Controlling the nonlinear chemical signal in a coupled system by delay

The effect of delay on nonlinear chemical signal in a coupled limit cycle system is investigated. Simulation results reveal that the inherent oscillatory signal can be significantly controlled by the delay in the coupled inter-system communication. Besides, under the influence of noise, the signal-to-noise ratio and signal frequency can also be prominently adjusted by the delay.     

Finite-dimensional representation of delay systems

It is shown that given a state delayed system, one can construct a finite-dimensional system whose partial state replicates the response of the delay system up to a small solution of the homogeneous delay system. Thus, in the absence of small solutions, the response of the delay system can be exactly replicated by a finite-dimensional system. reserved.     

Optimal autaptic and synaptic delays enhanced synchronization transitions induced by each other in Newman–Watts neuronal networks

In this paper, we numerically study the effect of electrical autaptic and synaptic delays on synchronization transitions induced by each other in Newman–Watts Hodgkin–Huxley neuronal networks. It is found that the synchronization transitions induced by synaptic delay vary with varying autaptic delay and become strongest when autaptic delay is optimal. Similarly, the synchronization transitions induced by autaptic delay vary with varying synaptic delay and become strongest at optimal synaptic delay. Also, there is optimal coupling strength by which the synchronization transitions induced by either synaptic or autaptic delay become strongest. These results show that electrical autaptic and synaptic delays can enhance synchronization transitions induced by each other in the neuronal networks. This implies that electrical autaptic and synaptic delays can cooperate with each other and more efficiently regulate the synchrony state of the neuronal networks. These findings could find potential implications for the information transmission in neural systems.     

Stability and bifurcation in a harvested one-predator–two-prey model with delays

It is known that one-predator–two-prey system with constant rate harvesting can exhibit very rich dynamics. If such a system contains time delayed component, it can have more interesting behavior. In this paper we study the effects of the time delay on the dynamics of the harvested one-predator–two-prey model. It is shown that time delay can cause a stable equilibrium to become unstable. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are finally performed for justifying the theoretical results.     

Dissipativity of the delay semigroup

Under mild conditions a delay semigroup can be transformed into a (generalized) contraction semigroup by modifying the inner product on the (Hilbert) state space into an equivalent inner product. Applications to stability of differential equations with delay and stochastic differential equations with delay are given as examples.     

Delay-induced synchronization transitions in small-world neuronal networks with hybrid synapses

We study delay-induced synchronization transitions in small-world networks of bursting neurons with hybrid excitatory-inhibitory synapses. Numerical results show that transitions of the spatiotemporal synchrony of neurons can be induced not only by the variations of the information transmission delay but also by changing the probability of inhibitory synapses and the rewiring probability. The delay can either promote or destroy synchronization of neuronal activity in the hybrid small-world neuronal network. In particular, regions of synchronization and nonsynchronization appear intermittently as the delay increases. In addition, for smaller and higher probability of inhibitory synapses, the intermittent synchronization transition is relative profound, while for the moderate probability of inhibitory synapses, synchronization transition seems less profound. More importantly, it is found that a suitable rewired network topology can always enhance the synchronized neuronal activity if only the delay is appropriate.     

Delay-induced diversity of firing behavior and ordered chaotic firing in adaptive neuronal networks

In this paper, we study the effect of time delay on the firing behavior and temporal coherence and synchronization in Newman–Watts thermosensitive neuron networks with adaptive coupling. At beginning, the firing exhibit disordered spiking in absence of time delay. As time delay is increased, the neurons exhibit diversity of firing behaviors including bursting with multiple spikes in a burst, spiking, bursting with four, three and two spikes, firing death, and bursting with increasing amplitude. The spiking is the most ordered, exhibiting coherence resonance (CR)-like behavior, and the firing synchronization becomes enhanced with the increase of time delay. As growth rate of coupling strength or network randomness increases, CR-like behavior shifts to smaller time delay and the synchronization of firing increases. These results show that time delay can induce diversity of firing behaviors in adaptive neuronal networks, and can order the chaotic firing by enhancing and optimizing the temporal coherence and enhancing the synchronization of firing. However, the phenomenon of firing death shows that time delay may inhibit the firing of adaptive neuronal networks. These findings provide new insight into the role of time delay in the firing activity of adaptive neuronal networks, and can help to better understand the complex firing phenomena in neural networks.     

