Types Of Time Delays Research Articles

Receding Horizon Synchronization of Delayed Neural Networks Using a Novel Inequality on Quadratic Polynomial Functions

This article investigates H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization of delayed neural networks under a receding horizon scheme, where two types of interval time-varying delays are considered according to whether the lower bound of the delay derivative is known or not. Note that a receding horizon synchronization law can be regarded as an optimization solution at each timeslot to a minimaxization problem related closely with a certain cost functional. In this article, two cost functionals with some delay-dependent matrices are introduced, respectively, for the two types of time delays. In order to obtain less conservative conditions, a novel inequality on quadratic polynomial functions is established, which includes some existing ones as its special cases. Based on the novel inequality, two sufficient conditions are derived to design the terminal weighting matrices of the cost functionals such that the resulting synchronization error system can be stabilized with a prescribed infinite horizon H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level. Finally, three numerical examples are used to demonstrate the validity of the proposed results.

Global properties of saturated chikungunya virus dynamics models with cellular infection and delays

This paper studies the global properties of chikungunya virus (CHIKV) dynamics models with both CHIKV-to-monocytes and infected-to-monocyte transmissions. We assume that the infection rate of modeling CHIKV infection is given by saturated mass action. The effect of antibody immune response on the virus dynamics is modeled. The models included three types of time delays, discrete or distributed. The first type of delay is the time between CHIKV entry an uninfected monocyte to be latently infected monocyte. The second time delay is the time between CHIKV entry an uninfected monocyte and the emission of immature CHIKV. The third time delay represents the CHIKV’s maturation time. Lyapunov method is utilized and LaSalle’s invariance principle is applied to address the global stability of equilibria. The model is numerically simulated to support theoretical results.

Wigner Time Delay Induced by a Single Quantum Dot

Resonant scattering of weak coherent laser pulses on a single two-level system realized in a semiconductor quantum dot is investigated with respect to a time delay between incoming and scattered light. This type of time delay was predicted by Wigner in 1955 for purely coherent scattering and was confirmed for an atomic system in 2013 [R. Bourgain etal., Opt. Lett. 38, 1963 (2013)OPLEDP0146-959210.1364/OL.38.001963]. In the presence of electron-phonon interaction, we observe deviations from Wigner's theory related to incoherent and strongly non-Markovian scattering processes which are hard to quantify via a detuning-independent pure dephasing time. We observe detuning-dependent Wigner delays of up to 530ps in our experiments which are supported quantitatively by microscopic theory allowing for pure dephasing times of up to 950ps.

Emergent dynamics of coordinated cells with time delays in a tissue.

In this article, we investigate the emergence of tissue dynamics with time delays of diffusion. Such emergent dynamics, describing the tissue homeostasis, usually correspond to particular tissue functions, which are attracting a tremendous amount of attention from both communities of mathematical modeling and systems biology. Specifically, in addition to the within-cell genome dynamics and the diffusion among the cells, we consider several types of time delays of diffusion present in the coordinated cells. We establish several generalized versions of the "monotonicity condition" (MC), whose traditional version [I. Rajapakse and S. Smale, Proc. Natl. Acad. Sci. U.S.A. 114, 1462-1467 (2017)] guaranteed the stability of the equilibrium in a system of coordinated cells without time delay. Indeed, we find that one generalized MC we establish still guarantees the stability of the time-delayed system's equilibrium, which corresponds to a formation of tissue functions depending primarily on individual genome dynamics but less on interacting structures and time delays of diffusion. We also find that, when the generalized MC is further relaxed, the system is able to sustain periodic oscillations, whose periods are verified to have delicate dependence with the selected time delays. These produced oscillations usually represent realistic behaviors of "alive" cells. We use several representative examples to demonstrate the usefulness of the established analytical conditions to the understanding of the emergent dynamics observed in computational models and in real systems as well.

