Internal Delay Research Articles

Generalized quantized intermittent control with adaptive strategy on finite-time synchronization of delayed coupled systems and applications

This paper is concerned with the finite-time synchronization problem of coupled drive-response systems with time-varying delays via quantized adaptive aperiodically intermittent control. Compared with previous research results, the intermittent control is aperiodic and coupling functions are nonlinear. Furthermore, both internal time-varying delays and coupling time-varying delays are considered. By employing Lyapunov–Krasovskii functional method and Kirchhoff’s Matrix Tree Theorem, some novel sufficient conditions are derived to guarantee that drive-response systems can achieve synchronization in finite time. Specially, the convergence time is discussed. It is worth pointing out that the convergence time is closely related to topological structure of networks and the maximum ratio of the rest width to the aperiodical time span. Finally, finite-time synchronization of a typical second-order Kuramoto model with time-varying delays and Chua’s circuits model with time-varying delays are studied by using our theoretical results. Meanwhile, the numerical simulations are given to illustrate the effectiveness of the theoretical results we obtained.

A synaptic theory of internal delays.

Neurons in the medial superior olive perform a coincidence analysis between inputs from the two ears, as predicted by Jeffress [J. Comp. Psychol. 41, 35-39 (1948)]. Jeffress also correctly predicted inputs to express a range of internal delays for which he invoked axonal delay lines. These, however, cannot explain that the inputs of many binaural neurons differ by a combination of a time delay and a phase shift. This study proposes an alternative source of internal delay. An interaural asymmetry in the activation threshold of the inner hair cell synapses is shown to reproduce the main features of internal delays of binaural neurons.

Existence of global solutions and decay estimates for a viscoelastic Petrovsky equation with internal distributed delay

In this article we consider a nonlinear viscoelastic Petrovsky equation in a bounded domain with distributed delay $$\begin{aligned} \begin{aligned}&|u_{t}(x,t)|^{l}u_{tt}(x,t)+\Delta ^{2}u(x,t)-\Delta u_{tt}(x,t)-\displaystyle \int _{0}^{t}h(t-\sigma )\Delta ^{2}u(x,\sigma )\,d\sigma +\mu _{1}u_{t}(x,t)\\&\quad +\int _{\tau _{1}}^{\tau _{2}}\mu _{2}(s)u_{t}(x,t-s)ds=0,\quad x\in \Omega ,\; t>0, \end{aligned} \end{aligned}$$ and prove a global solution existence result using the energy method combined with the Faedo–Galerkin approximation , under condition on the weight of the damping and the weight of distributed delay. Also we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.

Estimations of GNSS receiver internal delay using precise point positioning algorithm

Abstract Random and systematic errors affect navigation satellite observations on both pseudo-range and carrier phase. These errors are originated at satellites, propagation path and receivers. This study focuses on the GNSS receiver internal delay determination resulting from the receiver’s electronics circuit. The characterisation of the delay in the GNSS geodetic receivers is essential to enhance the accuracy for the time transfer and time comparisons as part of GNSS integrity chain determinations. The purpose of GNSS receiver internal delay at the National Institute of Metrology (Thailand), NIMT, is to estimate the characteristics and performances of the GNSS geodetic receiver used for international time comparisons. The experiments are simultaneously observed GNSS satellites by a GPS and a GNSS receivers and two separate antennas with short baseline (around 6 metres), where both receivers are connected to the identical external caesium frequency standard maintained as time and frequency standard of Thailand. The GPS receiver is well-defined for its receiver internal delay on the pseudo-range observation of C1, through comparisons using an internationally recognised method, while the geodetic GNSS receiver is to be defined on its receiver internal delay. These experiment observations started from 26 December 2017 to 17 January 2018 at NIMT, Pathumthani, Thailand. The determined unknowns are receiver position, receiver clock offset, tropospheric delay through the geodetic technique of static Precise Point Positioning observations with Bernese GNSS software version 5.2. Later the receiver internal delay of NIMT is computed and analysed. The receiver internal delay on GPS C1 code is successfully characterised, resulted as 346.0 nanoseconds as of this experiment.

