Involving Time Delays Research Articles

Oscillation Expression of NF- κ B Driven by Transcription and Translation Time Delays.

Oscillation expression of NF- [Formula: see text] signaling system can lead to nuclear NF- [Formula: see text] accumulation which involving various important cellular processes including immune response, inflammation and cancer development. Negative feedback circuits involved in NF- [Formula: see text] signaling system are generally believed to be responsible for the oscillation expression. In view of feedback loops involving time delays resulting from transcription, transcript splicing and processing, and protein synthesis, in this paper, a mathematical model with time delay to describe the core negative feedback circuits centered on NF- [Formula: see text] including [Formula: see text] and A20 -like proteins is developed. Here, the time delay refer to the time demand of transcription and translation process of [Formula: see text]. First, the results suggest that time delay can drive oscillation dynamics of NF- [Formula: see text] signaling system. Concretely, there exists a critical value of time delay. When the time delay exceeds the critical value, the system exhibits oscillation dynamics, and with the increase of time delay, the amplitude and period increase accordingly. Second, analysis indicate that A20 -like proteins are able to change the amplitude and period of the nuclear NF- [Formula: see text] oscillations. In addition, the effects of several important parameters on the nuclear NF- [Formula: see text] oscillations are also discussed. Finally, a prediction is formed, which is shortening time delay, repairing and maintaining the function of A20 -like proteins, and increasing [Formula: see text] transcription rate may be new clues to related disease treatment.

Ractional PI Stabilization of Delay Systems: Application to a Thermal System

In this paper, an application of fractional-order PIλ controller is given as an alternative to solve some control problems that can arise. It aims to apply the analytical tuning procedure to control the heat flow systems. This system, modeled by first-order system involving time delay, is one with open loop characteristic equations are fractional order quasi-polynomials. Using the proposed method, the entire stability region of PI λ controllers is obtained and visualized in the plane (Kp,Ki, λ ). The simulation was carried out on thermal systems and the results demonstrate the effectiveness of the proposed type of controllers and the tuning rule.

Finite-time stabilization of T–S fuzzy semi-Markov switching systems: A coupling memory sampled-data control approach

The present draft investigates the finite-time stabilization of T–S fuzzy semi-Markov switching systems by using a coupling memory sampled-data control approach. The main study concerned is how to effectively design the sampled-data control such that closed-loop T–S fuzzy semi-Markov switching systems is finite-time boundedness. By utilizing a Bernoulli distributed sequence, a more general coupling memory fuzzy sampled-data control strategy that involving time delay effect is derived. By virtue of fuzzy-basis-dependent membership functions, an asynchronous approach is proposed for T–S fuzzy semi-Markov switching system. Moreover, the inverted pendulum model is presented to demonstrate the feasibility and validity of the proposed strategies.

Thermoelastic interaction in the semi-infinite solid medium due to three-phase-lag effect involving memory-dependent derivative

The present study deals with the thermoelastic interaction in a semi-infinite elastic solid with a heat source in the context of three-phase-lag model with memory-dependent derivative. The governing coupled equations, involving time delay and kernel functions are expressed in the vector matrix differential equation form in the Laplace transform domain. The analytical formulations of the problem have been solved by eigenvalue technique. The Honig–Hirdes numerical method is used for the inversion of Laplace transformation. Numerical results are obtained by choosing various types of time delay parameters and kernel functions and graphical representations have been performed accordingly. An extrapolative capability is established by considering the memory-dependent derivative into a three-phase-lag model.

Spreading Speed in A Nonmonotone Equation with Dispersal and Delay

This paper is concerned with the estimation of spreading speed of a nonmonotone equation, which involves time delay and nonlocal dispersal. Due to the time delay, this equation does not generate monotone semiflows when the positive initial value is given. By constructing an auxiliary monotone equation, we obtain the spreading speed when the initial value admits nonempty compact support. Moreover, by passing to a limit function, we confirm the existence of traveling wave solutions if the wave speed equals to the spreading speed, which states the minimal wave speed of traveling wave solutions and improves the known results.

