An extended master-equation approach applied to aggregation in freeway traffic

We restudy the master-equation approach applied to aggregation in a one-dimensional freeway, where the decay transition probabilities for the jump processes are reconstructed based on a car-following model. According to the reconstructed transition probabilities, the clustering behaviours and the stochastic properties of the master equation in a one-lane freeway traffic model are investigated in detail The numerical results show that the size of the clusters initially below the critical size of the unstable cluster and initially above that of the unstable cluster all enter the same stable state, which also accords with the nucleation theory and is known from the result in earlier work. Moreover, we have obtained more reasonable parameters of the master equation based on some results of cellular automata models.     

State estimation for neural neutral-type networks with mixed time-varying delays and Markovian jumping parameters

This paper is concerned with a delay-dependent state estimator for neutral-type neural networks with mixed timevarying delays and Markovian jumping parameters.The addressed neural networks have a finite number of modes,and the modes may jump from one to another according to a Markov process.By construction of a suitable Lyapunov-Krasovskii functional,a delay-dependent condition is developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable in a mean square.The criterion is formulated in terms of a set of linear matrix inequalities(LMIs),which can be checked efficiently by use of some standard numerical packages.     

Estimation of spatially distributed processes using mobile sensor networks with missing measurements

This paper investigates the estimation problem for a spatially distributed process described by a partial differential equation with missing measurements.The randomly missing measurements are introduced in order to better reflect the reality in the sensor network.To improve the estimation performance for the spatially distributed process,a network of sensors which are allowed to move within the spatial domain is used.We aim to design an estimator which is used to approximate the distributed process and the mobile trajectories for sensors such that,for all possible missing measurements,the estimation error system is globally asymptotically stable in the mean square sense.By constructing Lyapunov functionals and using inequality analysis,the guidance scheme of every sensor and the convergence of the estimation error system are obtained.Finally,a numerical example is given to verify the effectiveness of the proposed estimator utilizing the proposed guidance scheme for sensors.     

Design and FPGA implementation of multi-wing chaotic switched systems based on a quadratic transformation

Based on a quadratic transformation and a switching function,a novel multi-wing chaotic switched system is proposed.First,a 4-wing chaotic system is constructed from a 2-wing chaotic system on the basis of a quadratic transformation.Then,a switching function is designed and by adjusting the switching function,the number and the distribution of the saddle-focus equilibrium points of the switched system can be regulated.Thus,a set of chaotic switched systems,which can produce 6-to-8-12-16-wing attractors,are generated.The Lyapunov exponent spectra,bifurcation diagrams,and Poincarémaps are given to verify the existence of the chaotic attractors.Besides,the digital circuit of the multi-wing chaotic switched system is designed by using the Verilog HDL fixed-point algorithm and the state machine control.Finally,the multi-wing chaotic attractors are demonstrated via FPGA platform.The experimental results show that the number of the wings of the chaotic attractors can be expanded more effectively with the combination of the quadratic transformation and the switching function methods.     

Stability and performance analysis of a jump linear control system subject to digital upsets

This paper focuses on the methodology analysis for the stability and the corresponding tracking performance of a closed-loop digital jump linear control system with a stochastic switching signal. The method is applied to a flight control system. A distributed recoverable platform is implemented on the flight control system and subject to independent digital upsets. The upset processes are used to stimulate electromagnetic environments. Specifically, the paper presents the scenarios that the upset process is directly injected into the distributed flight control system, which is modeled by independent Markov upset processes and independent and identically distributed(IID) processes. A theoretical performance analysis and simulation modelling are both presented in detail for a more complete independent digital upset injection. The specific examples are proposed to verify the methodology of tracking performance analysis. The general analyses for different configurations are also proposed. Comparisons among different configurations are conducted to demonstrate the availability and the characteristics of the design.     

Laser induced collisional energy transfer in Sr—Li system

A four-state model considering the relative velocity distribution function for calculating the cross section of laserinduced collisional energy transfer in a Sr-Li system is presented and profiles of laser-induced collision cross section are obtained.The resulting spectra obtained from different intermediate states are strongly asymmetrical in an opposite asymmetry.Both of the two intermediate states have contributions to the final state,and none of the intermediate states should be neglected.The peak of the laser-induced collisional energy transfer(LICET) profile shifts toward the red and the FWHM becomes narrower obviously with laser field intensity increasing.A cross section of 1.2 × 10-12 cm 2 at a laser field intensity of 2.17 × 10 7 V/m is obtained,which indicates that this collision process can be an effective way to transfer energy selectively from a storage state to a target state.The existence of saturation for cross section with the increase of the laser intensity shows that the high-intensity redistribution of transition probabilities is an important feature of this process,which is not accounted for in a two-state treatment.     

