Kinds Of Time Delays Research Articles

Novel Synchronization Criteria for Non-Dissipative Coupled Networks with Bounded Disturbances and Time-Varying Delays of Unidentified Bounds via Impulsive Sampling Control

The μ−synchronization issues of non-dissipative coupled networks with bounded disturbances and mixed delays are studied in this article. Different from existing works, three kinds of time delays, including internal delays, coupling delays, and impulsive sampling delays, have unidentified bounds and even evolve towards infinity over time, making the concerned network more practical. Considering μ−stability theory and impulse inequality techniques, a hybrid non-delayed and time-delayed impulsive controller including both current and historical state information is designed, and several novel sufficient conditions are derived to make nonlinear complex networks achieve μ−synchronization. Moreover, not only can the constriction of dissipative coupling conditions on network topology be relaxed, but also the restriction of various time delays on impulsive intervals can be weakened, which makes the theoretical achievements in this article more general than the previous achievements. Ultimately, numerical simulations confirm the effectiveness of our results.

Small-Signal Stability Analysis and Lead-Lag Compensation Control for DC Networked-Microgrid Under Multiple Time Delays

Networked microgrid (NMG) system is an effective solution to enhance the power system's reliability and resilience. The distributed control is promising for NMG system due to its high reliability, scalability and low computational burden. The distributed control relies on the information exchange among distributed generators and sub-microgrids (sub-MGs), which inevitably contain heterogenous time delays that can deteriorate system stability. This paper focuses on the multiple time-delays small-signal stability analysis of a DC NMG with a distributed layered control architecture. Firstly, a generalized time-delayed DC NMG small-signal model with a typical two-layer distributed control framework is developed. Then, stability analysis is conducted considering multiple time delays from communication and measurement stages in NMG layer and MG layer. The impact of multiple time delays on NMG stability is quantified. We reveal that both the electrical coupling among MGs and different kinds of time delays in distributed control loops will impact the NMG stability. Subsequently, based on the detailed analytical results, the critical eigenvalue is identified, and a new lead-lag compensation controller is proposed to enhance the system stability by compensating for the phase lag of the critical eigenvalue. Lastly, the effectiveness of the proposed method and the accuracy of the analytical findings are verified by OPAL-RT-based real-time tests.

Stability and Bifurcation Analysis of a Fractional‐Order Food Chain Model with Two Time Delays

In this study, the stability and bifurcation problems of a fractional food chain system with two kinds of delays are studied. Firstly, the nonnegative, bounded, and unique properties of the solutions of the system are proved. The asymptotic stability of the equilibrium points of the system is discussed. Furthermore, the global asymptotic stability of the positive equilibrium point is deduced by using Lyapunov function method. Secondly, the system takes two kinds of time delays as bifurcation parameters and calculates the critical values of Hopf bifurcation accurately. The results show that Hopf bifurcation can advance with increasing fractional order and another delay. In conclusion, numerical simulation verifies and illustrates the theoretical results.

Robust Burst Detection Algorithm for Distributed Unique Word TDMA Signal

In recent years, distributed unique word (DUW) has been widely used in satellite single carrier TDMA signals, such as very small aperture terminal (VSAT) satellite systems. Different from the centralized structure of traditional unique word, DUW is uniformly dispersed in a burst signal, where the traditional unique word detection methods are not applicable anymore. For this, we propose a robust burst detection algorithm based on DUW. Firstly, we allocated the sliding detection windows with the same structures as DUW in order to effectively detect it. Secondly, we adopt the method of time delay conjugate multiplication to eliminate the influence of frequency offset on detection performance. Due to the uniform dispersion of DUW, it naturally has two different kinds of time delays, namely the delay within the group and the delay between the two groups. So, we divide the traditional dual correlation formula into two parts to calculate them separately and obtain a dual correlation detection algorithm, which is suitable for DUW. Simulation and experimental results demonstrate that when the distribution structure of DUW changes, detection probability of the proposed algorithm fluctuates little, and its variance is 1.56×10−5, which is 99.83% lower than the existing DUW detection algorithms. In addition, its signal to noise ratio (SNR) threshold is about 1 dB lower than the existing algorithms under the same circumstance of the missed detection probability.

