Effect of the optimal velocity function on traffic phase transitions in lattice hydrodynamic models

The original lattice hydrodynamics models of traffic flow are extended to take into account the complex acceleration behavior of drivers. A new optimal velocity function which considers the stepwise acceleration effect and fits the observed data better is introduced. The stability conditions of these two models are obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the traffic phase transitions. In a certain vehicle’s density and driver’s sensitivity region, tri-stable states will occur. In addition, the properties of the multiple phases also depend on the asymmetry of the optimal velocity function and the stage number of multi-phase transitions is closely related to the turning points of the optimal velocity function. The validity and correctness of the analytical results is confirmed by numerical simulations.     

Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters

Most modeling efforts involve multiple physical or biological processes. All physical or biological processes take time to complete. Therefore, multiple time delays occur naturally and shall be considered in more advanced modeling efforts. Carefully formulated models of such natural processes often involve multiple delays and delay dependent parameters. However, a general and practical theory for the stability analysis of models with more than one discrete delay and delay dependent parameters is nonexistent. The main purpose of this paper is to present a practical geometric method to study the stability switching properties of a general transcendental equation which may result from a stability analysis of a model with two discrete time delays and delay dependent parameters that dependent only on one of the time delay. In addition to simple and illustrative examples, we present a detailed application of our method to the study of a two discrete delay SIR model.     

Resonance and chaos of micro and nano electro mechanical resonators with time delay feedback

The resonance and chaos of micro (nano) electro mechanical resonators with time delay feedback is concerned in the paper. Based on the experimental results, a lumped single degree-of-freedom (1DOF) model is studied and the effects of time delay displacement and velocity feedback on the system are investigated. In order to have a deep insight into the system, the amplitude frequency response curve of the system is firstly obtained using the multiple scales method. The Melnikov function method is then extended to the two time delay systems, and the analytically required condition for chaos was obtained. Finally, the fourth-order Runge–Kutta method, point-mapping method and spectrum diagram are used to simulate the evolution of the dynamic behavior of the time delay control system. Also, the stability of this time delay control system is studied thoroughly. The results show that time delay feedback is a good method for the control system and that reasonable selection of control system parameters can effectively suppress the vibration level for micro/nano-electro-mechanical resonator systems.     

Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays

Time delays are often sources of complex behavior in dynamic systems. Yet its complexity needs to be further explored, particularly when multiple time delays are present. As a purpose to gain insight into such complexity under multiple time delays, we investigate the mechanism for the action of multiple time delays on a particular non-autonomous system in this paper. The original mathematical model under consideration is a Duffing oscillator with harmonic excitation. A delayed system is obtained by adding delayed feedbacks to the original system. Two time delays are involved in such system, one of which in the displacement feedback and the other in the velocity feedback. The time delays are taken as adjustable parameters to study their effects on the dynamics of the system. Firstly, the stability of the trivial equilibrium of the linearized system is discussed and the condition under which the equilibrium loses its stability is obtained. This leads to a critical stability boundary where Hopf bifurcation or double Hopf bifurcation may occur. Then, the chaotic behavior of such system is investigated in detail. Particular emphasis is laid on the effect of delay difference between two time delays on the chaotic properties. A Melnikov’s analysis is employed to obtain the necessary condition for onset of chaos resulting from homoclinic bifurcation. And numerical analyses via the bifurcation diagram and the top Lyapunov exponent are carried out to show the actual time delay effect. Both the results obtained by the two analyses show that the delay difference between two time delays plays a very important role in inducing or suppressing chaos, so that it can be taken as a simple but efficient “switch” to control the motion of a system: either from order to chaos or from chaos to order.     

Stabilization of traffic flow in optimal velocity model via delayed-feedback control

Traffic jams may occur due to various reasons, such as traffic accidents, lane reductions and on-ramps. In order to suppress the traffic congestion in an optimal velocity traffic model without any driver’s delay taken into account, a delayed-feedback control of both displacement and velocity differences is proposed in this study. By using the delay-independent stability criteria and the H_∞-norm, the delayed-feedback control can be determined to stabilize the unstable traffic flow and suppress the traffic jam. The numerical case studies are given to demonstrate and verify the new control method. Furthermore, a comparison is made between the new control method and the method proposed by Konishi et al. [K. Konishi, M. Hirai, H. Kokame, Decentralized delayed-feedback control of an optimal velocity traffic model, Eur. Phys. J. B 15 (2000) 715–722]. The results show that the new control method makes the traffic flow more stable and improves the control performance.     