Effects of interaural delay, center frequency, and no more than ”slight” hearing loss on binaural processing: Behavioral data and quantitative analyses

Recent neurophysiological studies concerning “hidden hearing loss” have motivated investigators to attempt to uncover behaviorally-measured auditory deficits that might exist in human listeners who would be categorized via standard audiometry as having normal hearing or, at most, “slight” hearing loss. We hypothesized that behavioral measures of binaural auditory performance could reveal the presence of deficits that may not be discoverable via standard audiometric testing or via measures of monaural processing. That hypothesis was based on the notion that monaural (perhaps, peripheral) deficits would be effectively multiplied via binaural interaction. Groups of listeners, all having no greater than “slight” hearing loss were tested. Binaural detection thresholds were elevated across a wide range of center frequencies for listeners whose absolute thresholds at 4 kHz exceed 7.5 dB HL. Quantitative predictions made via an interaural correlation-based model of binaural processing suggest that the elevated binaural detection thresholds observed for listeners having slightly elevated absolute thresholds stem solely from their having elevated levels of internal noise. They appear to stem neither from reduced sensitivity to signal-dependent changes in information derived from the stimuli as processed internally nor from increased noise along the listener’s putative internal delay line.

Global synchronization in nonlinearly coupled delayed memristor-based neural networks with excitatory and inhibitory connections

This investigation establishes the global synchronization of an array of coupled memristor-based neural networks with delays. The coupled networks that are considered can incorporate both the internal delay in each individual network and the transmission delay across different networks. The coupling scheme, which consists of a nonlinear term and a sign term, is rather general. In particular, it can be asymmetric, and admits the coexistence of excitatory and inhibitory connections. Based on an iterative approach, the problem of synchronization is transformed into solving a corresponding linear system of algebraic equations. Subsequently, the respective synchronization criteria, which depend on whether the transmission delay exists, are derived respectively. Three examples are given to illustrate the effectiveness of the theories presented in this paper. The synchronization of the systems in two examples cannot be handled by existing techniques.

On finite-time consensus objectives in time-varying interconnected discrete linear dynamic systems under internal and external delays

This article formulates the properties of achievable consensus of linear interconnected discrete systems with multiple internal and external point delays. The formulation is stated in an algebraic generic context as the ability of achievement of (a non-necessarily zero) finite-time common error between the various subsystems. The consensus signals are generically defined so that they can be, in general, distinct of the output or state components. However, the consensus signals of all the interconnected subsystems have the same dimension for coherency reasons. A particular attention is paid to the case of weak interconnection couplings in both the open-loop case and the closed-loop one under, in general, linear output feedback. Some further extensions are given related to consensus over intervals and related to consensus of positive interconnected systems.

Stabilisation of stochastic delayed systems with Lévy noise on networks via periodically intermittent control

ABSTRACTThis paper investigates the stabilisation of stochastic coupled systems with time-varying delays and Lévy noise on networks (SCSTLN) via periodically intermittent control. And here, internal delays, white noise and Lévy noise are considered in the networks. To ensure stability of SCSTLN with a periodically intermittent controller, several simple and useful criteria are obtained by establishing a new differential inequality and using a graph-theoretic approach. The intensity of control is closely related to the coupling strength and the perturbed intensity of white noise and Lévy noise. In particular, the stabilisation of stochastic coupled oscillators with time-varying delays and Lévy noise on a network as a practical application of our theoretical results is studied. Finally, a numerical example about oscillators network is carried out to show the validity and feasibility of our analytical results.