VREMENSKO KAŠNJENJE SIGNALA U DISTRIBUTIVNOJ MREŽI

U radu se razmatra putanja signala prilikom komandovanja telemetrisanom tačkom i izvrša­vanja VVO CL funkcije. Razmatraju se tipovi vremenskog kašnjenja kao i samo vremensko kašnjenje koje se javlja prilikom komandovanja i izvršavanja VVO CL funkcije. Takođe, razmatra se i kako i na koji način vremensko kašnjenje utiče na proračune, nadzor sistema i komandovanje. Proračun vremenskog kašnjenja je izvršen na osnovu prikupljenih vremenskih kašnjenja.

Dynamics of a predator-prey model with nonlinear incidence rate, Crowley-Martin type functional response and disease in prey population

Abstract In this paper, a delayed predator-prey model has been developed. Here, on the basis of infectious disease, the prey population has been divided into two sub-populations such as (i) susceptible prey and (ii) infected prey population. It is also assumed that a predator may consume both susceptible prey as well as infected prey. Also here, the Crowley-Martin type functional form has been taken to consume the prey (both susceptible and infected) population by the predator. It also considers two types of time delays in this model, (i) one is disease transmission delay when susceptible prey moves to infected prey stage and (ii) other is predator maturation delay. As the predator consumes both susceptible and infected prey, so we have incorporated the fact in this model that disease in the prey species also effect on predator population growth. Here, positivity and boundedness of solutions of our proposed model have been discussed. Then calculating different equilibrium points, the stability of the system have been discussed around those. In this paper, the Hopf bifurcation analysis has been done for non-delayed system with respect to the crowding coefficient. Finally, some numerical simulations have been presented to validate our theoretical findings.

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.

Exponential synchronization of memristive neural networks with time delays

Abstract It is known that the parameters of memristive neural networks (MNNs) are state-dependent, and the unexpected parameter mismatch issue between driven system and response system might be caused by the special characteristics of MNNs, then the traditional state feedback synchronization control and analytical techniques cannot be applied directly. In order to solve this problem, one type of new sandwich control structure, which includes two types of sub-controllers and the different control gains, is designed to ensure the exponential synchronization of two MNNs. Meanwhile, in the process of synchronization, the time delays in MNNs and the time delays between drive system and response system in real environment are also considered by us. Based on the concept of Filippov solution, Lyapunov stability theory, matrix inequality, etc., the exponential synchronization conditions for the MNNs with two types of time delays via sandwich control are given. Finally, a numerical example is displayed to show the efficiency and feasibility of this method.

Functional observer based controller for stabilizing Takagi–Sugeno fuzzy systems with time-delays

This paper investigates the construction of a fuzzy functional observer for nonlinear systems with time-delays, and the application of the observer to estimate the state functions of the parallel distributed compensation controller for stabilizing the system. Two types of time-delays are considered: constant and time-varying delays with bounded time derivative. Stability conditions are obtained using Lyapunov–Krasovskii functional approach; and the conditions are transformed into linear matrix inequalities with equality constraints so that observer parameters can be calculated using the solution of these inequalities. Functional observer construction procedures are presented considering both constant and time-varying time-delays. Two examples, including one for obtaining a power system stabilizer for a single machine infinite bus system, are presented to illustrate effectiveness of the proposed design procedures.

Consensus of Discrete-Time Linear Multiagent Systems With Communication, Input and Output Delays

This note addresses the output consensus problem of discrete-time heterogeneous linear multiagent systems with switching topology and time delays. Three types of time delays are considered: communication delays, input delays, and output delays. A distributed predictor-based controller is proposed and it is shown that the output consensus problem can be solved via the proposed controller. A key to the proof of our main results is the establishment of a new property of graphs, that is, uniform sequential connectivity and uniform quasi-strong connectivity are equivalent. A simulation example is provided to illustrate the effectiveness of our results.