Stability and Oscillatory Behavior of the Solutions on a Class of Coupled Van der Pol-Duffing Equations with Delays

In the present paper, a class of coupled van der Pol-Duffing oscillators with a nonlinear friction of higher polynomial order model which involves time delays is investigated. The coefficients of the highest order of the polynomial determine the boundedness of the solutions. With special attention to the boundedness of the solutions and the instability of the unique equilibrium point of linearized system, some sufficient conditions to guarantee the existence of oscillatory solutions for the model are obtained based on the generalized Chafee's criterion. Convergence of the trivial solution is determined by the negative real part of eigenvalues of the linearized system. Examples are provided to demonstrate the reduced conservativeness for the parameters of the proposed results. The results obtained shown that the passive decay rate in the model affects the oscillatory frequency and amplitude. When a permanent oscillation occurred, time delays affect mainly oscillatory frequency and amplitude slightly.

Asymptotic behavior of gene expression with complete memory and two-time scales based on the chemical Langevin equations

Gene regulatory networks, which are complex high-dimensional stochastic dynamical systems, are often subject to evident intrinsic fluctuations. It is deemed reasonable to model the systems by the chemical Langevin equations. Since the mRNA dynamics are faster than the protein dynamics, we have a two-time scales system. In general, the process of protein degradation involves time delays. In this paper, we take the system memory into consideration in which we consider a model with a complete memory represented by an integral delay from \begin{document}$ 0 $\end{document} to \begin{document}$ t $\end{document} . Based on the averaging principle and perturbed test function method, this work examines the weak convergence of the slow-varying process. By treating the fast-varying process as a random noise, under appropriate conditions, it is shown that the slow-varying process converges weakly to the solution of a stochastic differential delay equation whose coefficients are the average of those of the original slow-varying process with respect to the invariant measure of the fast-varying process.

Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function

In this paper, a stochastic delay differential equations chemostat model with nonmonotone uptake function is considered, and the nutrient conversion process involves time delay. First, we verify that there is a unique global positive solution of the stochastic system. Second, we find that the solutions of stochastic system will oscillate around the equilibria of the corresponding deterministic model, moreover, results show that time delay has critical effects on the extinction and persistence of the microorganism, that is to say, under small noise, when the time delay is small, microorganism is persistent; when the time delay is large, microorganism will be extinct. In addition, we can find by the computer simulation that large noise may lead to microorganism become extinct, although microorganism is persistent in the deterministic systems when the time delay is small. Finally, computer simulations are carried out to illustrate the obtained results and the existence of bistability is observed.

The influence of time delay on epidemic spreading under limited resources

While epidemic spreading naturally involves time delay due to the order of propagation, its control depends on the resource amount to be devoted. However, it is unclear how time delay impacts epidemic spreading under limited resources. Here we analyze a simple model of epidemic spreading on a two-layer network, which considers both the time delay between the layers and the resource amount. Interestingly, we find that the delay can induce first-order, continuous and hybrid phases as well as transitions among them, depending on the resource amount, the connection strength between layers and their internal structures. In addition, we find that there is a critical threshold of time delay such that even a small resource amount can effectively control the epidemic spreading if the delay is beyond this threshold, and a large resource amount is needed otherwise. These findings would provide useful guidelines for government decisions on the control of epidemic spreading.

On a multivariate renewal-reward process involving time delays and discounting: applications to IBNR processes and infinite server queues

This paper considers a particular renewal-reward process with multivariate discounted rewards (inputs) where the arrival epochs are adjusted by adding some random delays. Then this accumulated reward can be regarded as multivariate discounted Incurred But Not Reported (IBNR) claims in actuarial science and some important quantities studied in queueing theory such as the number of customers in G/G/infinity queues with correlated batch arrivals. We study the long term behavior of this process as well as its moments. Asymptotic expressions and bounds for the quantities of our interest, and also convergence result for the distribution of this process after renormalization, are studied, when interarrival times and time delays are light tailed. Next, assuming exponentially distributed delays, we derive some explicit and numerically feasible expressions for the limiting joint moments. In such case, for an innite server queues with renewal arrival process, we obtain limiting results on the expectation of the workload, and the covariance of queue size and workload. Finally, some queueing theoretic applications are provided MSC classification: 60G50, 60K30, 62P05, 60K25