考虑等待提示策略的呼叫中心流体近似方法

向顾客公布需等待的排队时间用以缓解系统拥挤是目前呼叫中心运营管理的重要手段之一。为了有效刻画等待提示策略下顾客行为变化对呼叫系统性能的影响,采用流体近似方法建立了呼叫排队系统模型。首先,通过排队分析构造等待提示影响下排队行为框架,包含带有心理行为变化特征的多种行为要素概率函数;其次,利用流体方法构建了考虑顾客重拨影响的连续排队模型,并求解了稳态条件下的系统性能指标;最后,通过与仿真模型的对比,验证了该流体近似方法的有效性与精确性。研究结果对于带有等待时间提示的呼叫中心运营具有重要指导作用。     

Application of nonlocal continuum theory to the primary resonance analysis of an axially loaded nano beam under time delay control

The paper is concerned with the nonlinear primary resonance of nano beams with axial load under the velocity time delay control. In order to have a deep insight into the system, the amplitude frequency response curve of the system is firstly obtained using the multiple scales method. The effects of the control gains and time delays on the system stability are then investigated. The analyses illustrated that both delay feedback gain coefficient and velocity time delay control can mitigate the system vibrations properties (e.g. hardening nonlinearity, resonance amplitude and the corresponding width) to an excellent level. The nonlinear primary resonance of nano beam is also discussed with the influences of small scale effect, axial initial load, wave number, Winkler foundation modulus and the ratio of the length to the diameter. This paper establishes the relationship between the time delay controller and vibration properties of a nano beam system which provides the guidance for applying time delayed active control for different types of nano devices in engineering practices.     

Robust stability analysis of uncertain systems with two additive time-varying delay components

This paper is concerned with stability analysis for uncertain systems. The systems are based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components and parameter uncertainties. Numerical examples show that the proposed criteria are effective and are an improvement over some existing results in the literature.     

Bifurcation analysis in a diffusive Logistic population model with two delayed density-dependent feedback terms

The present paper is concerned with a diffusive population model of Logistic type with an instantaneous density-dependent term and two delayed density-dependent terms and subject to the zero-Dirichlet boundary condition. By regarding the delay as the bifurcation parameter and analyzing in detail the associated eigenvalue problem, the local asymptotic stability and the existence of Hopf bifurcation for the sufficiently small positive steady state solution are shown. It is found that under the suitable condition, the positive steady state solution of the model will become ultimately unstable after a single stability switch (or change) at a certain critical value of delay through a Hopf bifurcation. However, under the other condition, the positive steady state solution of the model will become ultimately unstable after multiple stability switches at some certain critical values of delay through Hopf bifurcations. In addition, the direction of the above Hopf bifurcations and the stability of the bifurcating periodic solutions are analyzed by means of the center manifold theory and normal form method for partial functional differential equations. Finally, in order to illustrate the correction of the obtained theoretical results, some numerical simulations are also carried out.     

Synchronizing time delay systems using variable delay in coupling

We present a mechanism for synchronizing time delay systems using one way coupling with a variable delay in coupling that is reset at finite intervals. We present the analysis of the error dynamics that helps to isolate regions of stability of the synchronized state in the parameter space of interest for single and multiple delays. We supplement this by numerical simulations in a standard time delay system like Mackey Glass system. This method has the advantage that it can be adjusted to be delay or anticipatory in synchronization with a time which is independent of the system delay. We demonstrate the use of this method in communication using the bi channel scheme. We show that since the synchronizing channel carries information from transmitter only at intervals of reset time, it is not susceptible to an easy reconstruction.     

Global analysis of a multi-group animal epidemic model with indirect infection and time delay

The transmission mechanism of some animal diseases is complex because of the multiple transmission pathways and multiple-group interactions, which lead to the limited understanding of the dynamics of these diseases transmission. In this paper, a delay multi-group dynamic model is proposed in which time delay is caused by the latency of infection. Under the biologically motivated assumptions, the basic reproduction number $R_0$ is derived and then the global stability of the disease-free equilibrium and the endemic equilibrium is analyzed by Lyapunov functionals and a graph-theoretic approach as for time delay. The results show the global properties of equilibria only depend on the basic reproductive number $R_0$: the disease-free equilibrium is globally asymptotically stable if $R_0\leq 1$; if $R_0>1$, the endemic equilibrium exists and is globally asymptotically stable, which implies time delay span has no effect on the stability of equilibria. Finally, some specific examples are taken to illustrate the utilization of the results and then numerical simulations are used for further discussion. The numerical results show time delay model may experience periodic oscillation behaviors, implying that the spread of animal diseases depends largely on the prevention and control strategies of all sub-populations.     

Stability and Hopf bifurcation of a Nonlinear oscillator with multiple time-delays

This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The effect of multiple time delays is studied in detail. The focus is on the influence of delay in the system. This naturally gives rise to a delay differential equation (DDE) model of the system. The domain where the control is efficient in reducing the amplitude of vibration is found by the harmonic balance method. Technical stability within definite time and asymptotic stability is derived for selected gain control parameters. The control gain parameters are chosen according to technical and asymptotic stability. The energy analysis is a combination of Lyapunov’s function and the averaging technique, and is used to analyze the Hopf bifurcation.     

Dynamical properties of a stage structured three-species model with intra-guild predation

This paper considers a stage-structured three species model with intra-guild predation (IGP). First, we show local and global stability of IGP model. It is known that introduction of IGP in tritrophic food chain can destabilize the system. So in order to ensure survival of all species for all future time, we show a necessary and sufficient condition for permanence of IGP model. Next, we consider the IGP model with a stage structure for predator. The model uses time delay to express a maturation period and a through-stage survival rate for the predator. By using stability switch criteria which can provide practical guidelines that combine graphical information with analytical work, we can show that the delay can stabilize the IGP model.     

公路货运平台延迟赔付服务定价策略研究

考虑延迟赔付率、车主延迟风险、货主物流时效关注度的影响下,研究两种延迟赔付定价策略的选择问题,通过逆向求解法获取最优均衡。发现:(1)车主网络外部性大于货主两倍的情况,平台始终选择C策略。反之,若车主延迟风险低于某临界值、货主对物流时效的关注度高于某临界值,应选F策略;否则选C策略。(2)无论F策略还是C策略,平台收益均随车主延迟风险的降低、货主对时效性关注度的提升而提升,不受赔付率影响。(3)若选F策略,则不对货主补贴。若选C策略,车主的网络外部性大于货主的情况下始终实行补贴;反之,只有当车主延迟风险、货主物流时效的关注度满足条件时进行补贴。最后,用数值仿真结论进行验证。     

Stability,bifurcation and global existence of a Hopf-bifurcating periodic solution for a class of three-neuron delayed network models

In this paper a system of three delay differential equations representing a Hopfield type general model for three neurons with two-way (bidirectional) time delayed connections between the neurons and time delayed self-connection from each neuron to itself is studied. Delay independent and delay dependent sufficient conditions for linear stability, instability and the occurrence of a Hopf bifurcation about the trivial equilibrium are addressed. The partition of the resulting parametric space into regions of stability, instability, and Hopf bifurcation in the absence of self-connection is realized. To extend the local Hopf branches for large delay values a particular bidirectional delayed tri-neuron model without self-connection is investigated. Sufficient conditions for global existence of multiple non-constant periodic solutions are obtained for such a model using the global Hopf-bifurcation theorem for functional differential equations due to J. Wu and the Bendixson criterion for higher dimensional ordinary differential equations due to Li and Muldowney, and following the approach developed by Wei and Li.     

Robust asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach

In this paper, the robust asymptotic stability problem is considered for a class of fuzzy Markovian jumping genetic regulatory networks with uncertain parameters and switching probabilities by delay decomposition approach. The purpose of the addressed stability analysis problem is to establish an easy-to-verify condition under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. A new Lyapunov–Krasovskii functional (LKF) is constructed by nonuniformly dividing the delay interval into multiple subinterval, and choosing proper functionals with different weighting matrices corresponding to different subintervals in the LKFs. Employing these new LKFs for the time-varying delays, a new delay-dependent stability criterion is established with Markovian jumping parameters by T–S fuzzy model. Note that the obtained results are formulated in terms of linear matrix inequality (LMI) that can efficiently solved by the LMI toolbox in Matlab. Numerical examples are exploited to illustrate the effectiveness of the proposed design procedures.     

Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for stochastic cellular neural networks with multiple discrete and distributed time varying delays. A novel linear matrix inequality (LMI) based stability criterion is derived to guarantee the asymptotic stability of stochastic cellular neural networks with multiple discrete and distributed time varying delays which are represented by T–S fuzzy models. The derived delay-dependent stability conditions are based on free-weighting matrices method, Lyapunov stability theory and LMI technique. In fact, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. The delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay is removed. Our results can be specialized to several cases including those studied extensively in the literature. Finally, numerical examples are given to demonstrate the effectiveness and conservativeness of our results.     

Flocking and asymptotic velocity of the Cucker–Smale model with processing delay

The processing delay is incorporated into the influence function of the well-known Cucker–Smale model for self-organized systems with multiple agents. Both symmetric and non-symmetric pairwise influence functions are considered, and a Lyapunov functional approach is developed to establish the existence of flocking solutions for the proposed delayed Cucker–Smale model. An analytic formula is given to calculate the asymptotic flocking velocity in terms of model parameters and the variation of the position during the initial time interval.     

Modeling and analysis of tilt-rotor aeromechanical phenomena

The paper presents a recent effort to explore tilt-rotor aeromechanical phenomena with an emphasize on aeroelastic stability in forward flight (airplane mode). A general tilt-rotor model has been developed and implemented using a numerical technique that preserves symbolic exactness of the equations of motion. The stability study is based on an eigenvalue analysis about a nonlinear periodic trim solution. The present method enables both high resolution periodic response, and clear tracing of the instability drivers by providing the exact partial derivatives of the involved degrees of freedom in each one of the associated equations of motion. In addition to the common way of identifying trends and sensitivities by parametric study, the present approach supplies information about the effectiveness of possible mechanisms that are not included in the baseline model. The present results demonstrate the ability of the method to provide such unique insight into the aeromechanical phenomena in forward flight. Illustrative indications regarding required tilt-rotor design features that will postpone the instability phenomena are discussed.