Dynamic seesaw model for rapid signaling responses in eukaryotic chemotaxis

Directed movement of eukaryotic cells toward spatiotemporally varied chemotactic stimuli enables rapid intracellular signaling responses. While macroscopic cellular manifestation is shaped by balancing external stimuli strength with finite internal delays, the organizing principles of the underlying molecular mechanisms remain to be clarified. Here, we developed a novel modeling framework based on a simple seesaw mechanism to elucidate how cells repeatedly reverse polarity. As a key feature of the modeling, the bottom module of bidirectional molecular transport is successively controlled by three upstream modules of signal reception, initial signal processing, and Rho GTPase regulation. Our simulations indicated that an isotropic cell is polarized in response to a graded input signal. By applying a reversal gradient to a chemoattractant signal, lamellipod-specific molecules (i.e. PIP3 and PI3K) disappear, first from the cell front, and then they redistribute at the opposite side, whereas functional molecules at the rear of the cell (i.e. PIP2 and PTEN) act oppositely. In particular, the model cell exhibits a seesaw-like spatiotemporal pattern for the establishment of front and rear and interconversion, consistent with those related experimental observations. Increasing the switching frequency of the chemotactic gradient causes the cell to stay in a trapped state, further supporting the proposed dynamics of eukaryotic chemotaxis with the underlying cytoskeletal remodeling.

General decay result for thermoelastic beam equation system with time-varying delay

In this paper, we study a thermoelastic beam system with internal time-varying delay. We show that the damping and viscoelastic terms are strong enough to stabilize the system at a general decay rate under suitable assumptions on the time-varying delay and the relaxation function.

Rapid stabilisation of multi-dimensional Schrödinger equation with the internal delay control

ABSTRACTIn this paper, we are concerned with the controller design for multi-dimensional Schrödinger equation with the internal delay control. We introduce a new approach to design the feedback control law based on the system equivalence. First, we construct a target system with the desired exponential stability. Second, we select a proper transformation and inverse transformation which guarantee the equivalence of both systems. In this procedure, we can get the expression of feedback control. Finally, exponential stability of the closed-loop system under the feedback controller is acquired through establishing equivalence relation between the closed-loop system and the target system.

A neural circuit for song pattern recognition in the cricket brain

Acoustic communication is based on amplitude and frequency modulation of sound signals. Temporal features of the signal require processing by central auditory neurons, the brain circuits, however that detect temporal features are poorly understood. We show how five neurons in the brain of female field crickets form an auditory feature-detector circuit for the pulse pattern of the male calling song, and exhibit properties of a delay-line and coincidence-detection mechanism. The network receives its direct input from a single ascending auditory interneuron. An internal delay that matches the pulse period of the calling song is established by a non-spiking brain neuron. In response to a sound pulse, it generates a transient inhibition that triggers a delayed rebound depolarization. The direct input and the delayed responses converge in a coincidence detector neuron, which responds best to the pulse pattern of the species-specific calling song as the rebound activation of the non-spiking neuron coincides with the response of the ascending interneuron to the subsequent sound pulse. The output of the coincidence detector neuron is further processed by a feature detector neuron to suppress unselective responses and background activity. The circuit reveals principal mechanisms of sensory processing underlying the perception of temporal auditory patterns.

Pinning Synchronization of Nonlinear and Delayed Coupled Neural Networks with Multi-weights via Aperiodically Intermittent Control

This paper deals with the synchronization issues of delayed neural networks with multi-weights under aperiodically intermittent pinning control. There are three main differences of this paper with previous works: firstly, aperiodically intermittent pinning control scheme is used to synchronize the proposed neural networks; secondly, the model is delayed neural networks with multi-weights, which have several different sorts of weights between two nodes; thirdly, internal delay and multi-coupling delays are considered simultaneously. By establishing new nonlinear inequalities and constructing Lyapunov function, several sufficient criteria are derived to guarantee exponential synchronization for the proposed neural network models. Moreover, an effective pinned-node selection scheme which determines what kind of nodes should be prior controlled is provided. Finally, two illustrative examples are presented to demonstrate the effectiveness of the theoretical results.

Decay of an Extensible Viscoelastic Plate Equation with a Nonlinear Time Delay

An extensible viscoelastic plate equation with a nonlinear time-varying delay feedback and nonlinear source term is considered. Under suitable assumptions on relaxation function, nonlinear internal delay feedback, and source term, we establish a general decay of energy by using the multiplier method if the weight of weak dissipation and the delay satisfy $$\mu _2<\frac{\mu _1\alpha _1(1-d)}{\alpha _2(1-\alpha _1d)}$$ , and extend some known results.

