate the consequences of this spectrum for equal wave propagation velocities, we prove that time delay effects are able of stabilizing the truncated version regardless of any relationship between coefficients of system. It is concluded that dissipative truncated versions of Bresse–Timoshenko equations are advantageous over the classical Bresse–Timoshenko equations in stabilization context.

On stability of neutral-type linear stochastic time-delay systems with three different delays

We study in this paper the mean square exponential stability of neutral-type linear stochastic time-delay systems with three different delays by using the Lyapunov–Krasovskii functionals (LKFs) based approach. First, for a specified augmented state vector, a complete augmented LKF is constructed to contain all possible integrals so that its time-derivatives (understood in the deterministic sense) can be written as a linear function of the augmented vector. The redundant variables in the LKF are eliminated so as to reduce the computational burden. Moreover, the absolute value requirement of certain terms in the constructed LKFs are removed by analyzing carefully the complex relationship among these three different time delays. Then, for ten different cases of time delays, sufficient stability conditions in terms of linear matrix inequalities are obtained with the help of the Ito formula and properties of stochastic integrals. The degenerated cases that the delays satisfy some equalities are also discussed. A numerical example is employed to illustrate the effectiveness of the proposed approach.

A discrete time domain approach on time delay estimation

A time delay estimation method based on the discrete time domain approach is introduced here. In this dual-channel time delay estimation model, the criterion function compares the time differences of time sequences between channels, not the magnitude values of time functions as in the conventional cross-correlation method. An estimation task is formulated as an extreme value problem in discrete index space. Using the index delay giving extreme value to the criterion function, it is possible to find the best estimate for time delay distribution in the meaning of that criterion. Using this method, the estimated delay distribution and criterion function are clearly separated. Thus, there are no theoretical problems in the determination of the average time delay or velocity in the non-constant or changing time delay case as long as a sufficient statistical similarity (correlation) exists between channel signals. <p class="Abstract">The theoretical values of several criterion functions and the probability of occurrence of an anomalous estimate with the cross-covariance criterion function are derived. A basic performance analysis of the estimation method is presented. Some potential real-time supervision methods based on the use of criterion functions in the detection of the possible unreliability of the time delay estimate are outlined.</p>

Consensus Based Control Algorithm for Nonlinear Vehicle Platoons in the Presence of Time Delay

The platoon control problem for nonlinear vehicles in the presence of time delay is investigated in this paper, where both constant time delay and time-varying delay cases are considered. A linearized third-order vehicle dynamic model is firstly derived by deploying the exact feedback linearization technique and the vehicle platoon control problem is converted into a consensus-seeking problem. Then, a consensus based vehicle platoon control algorithm with time delay is proposed, which drives vehicles to form an equally spaced platoon with the same velocity. By deploying the Lyapunov-Razumikhin theorem, the upper bound of time delay for vehicle platoon with constant time delay is derived and the sufficient conditions that guarantee the stability of the vehicle platoon are obtained. Meanwhile, the sufficient conditions that ensure the stability of vehicle platoon with time-varying delay are acquired via the Lyapunov-Krasovskii theorem. Numerical demonstrations verify the feasibility and correctness of the theoretical results.

Abstract WP506: Looking for Themes to Improve Outcomes Through Team Debriefing

Background: Acute ischemic stroke (AIS) patients risk grave disability when treatment is delayed. The benchmark for door to needle (DTN) time for thrombolysis in AIS is less than 60 minutes; The American Stroke Association's (ASA) Target Stroke, Phase II (TSP II) sets a higher standard of less than 45 minutes. Emergency department caregivers at a 377 bed community hospital with primary stroke center designation were educated about the TSP II toolbox; however DTN times in 2016 were less than 60 minutes only 29% of the time with a mean time of 78 minutes, a medium time of 77 minutes and a range of 178 minutes. Purpose: Using a lean methodology approach we organized team debriefings to evaluate cases of time delay with the aim to develop strategies to improve outcome. Methods: As a process improvement project, an interprofessinal team was assembled to debrief and evaluate all patients receiving thrombolytic therapy. A comprehensive checklist was developed to include all of the critical components of care along with target benchmark timelines. Each data point was scrutinized to evaluate for possible time delays. The caregiver team was encouraged to objectively identify time delays and look for themes. Through root cause analysis, the most common theme identified was the performance of unnecessary tasks that could wait until after initiation of therapy. The other theme identified was delay in critical interventions such as timely lowering of blood pressure to prevent hemorrhage in patients undergoing thrombolysis. We engaged in coaching conversations among members of the team in an effort to promote better critical thinking and better patient outcomes. Results: From January, 2017 to August, 2018 there were 69 thrombolytic therapy cases The DTN rate of less than 60 minutes was 78%. Mean, median and mode times were 53,51 and 57 minutes respectively. The range was from 28-93 minutes. DTN in 45 minutes or less occurred at a rate of 30%. Conclusion: Improved outcome for exemplary professional practices can be afforded through a systematic approach to debrief about time sensitive treatments. Bringing team members together for a guided discussion designed to look for themes that lead to performance deficits will develop better patient outcomes.

Double stochastic resonance in an insect ecosystem with time delays

Considering additive and multiplicative periodic signals, we have investigated the stochastic resonance (SR)phenomenon in an insect ecosystem with two different types of time delays, at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises. The signal-to-noise ratio (SNR) is calculated when two different weak periodic signals are added to the insect system. It is shown from the SNR that the additive and multiplicative periodic signals can cause the SR and double SR in the case of time delays in the stochastic and deterministic force, respectively. A detailed study of the SNR depending on various noise characteristics is performed, and the main results about SR are compared for two different cases of time delays.

