Global exponential stability of almost periodic solution for a large class of delayed dynamical systems

Research on delayed neural networks with variable self-inhibitions, interconnection weights, and inputs is an important issue. In this paper, we discuss a large class of delayed dynamical systems with almost periodic self-inhibitions, inter-connection weights, and inputs. This model is universal and includes delayed systems with timevarying delays, distributed delays as well as combination of both. We prove that under some mild conditions, the system has a unique almost periodic solution, which is globally exponentially stable. We propose a new approach, which is independent of existing theory concerning with existence of almost periodic solution for dynamical systems.

Time-delay feedback control in a delayed dynamical chaos system and its applications

The feedback control of a delayed dynamical system, which also includes various chaotic systems with time delays, is investigated. On the basis of stability analysis of a nonautonomous system with delays, some simple yet less conservative criteria are obtained for feedback control in a delayed dynamical system. Finally, the theoretical result is applied to a typical class of chaotic Lorenz system and Chua circuit with delays. Numerical simulations are also given to verify the theoretical results.

EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY

Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.

Editorial: Dynamics on delayed systems

In the representation of natural and social phenom- ena, there exist not only ordinary or partial differential equations which are independent of the past states and determined solely by the present states~ but also time delay differential equations which are related to some of the past states. Time delay is ubiquitous in mechanical, physical, ecological, physiological, biological, economic, electronic, and chemical systems due to finite propaga- tion speeds of signals, finite reaction times, and finite processing times. These realistic backgrounds drive var- ious investigations to consider effects of time delays on realistic phenomena which are modeled by delay differ- ential equations. It is impossible to make achievements only by extending theory of ordinary or partial differen- tial equations since time delay is of uncertainty in time scale. Therefore, the study will be very difficult for a problem in the infinite-dimensional space.

THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS

In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.

A Spatial-Temporal Network Perspective for the Propagation Dynamics of Air Traffic Delays

Intractable delays occur in air traffic due to the imbalance between ever-increasing air traffic demand and limited airspace capacity.As air traffic is associated with complex air transport systems,delays can be magnified and propagated throughout these systems,resulting in the emergent behavior known as delay propagation.An understanding of delay propagation dynamics is pertinent to modern air traffic management.In this work,we present a complex network perspective of delay propagation dynamics.Specifically,we model air traffic scenarios using spatial–temporal networks with airports as the nodes.To establish the dynamic edges between the nodes,we develop a delay propagation method and apply it to a given set of air traffic schedules.Based on the constructed spatial-temporal networks,we suggest three metrics-magnitude,severity,and speed-to gauge delay propagation dynamics.To validate the effectiveness of the proposed method,we carry out case studies on domestic flights in the Southeastern Asia region(SAR)and the United States.Experiments demonstrate that the propagation magnitude in terms of the number of flights affected by delay propagation and the amount of propagated delays for the US traffic are respectively five and ten times those of the SAR.Experiments further reveal that the propagation speed for US traffic is eight times faster than that of the SAR.The delay propagation dynamics reveal that about six hub airports in the SAR have significant propagated delays,while the situation in the United States is considerably worse,with a corresponding number of around 16.This work provides a potent tool for tracing the evolution of air traffic delays.

Oscillation of Third-order Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.

SOME OSCILLATION CRITERIA FOR A CLASS OF HIGHER ORDER NONLINEAR DYNAMIC EQUATIONS WITH A DELAY ARGUMENT ON TIME SCALES

In this paper,we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form[rnφ(⋯r2(r1x^(Δ))^(Δ)⋯)^(Δ)]^(Δ)(t)+h(t)f(x(τ(t)))=0 on an arbitrary time scale T with supT=∞,where n≥2,φ(u)=|u|^(γ)sgn(u)forγ>0,ri(1≤i≤n)are positive rd-continuous functions and h∈C_(rd)(T,(0,∞)).The functionτ∈C_(rd)(T,T)satisfiesτ(t)≤t and lim_(t→∞)τ(t)=∞and f∈C(R,R).By using a generalized Riccati transformation,we give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.The obtained results are new for the corresponding higher order differential equations and difference equations.In the end,some applications and examples are provided to illustrate the importance of the main results.