Augmented Lyapunov approach to H_∞ state estimation of static neural networks with discrete and distributed time-varying delays

This paper deals with H∞state estimation problem of neural networks with discrete and distributed time-varying delays. A novel delay-dependent concept of H∞state estimation is proposed to estimate the H∞performance and global asymptotic stability of the concerned neural networks. By constructing the Lyapunov–Krasovskii functional and using the linear matrix inequality technique, sufficient conditions for delay-dependent H∞performances are obtained, which can be easily solved by some standard numerical algorithms. Finally, numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.     

Impulsive control of chaotic systems and its applications in synchronization

In this paper,some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems.The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control.Compared with some existing results,our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings.Moreover,a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.     

Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over "fast" variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the case without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.     

Dynamical behaviors of a system with switches between the Rssler oscillator and Chua circuits

The behaviors of a system that alternates between the R¨ossler oscillator and Chua＇s circuit is investigated to explore the influence of the switches on the dynamical evolution.Switches related to the state variables are introduced,upon which a typical switching dynamical model is established.Bifurcation sets of the subsystems are derived via analysis of the related equilibrium points,which divide the parameters into several regions corresponding to different types of attractors.The dynamics behave typically in period orbits with the variation of the parameters.The focus/cycle periodic switching phenomenon is explored in detail to present the mechanism of the movement.The period-doubling bifurcation to chaos can be observed via the doubling increase of the turning points related to the switches.Furthermore,period-decreasing sequences have been obtained,which can be explained by the variation of the eigenvalues associated with the equilibrium points of the subsystems.     

Symmetry groups and spiral wave solution of a wave propagation equation

We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.     

Dynamical behaviors of a system with switches between the Rssler oscillator and Chua circuits

The behaviors of a system that alternates between the R¨ossler oscillator and Chua’s circuit is investigated to explore the influence of the switches on the dynamical evolution.Switches related to the state variables are introduced,upon which a typical switching dynamical model is established.Bifurcation sets of the subsystems are derived via analysis of the related equilibrium points,which divide the parameters into several regions corresponding to different types of attractors.The dynamics behave typically in period orbits with the variation of the parameters.The focus/cycle periodic switching phenomenon is explored in detail to present the mechanism of the movement.The period-doubling bifurcation to chaos can be observed via the doubling increase of the turning points related to the switches.Furthermore,period-decreasing sequences have been obtained,which can be explained by the variation of the eigenvalues associated with the equilibrium points of the subsystems.     

Molecular Dynamics Simulation of Microstructure Transitions in a Large-Scale Liquid Metal Al System During Rapid Cooling Processes

We perform a molecular dynamics simulation of microstructure transitions in a large-scale system consisting of 400000 atoms of liquid metal Al by the Clare supercomputer.A cluster-type index method is proposed to describe the structures of various short-range-order clusters in the liquid system.It is demonstrated that the icosahedron cluster (12 0 12 0) plays the most important role in the microstructure transition and that some larger clusters (containing more than 130 atoms) are formed in the system during the rapid cooling processes.It is obvious that the larger clusters are formed by means of combining some middle clusters,and that the middle clusters are formed with several smaller clusters.However,the larger clustens are not formed to be the multi-shell configuration as shown in the mass spectrum analysis of the cluster configurations of Al obtained by gaseous deposition,ionic spray methods and so on.This result can be used to explain the essential distinction between the cluster configurations of Al formed in two different ways.     

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional(2D) systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded(polytope type) uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.     

Relaxation theory of spin-3/2 Ising system near phase transition temperatures

<正>Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics.First,the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures,i.e.the first- and second-order and the tricritical points.Then,the Onsager theory is applied to the model and the kinetic or rate equations are obtained.By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points.Moreover,the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically,and they are found to be in good agrement.     

Stability and Group Index Switching in a Four-Level Atomic System

A four-level atomic system is proposed for stability and group index switching in the presence of spontaneously generated coherence. It is found that the transition from optical bistability （OB） to optical multistability （OM） and subluminal to superluminal can be obtained simultaneously. It is shown that the relative phase between applied fields can affect the stability and group index behaviors of weak probe light in the medium. Our proposed model provides a new scheme for simultaneous switching from OB to OM and （sub-to-super） luminal light propagation in an atomic system.     

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional(LKF), sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities(LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.     

Parametric study of the clustering transition in vibration driven granular gas system

A parametric study of the clustering transition of a vibration-driven granular gas system is performed by simulation.The parameters studied include the global volume fraction of the system, the size of the system, the friction coefficient, and the restitution coefficient among particles and among particle–walls. The periodic boundary and fixed boundary of sidewalls are also checked in the simulation. The simulation results provide us the necessary "heating" time for the system to reach steady state, and the friction term needed to be included in the "cooling" time. A gas-cluster phase diagram obtained through Kolmogorov–Smirnov(K–S) test analysis using similar experimental parameters is given. The influence of the parameters to the transition is then investigated in simulations. This simulation investigation helps us gain understanding which otherwise cannot be obtained by experiment alone, and makes suggestions on the determination of parameters to be chosen in experiments.     

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.