MEAN-SQUARE STABILITY OF NONLINEAR SYSTEMS WITH TIME-VARYING,RANDOM DELAY

A class of nonlinear systems with a time-varying delay is considered.The delay is modeled by a continuous-time Markov process with a finite number of states. Systems of this type may arise in real-time control applications. Employing a “delay-averaging” approach we demonstrate how certain mean-square stochastic stability conditions can be derived in terms of transition functions of the Markov process and stability properties of a system with a constant delay.     

Stability and bifurcation analysis of a nutrient-phytoplankton model with time delay

We proposed a nutrient-phytoplankton interaction model with a discrete and distributed time delay to provide a better understanding of phytoplankton growth dynamics and nutrient-phytoplankton oscillations induced by delay. Standard linear analysis indicated that delay can induce instability of a positive equilibrium via Hopf bifurcation. We derived the conditions guaranteeing the existence of Hopf bifurcation and tracked its direction and the stability of the bifurcating periodic solutions. We also obtained the sufficient conditions for the global asymptotic stability of the unique positive steady state. Numerical analysis in the fully nonlinear regime showed that the stability of the positive equilibrium is sensitive to changes in delay values under select conditions. Numerical results were consistent with results predicted by linear analysis.     

Stability analysis of nonlinear dynamic systems with slowly and periodically varying delay

On the basis of the geometric singular perturbation theory and the theory of delayed Hopf bifurcation in slow–fast systems with delay, the stability of nonlinear systems with slowly and periodically varying delay is investigated in this paper. Sufficient conditions ensuring asymptotic stability of those systems are obtained. Especially, though a time-varying delay usually increases complexity in the analysis of system dynamics and it usually deteriorates system stability as well, the study indicates that under certain conditions, the stability of the systems with a time-invariant delay only can be improved by incorporating a slowly and periodically varying part into the constant delay. Two illustrative examples are given to validate the analytical results.     

Delay induced Hopf bifurcation in a dual model of Internet congestion control algorithm

This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing communication delay as the bifurcation parameter, we demonstrate that the system loses its stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Moreover, the bifurcating periodic solution of the system is calculated by means of the perturbation method. Discussion of stability of the periodic solutions involves the computation of Floquet exponents by considering the corresponding Poincaré–Lindstedt series expansion. Finally, numerical simulations for verifying the theoretical analysis are provided.     

Analysis and design of a playout buffer for VBR streaming video

A critical component in the delivery of VBR streaming video over packet-based networks, is the playout buffer at the receiver side. As packets will incur a variable delay within the network, a mechanism is needed to dejitter the stream and assure that packets are played out at exactly the same rate at which they were generated by the sender. Packet loss at the playout buffer can be induced by either underflow or overflow, and we first identify the general conditions under which these events occur. These general rules require some knowledge on the network delay characteristics of an arbitrary packet, and are then further developed and refined, by taking a closer look at the case where a single delay bottleneck exists within the network. This analysis allows us to derive useful design rules, where we consider two cases, depending on whether or not the receiver has knowledge about the delay the first packet of the stream has incurred. We conclude by demonstrating that the traditional playout paradigm can be enhanced to guard against large initial delays.     

Stability and Hopf bifurcation in a delayed competition system

In this paper, Hopf bifurcation for two-species Lotka–Volterra competition systems with delay dependence is investigated. By choosing the delay as a bifurcation parameter, we prove that the system is stable over a range of the delay and beyond that it is unstable in the limit cycle form, i.e., there are periodic solutions bifurcating out from the positive equilibrium. Our results show that a stable competition system can be destabilized by the introduction of a maturation delay parameter. Further, an explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the theory of normal forms and center manifolds, and numerical simulations supporting the theoretical analysis are also given.     