Inertia compensation scheme of WTS considering time delay for emulating large‐inertia turbines

Wind turbine simulators (WTSs), devised for pre-validation of control strategies for wind energy conversion system, commonly employ the inertia compensation scheme for reproducing mechanical behaviours similar to real wind turbines (WTs). However, it is found in this study that when a WT with large inertia is simulated, the time delay in command communication from control unit to motor driver, usually neglected in the existing inertia compensation scheme, results in the oscillating acceleration response and consequently leads to instability of the WTS system. As a result, the existing WTS is unable to stably simulate large-inertia WTs, which significantly limits its applicability. Hence, in this study, a linear discrete model of the inertia compensation part that considers time delay of acceleration observation and communication is developed. On the basis of this model, an improved inertia compensation scheme in which a high-order filter is introduced to eliminate the deviation of acceleration response caused by the two types of time delay is proposed. Finally, the improved inertia compensation scheme and its applicability to simulating a 600 kW WT developed by National Renewable Energy Laboratory are experimentally verified.

Topology Detection for Output-Coupling Weighted Complex Dynamical Networks with Coupling and Transmission Delays

Topology detection for output-coupling weighted complex dynamical networks with two types of time delays is investigated in this paper. Different from existing literatures, coupling delay and transmission delay are simultaneously taken into account in the output-coupling network. Based on the idea of the state observer, we build the drive-response system and apply LaSalle’s invariance principle to the error dynamical system of the drive-response system. Several convergent criteria are deduced in the form of algebraic inequalities. Some numerical simulations for the complex dynamical network, with node dynamics being chaotic, are given to verify the effectiveness of the proposed scheme.

Local Pinning of Networks of Multi-Agent Systems With Transmission and Pinning Delays

We study the stability of networks of multi-agent systems with local pinning strategies and two types of time delays, namely the transmission delay in the network and the pinning delay of the controllers. Sufficient conditions for stability are derived under specific scenarios by computing or estimating the dominant eigenvalue of the characteristic equation. In addition, controlling the network by pinning a single node is studied. Moreover, perturbation methods are employed to derive conditions in the limit of small and large pinning strengths. Numerical algorithms are proposed to verify stability, and simulation examples are presented to confirm the efficiency of analytic results.

Impact of two types of time delays and cross-correlated multiplicative and additive noises on stability and stochastic resonance for a metapopulation system

In this paper, we investigate the stability and the shift between the extinction state and the stable one of a large density and the stochastic resonance (SR) for a metapopulation system subjected to two types of time delay terms, cross-correlation noises and multiplicative signal. By using the fast descent method and the method of small delay approximation, the expressions of the effective potential function and the signal-to-noise ratio (SNR) are obtained. We denote by Q the intensity of the multiplicative noise, and M the intensity of the additive noise, θ and τ the two time delay terms introduced into the metapopulation system. Our main results show some facts that time delay θ and the strength of correlation noise λ can restrain the development of the metapopulation, while the other term of time delay τ can accelerate the expansion of the population from the extinction state to the large stable one. We discover that it is possible to enhance the signal-to-noise ratio by adjusting the intensities of the multiplicative, additive noises and the time delays of the stochastic metapopulation system

Stability, bifurcation, and synchronization of delay-coupled ring neural networks

This paper studies the nonlinear dynamics of coupled ring networks each with an arbitrary number of neurons. Different types of time delays are introduced into the internal connections and couplings. Local and global asymptotical stability of the coupled system is discussed, and sufficient conditions for the existence of different bifurcated oscillations are given. Numerical simulations are performed to validate the theoretical results, and interesting neuronal activities are observed, such as rest state, synchronous oscillations, asynchronous oscillations, and multiple switches of the rest states and different oscillations. It is shown that the number of neurons in the sub-networks plays an important role in the network characteristics.

Stability and multi-parametric Hopf bifurcation analyses of viral infection model with time delay

Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with stability and bifurcation analyses of mathematical model that represents the dynamics of HIV infection of thymus. The existence and stability of the equilibria are investigated. The model is described by a system of delay differential equations with logistic growth term, cure rate and discrete type of time delay. Choosing the time delay as a bifurcation parameter, the analysis is mainly focused on the Hopf bifurcation problem to predict the existence of a limit cycle bifurcating from the infected steady state. Further, using center manifold theory and normal form method we derive explicit formulae to determine the stability and direction of the limit cycles. Moreover the mitosis rate r also plays a vital role in the model, so we fix it as second bifurcation parameter in the incidence of viral infection. Our analysis shows that, while both the bifurcation parameters can destabilize the equilibrium E* and cause limit cycles. Numerical simulations are performed to investigate the qualitative behaviors of the inherent model.