Asynchronous filtering for 2-D switched systems with missing measurements

This work is concerned with $$\mathscr {H}_{\infty }$$ filter design with missing measurements for a class of two-dimensional (2-D) switched systems represented by Fornasini–Marchesini local state-space model. The switching signal of the switched filters involve time delays, which result in the asynchronism between the filter and the system switching. The issues of asymptotic mean-square stability and $$\ell _{2}$$ -gain analysis for the 2-D switched systems are addressed firstly, based on which mode-dependent filters are designed with mode-dependent average dwell time scheme. Finally, two examples are given to demonstrate the validity of the proposed technique.

Practical output tracking for a class of uncertain nonlinear time-delay systems via state feedback

In this paper, the problem of global practical output tracking is investigated by state feedback for a class of uncertain nonlinear time-delay systems. Under mild conditions on the system nonlinearities involving time delay, we construct a homogeneous state feedback controller with an adjustable scaling gain. By a homogeneous Lyapunov-Krasovskii functional, the scaling gain is adjusted to dominate the time-delay nonlinearities bounded by homogeneous growth conditions and render the tracking error can be made arbitrarily small while all the states of the closed-loop system remain to be bounded.

Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels

This paper considers an optimal production scheduling problem in a single-supplier-multi-manufacturer supply chain involving production and delivery time-delays, where the time-delays for the supplier and the manufacturers can have different values. The objective of both levels is to find an optimal production schedule so that their production rates and their inventory levels are close to the ideal values as much as possible in the whole planning horizon. Each manufacturer's problem, which involves one time-delayed argument, can be solved analytically by using the necessary condition of optimality. To tackle the supplier's problem involving $n+1$ different time-delayed arguments (where $n$ is the number of manufacturers) by the above approach, we need to introduce a model transformation technique which converts the original system of combined algebraic/differential equations with $n+1$ time-delayed arguments into a sum of $n$ sub-systems, each of which consists of only two time-delayed arguments. Thus, the supplier's problem can also be solved analytically. Numerical examples consisting of a single supplier and four manufacturers are solved to provide insight of the optimal strategies of both levels.

Asynchronous control for 2-D switched systems with mode-dependent average dwell time

This work is concerned with asynchronous control for a class of two-dimensional switched systems with mode-dependent average dwell time. The systems are formulated by the famous Fornasini–Marchesini local state-space model, and the switching signal of the switched controller involves time delays which lead to the asynchronism between controllers and subsystems. By extending mode-dependent average dwell time with the switched quadratic Lyapunov functional approach, the stabilization condition is established for 2-D asynchronously switched systems. Based on the stabilization result, mode-dependent state-feedback controllers are designed to guarantee H∞ performance and asymptotic stability of the corresponding closed-loop system. Finally, two examples are provided to illustrate the effectiveness of the proposed design scheme.

Bifurcation Analysis of a Modified Tumor-immune System Interaction Model Involving Time Delay

We study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a reaction-diffusion system including time delay under the Neumann boundary conditions, and is based on Kuznetsov-Taylor's model. Choosing the delay parameter as a bifurcation parameter, we first show that Hopf bifurcation occurs. Second, we determine two properties of the periodic solution, namely its direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations. Furthermore, we discuss the effects of diffusion on the dynamics by analyzing a model with constant coefficients and perform some numerical simulations to support the analytical results. The results show that diffusion has an important effects on the dynamics of a mathematical model.