Cooperative output regulation of linear discrete-time time-delay multi-agent systems by adaptive distributed observers

In this paper, we study the cooperative output regulation problem for heterogeneous linear discrete-time time-delay multi-agent systems by adaptive distributed observers. An adaptive distributed observer-based approach was recently proposed for estimating both a leader’s state and its system dynamics, to each follower. This approach is applied to discrete-time multi-agent systems with input-delays to relax the assumption that all the followers know the leader’s system dynamics. Based on the adaptive distributed observer, we further generalize the adaptive dynamic solver for solving the regulator equations associated with each follower from delay-free case to time-delay case. Finally, the problem is solved by a distributed dynamic output feedback controller.

Leader-Follower Consensus of Second-Order Multiagent Systems with Absent Velocity Measurement and Time Delay

The leader-follower consensus problem of second-order multiagent systems with both absent velocity measurement and time delay is considered. First of all, the consensus protocol is designed by introducing an auxiliary system to compensate for the unavailability of the velocity information. Then, time delay is incorporated into the consensus protocol and two cases with, respectively, constant time delay and time-varying delay are investigated. For the case of constant time delay, Lyapunov-Razumikhin theorem is deployed to obtain the sufficient conditions that guarantee the stability of the consensus algorithm. For the case of time-varying delay, the sufficient conditions are also derived by resorting to the Lyapunov-Razumkhin theorem and linear matrix inequalities (LMIs). Various numerical simulations demonstrate the correctness of the theoretical results.

Effects of partial time delay on detecting subthreshold signal in Newman–Watts neuronal networks

Information transition delay is an inherent factor in neuronal systems and has great influences on their dynamical behaviors. For theoretical studies about time delay in neuronal systems, researchers usually set all connections between neurons to be delayed. However, in real neural systems, communication between some connected neurons maybe instantaneous which make the connection be delay-free. Thus, we will discuss effects of partial time delay on detecting subthreshold signal of neuronal systems in this paper from the viewpoint of stochastic resonance. Partial time delay is introduced by assuming that time delay between two connected neurons to be τ (which is not zero) with a probability pdelay. With the obtained numerical results, we show that the ability of detecting subthreshold signal could be reduced or enhanced strongly depending on the values of pdelay and τ. Especially, the detecting ability could be enhanced by a wide range of time delay τ when pdelay is small. It means that partial time delay could have quite different influences on the ability of detecting subthreshold signal as comparing with the full time delay case (all connections are delayed). Meanwhile, we also exhibit that network topology, noise intensity and coupling strength could have great influences on the effects of partial time delay on detecting subthreshold signal of the neuronal systems.

IQC analysis of reset control systems with time-varying delay

ABSTRACTThe study of input–output stability of reset control systems with time-varying delay is addressed in this work. The time-varying function that defines the delay is assumed to be bounded on magnitude and variation. This approach also covers the particular case of constant time delay, but it is studied separately to obtain less conservative results. After proposing a convenient loop transformation, the stability analysis is performed by means of the integral quadratic constraint framework. Then by applying the Kalman–Yakubovich–Popov lemma, easily checkable conditions in form of linear matrix inequalities are obtained. To conclude, some numerical examples are provided illustrating the proposed criteria.

Predictive Control Adapting to Fractional Values of Time Delay

A combination of identification and control procedures is presented which is aimed at precise control of systems with any value of time delay. Suggested strategy allows the predictive controller to adapt its parameters to a value of the time delay identified during the control process. The system flexibility resides in the ability to work precisely even with time-delay values that are not integer multiples of the sampling period. Overall, the designed approach presents a more precise method to control systems with both static and variable cases of time delay.

Delay-Dependent Exponential Stabilization for Linear Distributed Parameter Systems With Time-Varying Delay

This paper extends the framework of Lyapunov–Krasovskii functional to address the problem of exponential stabilization for a class of linearly distributed parameter systems (DPSs) with continuous differentiable time-varying delay and a spatiotemporal control input, where the system model is described by parabolic partial differential-difference equations (PDdEs) subject to homogeneous Neumann or Dirichlet boundary conditions. By constructing an appropriate Lyapunov–Krasovskii functional candidate and using some inequality techniques (e.g., spatial integral form of Jensen's inequalities and vector-valued Wirtinger's inequalities), some delay-dependent exponential stabilization conditions are derived, and presented in terms of standard linear matrix inequalities (LMIs). These stabilization conditions are applicable to both slow-varying and fast-varying time delay cases. The detailed and rigorous proof of the closed-loop exponential stability is also provided in this paper. Moreover, the main results of this paper are reduced to the constant time delay case and extended to the stochastic time-varying delay case, and also extended to address the problem of exponential stabilization for linear parabolic PDdE systems with a temporal control input. The numerical simulation results of two examples show the effectiveness and merit of the main results.

The WS transform for the Kuramoto model with distributed amplitudes, phase lag and time delay

We apply the Watanabe–Strogatz (WS) transform to a generalized Kuramoto model with distributed parameters describing the amplitude of oscillation, phase lag, and time delay at each node of the system. The model has global coupling and identical frequencies, but allows for repulsive interactions at arbitrary nodes leading to conformist-contrarian phenomena together with variable amplitude and time-delay effects. We show how to determine the initial values of the WS system for any initial conditions for the Kuramoto system, and investigate the asymptotic behaviour of the WS variables. For the case of zero time delay the possible asymptotic configurations are determined by the sign of a single parameter μ which measures whether or not the attractive nodes dominate the repulsive nodes. If the system completely synchronizes from general initial conditions, whereas if one of two types of phase-locked synchronization occurs, depending on the initial values, while for periodic solutions can occur. For the case of arbitrary non-uniform time delays we derive a stability condition for completely synchronized solutions.