Synchronous Hybrid Event- and Time-Driven Consensus in Multiagent Networks With Time Delays.

This paper studies the delay robustness of a class of synchronous hybrid event- and time-driven consensus protocols in undirected networks. These protocols can ensure the system performance at reduced data-sampling rates. We consider three types of time delays in feedbacks, including one common time delay, multiple time-invariant delays, and multiple time-varying delays; and by sampled-data control techniques, we characterize the maximum allowable time delay and the event-detecting period for solving the average consensus problem in terms of the algebraic structure of interaction topologies. Simulations are given to show the effectiveness of theoretical results.

Stability switches and bifurcation in a system of four coupled neural networks with multiple time delays

This paper reveals the dynamical behaviors of a coupled network consisting of four neural sub-networks and multiple two-way couplings of neurons between the individual sub-networks. Different types of time delays are introduced into the internal connections within the individual sub-networks and the couplings between the sub-networks. Stability switches of the network equilibrium and Hopf bifurcation are analyzed by discussing the associated characteristic equation. The conditions for the existence of different patterns of oscillations are discussed. By using the Lyapunov’s second method, the global stability of the network equilibrium is studied. Numerical simulations are performed to validate the theoretical results, and rich dynamical behaviors are observed, such as synchronous oscillations, multiple stability switches between the rest state and oscillations, phase-locked oscillations, asynchronous oscillations, and the coexistence of different patterns of bifurcated oscillations.

Simplified stochastic models with time delay for studying the degradation process of mRNA molecules.

Message RNA (mRNA) is the template for protein synthesis. It carries information from DNA in the nucleus to the ribosome sites of protein synthesis in the cell. The turnover process of mRNA is a chemical event with multiple small step reactions and the degradation of mRNA molecules is an important step in gene expression. A number of mathematical models have been proposed to study the dynamics of mRNA turnover, ranging from a one-step first order reaction model to the linear multi-component models. Although the linear multi-component models provide detailed dynamics of mRNA degradation, the simple first-order reaction model has been widely used in mathematical modelling of genetic regulatory networks. To illustrate the difference between these models, we first considered a stochastic model based on the multi-component model. Then a simpler stochastic model was proposed to approximate the linear multi-component model. We also discussed the delayed one-step reaction models with different types of time delay, including the constant delay, exponentially distributed delay and Erlang distributed delay. The comparison study suggested that the one-step reaction models failed to realise the dynamics of mRNA turnover accurately. Therefore, more sophisticated one-step reaction models are needed to study the dynamics of mRNA degradation.

Realization of Parameters Identification in Only Locally Lipschitzian Dynamical Systems with Multiple Types of Time Delays

Most of the existing results for identifying parameters in dynamical systems through adaptive coupling techniques always require a uniform Lipschitz condition on system vector fields. However, it is not this requirement but the only locally Lipschitz condition that is more suitable for many nonlinear systems in real applications. Also time delays sometimes are essential for modeling real systems, so that in addition to the discrete form, time delays in the distributed form could be considered. This paper thus considers the problem of parameters identification in only locally Lipschitzian dynamical systems with multiple types of time delays through adaptive coupling techniques. In particular, the paper proposes some linear independence conditions for realization of parameters identification in both nonautonomous and autonomous systems and draws a comparison between these conditions and the persistent of excitation condition which is used frequently in the literature. Moreover, the paper proposes an index to determine the nonlinear degree of the considered systems, which enables us to distinguish the systems in which the parameters identification can be globally or only locally achieved. The paper also uses some representative and elaborate examples to illustrate the practical usefulness of the obtained theoretical results. During the discussion, the paper takes into full consideration the property of infinite dimensions for nonautonomous or autonomous dynamical systems with time delays.