Distributed $${H_\infty }$$ State Estimation in Sensor Network Subject to State and Communication Delays

The distributed $$H_\infty $$ state estimation of delayed sensor network is dealt with in this paper. To deeply reflect the time-delay phenomenon in the process of information fusion, a model containing state time-varying delay and different communication delays is set up. Afterwards, a fresh Lyapunov–Krasovskii functional (LKF) is given, which contains different kinds of time delays, delay-dependent matrix and multiple integral terms. Meanwhile, in order to cooperate with the constructed LKF to bring down the conservatism of the result effectively, relaxed-function-based single integral inequality and convex combination are employed to estimate the functional derivative. Thus, a less conservative criterion is gained to guarantee the asymptotic stability with desirable attenuation level of the estimation error system. Several simulation examples are used to testify the validity of the proposed approach.

Finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks via non-reduced order method

In this paper, we focus on the finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks. To cope with the effect caused by inertial (second-order) term, most of the previous literature use the variable translation to reduce the order. Different from that, by directly designing a Lyapunov functional and feedback controller, a novel non-reduced order method is proposed in this paper to solve the finite-time (fixed-time) stabilization problem of inertial memristive Cohen-Grossberg neural networks. Two kinds of time delays are considered in our network model, novel criteria are then derived for both cases. Lastly, numerical examples are given to verify the validity of the theoretical results.

Synchronization Analysis of Complex Dynamical Networks Subject to Delayed Impulsive Disturbances

This paper studies the problem of leader-following synchronization for complex networks subject to delayed impulsive disturbances, where two kinds of time delays considered exist in internal complex networks and impulsive disturbances. Some delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs) by using the delayed impulsive differential inequality method. Moreover, a feedback controller is designed to realize desired synchronization via the established LMIs. Our proposed results show that the requirements of impulse intervals and impulse sizes are dropped, and delayed impulses and large scale impulses are allowed to coexist. Finally, some examples are given to show the effectiveness of the obtained results.

The influence of two kinds of time delays on the vibrational resonance of a fractional Mathieu–Duffing oscillator

Vibrational resonance is studied in a fractional Mathieu–Duffing oscillator with two types of time delays: fixed and distributed delays. The theoretical expression of the response amplitude is obtained by utilising the method of direct partition of slow and fast motions. Relative errors between the theoretical prediction and the numerical simulation are introduced to verify the validity of analytical approaches. The relative error of the displacement and the relative error of the response amplitude are calculated. Small relative errors show that the theoretical analysis is statistically correct. Therefore, the effects of fractional order, linear stiffness coefficient, low-frequency signal, time delay intensity and damping coefficient on the Mathieu–Duffing oscillator with distributed delay are studied successively. In order to better illustrate the impact of distributed time delay on the model, the case of fixed time delay is analysed and compared, and it can be found that the distributed delay has more significant influence than fixed delay on the system. In addition, the influence of distributed delay on the system is more significant than that of the fixed delay.

Semiactive Control of High‐Speed Railway Vehicle Suspension Systems with Magnetorheological Dampers

Using the magnetorheological (MR) damper model, this paper derives a semiactive suspension model for a high‐speed railway vehicle, and a new evaluating method is proposed to analyze the effect of two kinds of time delay existing in control systems on vehicle dynamic performance. The railway vehicle is modeled by a 50 degree‐of‐freedom (DOF) system which considers the full 6 DOF of each wheelset, bogie, car body, and the pitch angle of each axle box. Several control strategies, sky‐hook (SH), acceleration‐driven damping (ADD), and mixed SH‐ADD, are considered in the semiactive suspension system. To evaluate the effect of these semiactive controls and the different kinds of time delay on the lateral ride index of a high‐speed railway vehicle, a 3D surface in a rectangular coordinate system is described. The cross curve between the 3D surface and a horizontal plane which represents the performance of passive suspension is projected on the X‐Y plane, and the area enclosed by the contour line, X‐axis, and Y‐axis can be used to evaluate the performance of semiactive controls. The results show that the new method is convenient to evaluate the performance of semiactive control strategies visually when there is more than one kind of time delay.