Effects of time delay and coupling strength on synchronization transitions in excitable homogeneous random network

In this paper we numerically investigate the effects of time delay and coupling strength on synchronization transitions in excitable homogeneous random network. Different roles of time delay and coupling strength have been discovered by synchronization parameter and space–time plots. Specifically, we have found three distinct parameter regions, i.e., asynchronous region (domain I for small time delay), transition region (domain II for moderate time delay) and synchronous region (domain III for large time delay) as time delay is increased. The phenomenon of multi-stability is observed in the transition region. While coupling strength can enhance synchronization in the transition region and can reduce synchronization time in the synchronous region. All these results are independence on the system size.     

货架和仓库商品共同影响需求的供应链延期支付协调

针对单一制造商和单一零售商组成的供应链,研究了需求受货架和仓库库存水平共同影响的企业间延期支付协调问题.首先根据制造商主导的Stackelberg对策结构,对供应链成员间的决策问题进行了分析;然后为制造商提出了一个改善整个供应链运作效率的延期支付策略,研究结果表明该延期支付模型不仅能提高制造商的利润,而且能提高零售商的利润.最后给出了数值例子,并对模型参数灵敏度进行了分析.     

A delay model for viral infection in toxin producing phytoplankton and zooplankton system

An eco-epidemiological delay model is proposed and analysed for virally infected, toxin producing phytoplankton (TPP) and zooplankton system. It is shown that time delay can destabilize the otherwise stable non-zero equilibrium state. The coexistence of all species is possible through periodic solutions due to Hopf bifurcation. In the absence of infection the delay model may have a complex dynamical behavior which can be controlled by infection. Numerical simulation suggests that the proposed model displays a wide range of dynamical behaviors. Different parameters are identified that are responsible for chaos.     

Influence of discrete delay on pattern formation in a ratio-dependent prey–predator model

In this paper we explore how the two mechanisms, Turing instability and Hopf bifurcation, interact to determine the formation of spatial patterns in a ratio-dependent prey–predator model with discrete time delay. We conduct both rigorous analysis and extensive numerical simulations. Results show that four types of patterns, cold spot, labyrinthine, chaotic as well as mixture of spots and labyrinthine can be observed with and without time delay. However, in the absence of time delay, the two aforementioned mechanisms have a significant impact on the emergence of spatial patterns, whereas only Hopf bifurcation threshold is derived by considering the discrete time delay as the bifurcation parameter. Moreover, time delay promotes the emergence of spatial patterns via spatio-temporal Hopf bifurcation compared to the non-delayed counterpart, implying the destabilizing role of time delay. In addition, the destabilizing role is prominent when the magnitude of time delay and the ratio of diffusivity are comparatively large.     

Calculation of delay characteristics for multiserver queues with constant service times

We consider a discrete-time infinite-capacity queueing system with a general uncorrelated arrival process, constant-length service times of multiple slots, multiple servers and a first-come-first-served queueing discipline. Under the assumption that the queueing system can reach a steady state, we first establish a relationship between the steady-state probability distributions of the system content and the customer delay. Next, by means of this relationship, an explicit expression for the probability generating function of the customer delay is obtained from the known generating function of the system content, derived in previous work. In addition, several characteristics of the customer delay, namely the mean value, the variance and the tail distribution of the delay, are derived through some mathematical manipulations. The analysis is illustrated by means of some numerical examples.     

Equivalence between the Lyapunov–Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems

The stability of discrete-time systems with time varying delay in the state can be analyzed by using a discrete-time extension of the classical Lyapunov–Krasovskii approach. In the networked control systems domain a similar delay stability problem is treated using a switched system transformation approach. The paper aims to establish a relation between the switched system transformation approach and the classical Lyapunov–Krasovskii method. It is shown that using the switched systems transformation is equivalent to using a general delay dependent Lyapunov–Krasovskii functionals. This functional represents the most general form that can be obtained using sums of quadratic terms. Necessary and sufficient LMI conditions for the existence of such functionals are presented.     

Delay analysis of a two-class batch-service queue with class-dependent variable server capacity

In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer.