Traffic flow velocity disturbance characteristics and control strategy at the bottleneck of expressway

In the three-phase traffic flow studies, the traffic flow characteristic at the bottleneck section is a hot spot in the academic field. The controversy about the characteristics of the synchronized flow at bottleneck is also the main contradiction between the three-phase traffic flow theory and the traditional traffic flow theory. Under the framework of three-phase traffic flow theory, this paper takes the on-ramp as an example to discuss the traffic flow characteristics at the bottleneck section.In particular, this paper mainly conducts the micro-analysis to the effect of lane change under the two lane conditions, as well as the effect of the on-ramp on the main line traffic flow. It is found that when the main road flow is low, the greater the on-ramp inflow rate, the higher the average speed of the whole road section. As the probability of vehicles entering from the on-ramp increases, the flow and the average speed of the main road are gradually stabilized, and then the on-ramp inflow vehicles no longer have a significant impact on the traffic flow. In addition, this paper focuses on the velocity disturbance generated at the on-ramp, and proposes the corresponding on-ramp control strategy based on it, and the simulation verified that the control strategy can reasonably control the traffic flow by the on-ramp, which can meet the control strategy requirements to some extent.     

Dynamics of coin tossing is predictable

The dynamics of the tossed coin can be described by deterministic equations of motion, but on the other hand it is commonly taken for granted that the toss of a coin is random. A realistic mechanical model of coin tossing is constructed to examine whether the initial states leading to heads or tails are distributed uniformly in phase space. We give arguments supporting the statement that the outcome of the coin tossing is fully determined by the initial conditions, i.e. no dynamical uncertainties due to the exponential divergence of initial conditions or fractal basin boundaries occur. We point out that although heads and tails boundaries in the initial condition space are smooth, the distance of a typical initial condition from a basin boundary is so small that practically any uncertainty in initial conditions can lead to the uncertainty of the results of tossing.     

Phase transition of traffic states with on-ramp

We study the phase transition on a highway in a modified anisotropic continuum model with an on-ramp, which is recently developed by Gupta and Katiyar (J. Phys. A: Math. Nucl. Gen. 38 (2005) 4069]. To investigate whether this model can describe several distinct traffic states that are identified from real-traffic data [Kerner and Rehborn, Phys. Rev. Lett. 79 (1997) 4030; Kerner, Phys. Rev. Lett. 81 (1998) 3797], we carry out numerical simulations with an open boundary condition. The observed transition between free flow and various types of congested flow such as localized clusters, stop-and-go traffic and different kinds of synchronized traffic flow is obtained by applying a triggering pulse through an on-ramp in our simulation.We present the phase diagram for three representative values of the upstream boundary flux and for the whole range of the on-ramp flux. Several states like pinned localized cluster, triggered stop-and-go, recurring hump state, the oscillatory congested traffic and the homogeneous congested traffic are observed in phase transition from free flow to traffic-jam state. The phase diagram for our model near on-ramp is consistent with the results obtained by Lee et al. [Phys. Rev. E 59(5) (1999) 5101]. The results suggest that the modified model is able to describe all the three phases of traffic-flow theory developed by Kerner [Physica A 333 (2004) 379].     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

Towards a dynamical temperature of finite Hamiltonian systems

With the aid of numerical simulations of the β Fermi-Pasta-Ulam (FPU) system, we compare the different definitions of dynamical temperature for Hamiltonian systems. We have shown that each definition gives different values of temperature for a system with a small number of degrees of freedom (DOF). Only for systems with a sufficiently large number of DOF, do all the definitions of dynamical temperature approach the same value.     

Combined bottleneck effect of on-ramp and bus stop in a cellular automaton model

The combined bottleneck effect is investigated by modeling traffic systems with an on-ramp and a nearby bus stop in a two-lane cellular automaton model. Two cases, i.e. the bus stop locates in the downstream section of the on-ramp and the bus stop locates in the upstream section of the on-ramp, are considered separately. The upstream flux and downstream flux of the main road, as well as the on-ramp flux are analysed in detail, with respect to the entering probabilities and the distance between the on-ramp and the bus stop. It is found that the combination of the two bottlenecks causes the capacity to drop off, because the vehicles entering the main road from the on-ramp would interweave with the stopping (pulling-out) buses in the downstream (upstream) case. The traffic conflict in the former case is much heavier than that in the latter, causing the downstream main road to be utilized inefficiently. This suggests that the bus stop should be set in the upstream section of the on-ramp to enhance the capacity. The fluxes both on the main road and on the on-ramp vary with the distance between the two bottlenecks in both cases. However, the effects of distance disappear gradually at large distances. These findings might give some guidance to traffic optimization and management.     

The effect of restricted velocity in the two-lane on-ramp system

Usually there are multi-lane on the main road of the on-ramp system. The drivers may decelerate for more safety when they are near the on-ramp. In addition, the car velocity may be restricted according to the traffic regulation. In this paper, we study phenomenon using the cellular automata traffic flow model. We find that: (i) the phase diagram of the two-lane on-ramp system appears a new region, in which the traffic of the on-ramp reaches maximum flow. (ii) The introduction of restricted velocity region will decrease capacity of the on-ramp, but reduce the drastic velocity fluctuation near the on-ramp.     

Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps

The numerical approximation of Perron-Frobenius operators allows efficient determination of the physical invariant measure of chaotic dynamical systems as a fixed point of the operator. Eigenfunctions of the Perron-Frobenius operator corresponding to large subunit eigenvalues have been shown to describe “almost-invariant” dynamics in one-dimensional expanding maps. We extend these ideas to hyperbolic maps in higher dimensions. While the eigendistributions of the operator are relatively uninformative, applying a new procedure called “unwrapping” to regularised versions of the eigendistributions clearly reveals the geometric structures associated with almost-invariant dynamics. This unwrapping procedure is applied to a uniformly hyperbolic map of the unit square to discover this map’s dominant underlying dynamical structure, and to the standard map to pinpoint clusters of period 6 orbits.     

A universal scaling theory for complexity of analog computation

We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex solution. We analyze various probability ensembles of linear programming problems. For each one of these we obtain numerically the probability distribution functions of certain quantities which measure the complexity. Remarkably, in the asymptotic limit of very large problems, each of these probability distribution functions reduces to a universal scaling function, depending on a single scaling variable and independent of the details of its parent probability ensemble. These functions are reminiscent of the scaling functions familiar in the theory of phase transitions. The results reported here extend analytical and numerical results obtained recently for the Gaussian ensemble.     

Dynamics and schedule of shuttle bus controlled by traffic signal

We study the dynamical behavior of a shuttle bus moving through a traffic signal. The dynamics of the bus is expressed in terms of the nonlinear maps. The bus dynamics is controlled by varying the loading parameter, the cycle time of signal, and the degree of speedup. We show the dependence of the tour time on both loading parameter and cycle time. The fluctuation of boarding passengers is highly reduced by varying the cycle time. When the bus speeds up to retrieve the delay induced by loading the passengers, the bus behavior also changes highly. The shuttle bus schedule is connected with the complex motion of the shuttle bus. The region map (phase diagram) is shown to control the complex motion of the bus.     

Correlated noises in an absorptive optical bistable model

We study the steady state properties of an absorptive optical bistable model in the presence of correlated noises. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution and the average value of the transmitted light have been investigated. We have found that fluctuations of the input light amplitude improve the transmitted light and an optimized value exists for the fluctuations of the population difference at which the transmitted light takes its maximum value. The correlation between the two noises reduce the transmitted light and the noises in the model can induce a phase transition.     

Synchronization analysis of delayed complex networks with time-varying couplings

In this paper, a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays. The coupling configurations are not restricted to the symmetric and irreducible connections or the non-negative off-diagonal links. The stability criteria are obtained by using Lyapunov-Krasovskii functional method and subspace projection method. These criteria reveal the relationship between coupling matrices and stability of the dynamical networks.     

Effect of irregularity on vehicular traffic through a sequence of traffic lights

We present the stochastic nonlinear-map model of vehicular traffic controlled by irregular signals. The signal’s interval, the split of signal, and the offset time changes irregularly from signal to signal on a roadway. We study the effect of irregularity on dynamical behavior of vehicular traffic through a sequence of traffic lights. The vehicle exhibits the very complex behavior with varying cycle time. When the strength of irregularity is small, the arrival time does not change with irregularity for some values of cycle time, while it changes for other values of cycle time. The region in which the arrival time changes is expanding with increasing irregularity’s strength. The region map (phase diagram) is shown in the cycle time-irregularity’s strength space.     

Mode-Locking Behaviour in Driven Colloids with Random Pinning

We find mode-locking steps in simulated force-velocity characteristics of external alternating-force （AF） driven colloids on a disordered substrate. Studies of mode-locking patterns in systems show that mode-locking steps are accompanied with the emergence of a dynamics phase： transverse solid phase. We also study the influence of temperature on the width of mode-locking steps. The mode-locked state is destroyed by thermal fluctuation and the width of mode-locking steps decreases rapidly with increasing temperature. In high velocity and low temperature regimes, due to the appearance of transverse solid phase and microscopically periodic velocity modulation, the step width changes little as temperature is varied.     

A Hyperchaotic Attractor Coined from Chaotic Lü System

We report a new hyperchaotic attractor coined from the chaotic Lü system by using a state feedback controller. Theoretical analyses and simulation experiments are conducted to investigate the dynamical behaviour of the proposed hyperchaotic system     

Detrended Fluctuation Analysis of Traffic Data

Different routing strategies may result in different behaviour of traffic on internet. We analyse the correlation of traffic data for three typical routing strategies by the detrended fluctuation analysis （DFA） and lind that the aregree of correlation of the data can be divided into three regions, i.e. weak, medium, and strong correlation. The DFA scalings are constants in both the regions of weak and strong correlations but monotonically increase in the region of medium correlation. We suggest that it is better to consider the traffic on complex network as three phases, i.e. the free, buffer, and congestion phase, than just as two phases believed before, i.e. the free and congestion phase.     

Stability change of intrinsic localized mode in finite nonlinear coupled oscillators

Intrinsic localized mode (ILM) is spatially localized and temporally periodic oscillation in nonlinear coupled oscillators. We numerically investigate the dynamical stability of ILMs in a microcantilever array, in which ILMs were experimentally observed by Sato et al. It is found that the stability change of ILMs is due to the ratio in nonlinear potentials. This phenomenon also occurs in the array without harmonic potentials. Consequently, the stability of ILMs substantially depends on the ratio in nonlinear on-site and inter-site potentials.