Towards SDN Based Queuing Delay Estimation

As one of Qo S(Quality of Service) metrics, delay is critical important to delay sensitive applications, such as interactive video, network game and online surgery. In this paper, we exploit SDN(Software Defined Networking) advantages to solve delay Qo S problem. Our work mainly focuses on SDN based queuing delay estimation with real traffic and end-to-end delay control. First, we propose a queuing estimation model and extended it for end-to-end delay of the whole path. It is proved to be feasible and accurate with experimental results in SDN environment. Second, in order to demonstrate the use of our proposed model, we also implement an end-to-end delay control application in SDN. It fulfills specific delay Qo S requirements by dynamically switching flows to a suitable queue based on estimation results and delay requirements.

Dynamics of the HBV model with diffusion and time delay

Chronic hepatitis B infection is a major health problem,with approximately 350 million virus carriers worldwide.In Africa,about 30%-60% of children and 60%-100% of adults have

Principle and key technology of generalized high precision simulation of TT&C channel

A generalized simulation method of the tracking,telemetry and control（TT＆C） channel,which is applicable to wideband and arbitrary radio frequency（RF） signal,is proposed.It can accurately simulate the dynamic transmission delay of the arbitrary RF signal in channels,especially regardless of any prior knowledge including signal form,signal parameters,and so on.The proposed method orthogonally demodulates the wideband and arbitrary RF signal to complex baseband by a known local oscillator（LO） signal.Whereafter,it takes measures to obtain the delay reconstruction signal of baseband signals based on the dynamic transmission delay between a ground station and a responder.Meanwhile,it manages to obtain the delay reconstruction signal of LO signals.The simulation output signal（the delayed RF signal） can be achieved through the synthesis of the two delay reconstruction signals mentioned above.The principle and its related key technology are described in detail,and the realizable system architecture is given.

Dynamic data packing towards the optimization of QoC and QoS in networked control systems

A class of networked control systems is investigated whose communication network is shared with other applications. The design objective for such a system setting is not only the optimization of the control performance but also the efficient utilization of the communication resources. We observe that at a large time scale the data packet delay in the communication network is roughly varying piecewise constant, which is typically true for data networks like the Internet. Based on this observation, a dynamic data packing scheme is proposed within the recently developed packet-based control framework for networked control systems. As expected this proposed approach achieves a fine balance between the control performance and the communication utilization: the similar control performance can be obtained at dramatically reduced cost of the communication resources. Simulations illustrate the effectiveness of the proposed approach.

Oscillation of fourth-order delay dynamic equations

This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale.In the general time scales case,four oscillation theorems are presented that can be used in cases where known results fail to apply.The results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time scale.These criteria improve a number of related contributions to the subject.Some illustrative examples are provided.

Oscillation Theorems for Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales

By employing the generalized Riccati transformation technique,we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation [r(t)[y(t)+p(t)y(■(t))]~Δ]~Δ+q(t)f(y((δ(t)))=0 on a time scale■.The results improve some oscillation results for neutral delay dynamic equations and in the special case when■our results cover and improve the oscillation results for second- order neutral delay differential equations established by Li and Liu[Canad.J.Math.,48(1996), 871 886].When■,our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh[Comp.Math.Appl.,36(1998),123-132].When ■ ■our results are essentially new.Some examples illustrating our main results are given.

Oscillation Criteria of Second Order Half Linear Delay Dynamic Equations on Time Scales

In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation （r（t）g（x△（t）））△＋p（t）f（x（τ（t）））=0 on a time scale T. Oscillation behavior of this equation is not studied before. Our results not only apply on differential equations when T=R, difference equations when T=N but can be applied on different types of time scales such as when T=N for q〉1 and also improve most previous results. Finally, we give some examples to illustrate our main results.

OSCILLATION CRITERIA FOR SECOND-ORDER NEUTRAL DELAY DYNAMIC EQUATIONS ON TIME SCALES

In this paper, we consider a class of second-order neutral delay dynamic equations on a time scale T. By means of Riccati transformation technique, we establish some new oscillation criteria in two different conditions. The obtained results enrich the well-known oscillation results for some dynamic equations.