Modeling auditory-visual evoked eye-head gaze shifts in dynamic multisteps.

In dynamic visual or auditory gaze double-steps, a brief target flash or sound burst is presented in midflight of an ongoing eye-head gaze shift. Behavioral experiments in humans and monkeys have indicated that the subsequent eye and head movements to the target are goal-directed, regardless of stimulus timing, first gaze shift characteristics, and initial conditions. This remarkable behavior requires that the gaze-control system 1) has continuous access to accurate signals about eye-in-head position and ongoing eye-head movements, 2) that it accounts for different internal signal delays, and 3) that it is able to update the retinal ( TE) and head-centric ( TH) target coordinates into appropriate eye-centered and head-centered motor commands on millisecond time scales. As predictive, feedforward remapping of targets cannot account for this behavior, we propose that targets are transformed and stored into a stable reference frame as soon as their sensory information becomes available. We present a computational model, in which recruited cells in the midbrain superior colliculus drive eyes and head to the stored target location through a common dynamic oculocentric gaze-velocity command, which is continuously updated from the stable goal and transformed into appropriate oculocentric and craniocentric motor commands. We describe two equivalent, yet conceptually different, implementations that both account for the complex, but accurate, kinematic behaviors and trajectories of eye-head gaze shifts under a variety of challenging multisensory conditions, such as in dynamic visual-auditory multisteps.

Impulsive mean square exponential synchronization of stochastic dynamical networks with hybrid time-varying delays

This paper investigates the mean square exponential synchronization problem for complex dynamical networks with stochastic disturbances and hybrid time-varying delays, both internal delay and coupling delay are considered in the model. At the same time, the coupled time-delay is also probabilistic in two time interval. Impulsive control method is applied to force all nodes synchronize to a chaotic orbit, and impulsive input delay is also taken into account. Based on the theory of stochastic differential equation, an impulsive differential inequality and some analysis techniques, several simple and useful criteria are derived to ensure mean square exponential synchronization of the stochastic dynamical networks. Furthermore, pinning impulsive strategy is studied. An effective method is introduced to select the controlled nodes at each impulsive constants. Numerical simulations are exploited to demonstrate the effectiveness of the theory results in this paper.

A comparative study of two tuning rules for delayed compensation controllers

The focus of this contribution is on the use of two controller tuning techniques for delayed controllers designed by an algebraic approach for linear time-invariant time delay systems. The well-known Chien-Hrones-Reswick (CHR) method and the Equalization Method (EM) are used. The tuning procedure is applied to compensation-type controllers that include internal delays, and hence there can be found a link to the habitual Smith predictor structure. This study considers two typical representatives of controlled plants with both input-output and internal delays; namely, the first- and second-order (of derivatives) systems are taken. Numerical comparative experiments are presented and discussed.

On the positivity, excitability and transparency properties of a class of time-varying bilinear dynamic systems under multiple point internal and external delays

AbstractThis paper investigates formally the internal and external positivity, together with its excitability and transparency properties, of a class of bilinear time-varying continuous-time dynami...

Well-posedness and asymptotic stability for the Lamé system with internal distributed delay

Well-posedness and asymptotic stability for the Lamé system with internal distributed delay

Effect of Surface Excess Energy Transport on the Rupture of an Evaporating Film

In most of existing works on the instabilities of an evaporating film, the energy boundary condition only takes into account contributions of the evaporation latent heat and the heat conduction in the liquid. We use a new generalized energy boundary condition at the evaporating liquid-vapor interface, in which the contribution of the transport of the Gibbs excess energy is included. We have derived the long-wave equations in which the thickness of film and the interfacial temperature are coupled to describe the dynamics of an evaporating thin film. The results of our computation show that the transport of the Gibbs excess internal energy delay the rupture of thin films due to van de Waals force, evaporating effect and vapor recoil.