Consensus conditions of continuous-time multi-agent systems with time-delays and measurement noises

This work is concerned with stochastic consensus conditions of multi-agent systems with both time-delays and measurement noises. For the case of additive noises, we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations. By the martingale convergence theorem, we obtain necessary conditions and sufficient conditions for stochastic strong consensus. For the case of multiplicative noises, we consider two kinds of time-delays, appeared in the measurement term and the noise term, respectively. We first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus. Then by constructing degenerate Lyapunov functional, we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time-delay in the measurement term.

Freely-Moving Delay Induces Periodic Oscillations in a Structured SEIR Model

In this paper, a disease transmission model of SEIR type with stage structure is proposed and studied. Two kinds of time delays are considered: the first one is the mature delay which divides the population into two stages; the second one is the time lag between birth and being able to move freely, which we call the freely-moving delay. Our mathematical analysis establishes that the global dynamics are determined by the basic reproduction number [Formula: see text]. If [Formula: see text], then the disease free equilibrium [Formula: see text] is globally asymptotically stable, and the disease will die out. If [Formula: see text], then a unique positive equilibrium [Formula: see text] exists, and [Formula: see text] is locally asymptotically stable when the freely-moving delay is less than the critical value. We show that increasing this delay can destabilize [Formula: see text] and lead to Hopf bifurcations and stable periodic solutions. By using the normal form theory and the center manifold theory, we derive the formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Finally, some numerical simulations are carried out to verify the theoretical analysis and some biological implications are discussed.

A delayed predator–prey system with impulsive diffusion between two patches

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete. However, in the real world, it is often the case that diffusion occurs at certain moment every year, impulsive diffusion can provide a more suitable manner to model the actual dispersal (or migration) behaviors for many ecological species. In addition, it is generally recognized that some kinds of time delays are inevitable in population interactions. In view of these facts, a delayed predator–prey system with impulsive diffusion between two patches is proposed. By using comparison theorem of impulsive differential equation and some analysis techniques, criteria on the global attractivity of predator-extinction periodic solution are established, sufficient conditions for the permanence of system are obtained. Finally, numerical simulations are presented to illustrate our theoretical results.

Dynamics and stability for a class of evolutionary games with time delays in strategies

This paper investigates the modeling and stability of a class of finite evolutionary games with time delays in strategies. First, the evolutionary dynamics of a sequence of strategy profiles, named as the profile trajectory, is proposed to describe the strategy updating process of the evolutionary games with time delays. Using the semi-tensor product of matrices, the profile trajectory dynamics with two kinds of time delays are converted into their algebraic forms respectively. Then a sufficient condition is obtained to assure the stability of the delayed evolutionary potential games at a pure Nash equilibrium.

Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate

In this paper, a delayed viral infection model with nonlinear immune response and general incidence rate is discussed. We prove the existence and uniqueness of the equilibria. We study the effect of three kinds of time delays on the dynamics of the model. By using the Lyapunov functional and LaSalle invariance principle, we obtain the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. It is shown that an increase of the viral-infection delay and the virus-production delay may stabilize the infection-free equilibrium, but the immune response delay can destabilize the equilibrium, leading to Hopf bifurcations. Numerical simulations are given to verify the analytical results. This can provide a possible interpretation for the viral oscillation observed in chronic hepatitis B virus (HBV) and human immunodeficiency virus (HIV) infected patients.

Stochastic Resonance in a Bacterium Growth System with Time Delay and Colored Noise

The phenomenon of stochastic resonance in a bacterium growth system that is with two different kinds of time delays and is driven by colored noises is investigated. Based on the extended unified colored noise theory and the method of the probability density approximation, the Fokker–Planck equation and the stationary probability density function are derived. Then via the theory of adiabatic limit, the analytical expression of the signal-to-noise ratio (SNR) is obtained. The different effects of the time delays existed in the nonlinear system and the noise correlation times on the stationary probability density and the signal-to-noise rate are discussed respectively. Finally, numerical simulations are offered and are consistent with approximate analytical results.