Effects of dynamic synapses, neuronal coupling, and time delay on firing of neuron

Neuronal firing plays a key role in the neuronal information transmission, and different neuronal firing patterns are reported, such as spiking, bursting. A number of neuron models are introduced to reproduce the firing patterns of single neuron or neuronal network. The key factors determining the firing pattern gain more and more attention in the study of neuron system, such as noise, network topology. Noise is able to induce sub-or super-threshold coherent neuronal firing easily, and a number of coherence resonances are reported in the noise induced firing. The network topology determines the synchronization of the firing patterns of the neuronal network, and the change of network topology may induce fruitful synchronization transitions. It is well known that synapses exhibit a high variability with a diverse origin during information transmission, such as the stochastic release of neurotransmitters, variations in chemical concentration through synapses, and spatial heterogeneity of synaptic response over dendrite tree. The collective effect of all of these factors might result in the notion of dynamic synapses. In reality, the neuronal network often involves time delay due to the ?nite signal propagation time in biological networks. Recently, neuronal networks with time delay have received considerable attention. Delay-sustained neuronal firing patterns may be relevant to neuronal networks for establishing a concept of collective information processing in the presence of delayed information transmission. According to the above-mentioned motivations, the firing dynamics of the single postsynapic neuron is investigated based on a simple postsynaptic neuron model by using numerical simulation and Fourier transform analysis. In this model, the postsynapic neuron receives dynamic synaptic currents from a population of presynaptic neurons. It is found that the firing rate resonance between the pre-and postsynaptic neuron determines the firing of the postsynaptic neuron. Stimulus currents in specific frequency range are easy to stimulate postsynaptic neuron firing. The random currents released from dynamic synapses determine the postsynaptic firing rate. Then the single postsynaptic neuron is extended to a neuronal network, in which 100 neurons connect to its 4 nearest neighbors regularly and receive delayed synaptic currents from connected neurons. All the neurons in the network receive the same dynamic synaptic currents from the presynaptic neurons. The results show that the synaptic coupling in the network is able to promote the neuron firing in the network, and time delay in the synaptic coupling could reinforce the promotion, but the mode of the promotion is not changed.

LEAP: constructing gene co-expression networks for single-cell RNA-sequencing data using pseudotime ordering.

To construct gene co-expression networks based on single-cell RNA-Sequencing data, we present an algorithm called LEAP, which utilizes the estimated pseudotime of the cells to find gene co-expression that involves time delay. R package LEAP available on CRAN. jun.li@nd.edu. Supplementary data are available at Bioinformatics online.

Global cluster synchronization in nonlinearly coupled community networks with heterogeneous coupling delays

This investigation establishes the global cluster synchronization of complex networks with a community structure based on an iterative approach. The units comprising the network are described by differential equations, and can be non-autonomous and involve time delays. In addition, units in the different communities can be governed by different equations. The coupling configuration of the network is rather general. The coupling terms can be non-diffusive, nonlinear, asymmetric, and with heterogeneous coupling delays. Based on this approach, both delay-dependent and delay-independent criteria for global cluster synchronization are derived. We implement the present approach for a nonlinearly coupled neural network with heterogeneous coupling delays. Two numerical examples are given to show that neural networks can behave in a variety of new collective ways under the synchronization criteria. These examples also demonstrate that neural networks remain synchronized in spite of coupling delays between neurons across different communities; however, they may lose synchrony if the coupling delays between the neurons within the same community are too large, such that the synchronization criteria are violated.

Heterogeneous delay-induced asynchrony and resonance in a small-world neuronal network system

A neuronal network often involves time delay caused by the finite signal propagation time in a given biological network. This time delay is not a homogenous fluctuation in a biological system. The heterogeneous delay-induced asynchrony and resonance in a noisy small-world neuronal network system are numerically studied in this work by calculating synchronization measure and spike interval distribution. We focus on three different delay conditions: double-values delay, triple-values delay, and Gaussian-distributed delay. Our results show the following: 1) the heterogeneity in delay results in asynchronous firing in the neuronal network, and 2) maximum synchronization could be achieved through resonance given that the delay values are integer or half-integer times of each other.

Delay-dependent decentralized control for nonlinear similar interconnected large-scale systems

In this paper, the problem of delay-dependent decentralized control for a class of nonlinear large-scale interconnected systems with similar structure is investigated, where the linear state vectors, the nonlinear state vectors and the nonlinear interconnections involve time delays. The new similar structure is presented via memory feedback. Based on which, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, a decentralized memory derivative feedback control strategy is proposed to stabilize the resulting interconnected systems uniformly asymptotically, in addition, the stability domain is estimated. Finally, simulation results show the effectiveness of the proposed approach.