Analysis of a Car-Following Model with Driver Memory Effect

A nonlinear car-following model considering memory effect of human drivers is studied by means of theoretical analysis and numerical simulation. We model the memory effect of the response of drivers to the traffic situation for a car-following model by introducing a system variable related to velocity. The memory effect of the drivers is a kind of state-dependent delay. The stability of the car-following model with two kinds of time delay is studied. The hysteresis loop of traffic flow from different initial states is compared. The effect of the maximum time delay on the stability is discussed.

Stability and mean extinction time for a metapopulation system subjected to two kinds of time delays and associated multiplicative and additive noises

In this paper, the stability and the mean extinction time for a double time-delayed metapopulation system driven by associated multiplicative and additive noises are investigated. By using the Fokker–Planck equation, the fast descent method and the method of small time delay, we obtain the expressions of stationary probability distribution and the mean extinction time. The numerical results demonstrate that the multiplicative, additive noises and time delay θ can destroy the stability of the system. Whereas, the associated noise and time delay τ can consolidate the population system. Meanwhile, the resonant phenomenon of the mean first-passage time (MFPT) occurs in the metapopulation system due to the joint action of different types of noises and time delays. The increase of the strength of associated noise and time delay τ can effectively prolong the extinction time of the metapopulation. Inversely, the additive noise plays a negative role in restraining the collapse of the population. On the other hand, the appropriate multiplicative noise intensity can also extend the life of the metapopulation system. However, the varying of time delay θ cannot change the maximum of the mean extinction time, but it could produce different effects on the MFPT under the conditions of different parameters.

Delay-Dependent State Estimation of Static Neural Networks with Time-Varying and Distributed Delays

This paper focuses on studying the state estimation problem of static neural networks with time-varying and distributed delays. By constructing a suitable Lyapunov functional and employing two integral inequalities, a sufficient condition is obtained under which the estimation error system is globally asymptotically stable. It can be seen that this condition is dependent on the two kinds of time delays. To reduce the conservatism of the derived result, Wirtinger inequality is employed to handle a cross term in the time-derivative of Lyapunov functional. It is further shown that the design of the gain matrix of state estimator is transformed to finding a feasible solution of a linear matrix inequality, which is efficiently facilitated by available algorithms. A numerical example is explored to demonstrate the effectiveness of the developed result.

DELAYS INDUCE DIFFERENT SWITCH IN A STOCHASTIC SINGLE GENETIC REGULATION SYSTEM WITH A POSITIVE AUTOREGULATORY FEEDBACK LOOP

The steady properties of a stochastic single genetic regulation system with the different time delays, which appear in the deterministic and fluctuating forces, are investigated based on the small delay time approximation method. Using the approximation probability density approach, the delayed Fokker–Planck equation is obtained. The effects of two different time delays on the stationary probability distribution and the mean value are discussed. It is found that with the time delay τ1in the deterministic force increasing, the TF-A monomer concentration shifts from "off" state to "on" state. However, with the time delay τ2in the fluctuating force increasing, the TF-A monomer concentration shifts from "on" state to "off" state. In the switch process, two kinds of time delays play an opposite role. The theoretical predictions are found to be in good agreement with numerical results.

Synchronization of Boolean networks with time delays

This paper studies analytically synchronization of two deterministic Boolean networks with time delays, which are unidirectionally coupled in the drive-response configuration. Necessary and sufficient conditions of synchronization are established based on the algebraic representations of logical dynamics in terms of the semi-tensor product of matrices. The synchronization conditions show that, for drive-response Boolean networks, different relations between the inherent state delay and the unidirectional coupling delay may result in distinct synchronization phenomena, and both kinds of time delays that ensure synchronization, if existent, are not unique. Examples are worked out to illustrate the present results.