effects of the lattice point drivers heterogeneity of the disturbance risk preference on traffic flow instability abstract this paper defines the lattice point drivers heterogeneity of the disturbance risk preference and proposes a new one dimensional traffic flow lattice model to research the effects of the lattice point drivers heterogeneity of the disturbance risk preference on traffic flow instability by the analytical analysis we obtain the traffic flow instability condition and the modified korteweg de vries mkdv equation and the calculation formula of the unstable area density range and the calculation method of the probability of traffic congestion caused by a small disturbance both the analytical and the simulation analysis show that there are important effects of the lattice point drivers heterogeneity of the disturbance risk preference on traffic flow instability namely the smaller the ratio of the preceding lattice point drivers coefficient of the disturbance risk preference to the following lattice point drivers coefficient of the disturbance risk preference is the smaller the traffic flow instability is and vice versa it provides a viable idea to ease traffic congestion

analysis of a novel lattice hydrodynamic model considering density integral and backward looking effect abstract by introducing the backward looking influence and the integration form of the density difference between the front and rear vehicles an improved lattice hydrodynamic model is proposed the linear stability condition is derived by linear stability analysis the results of the linear stability analysis demonstrate that the influence of backward looking and density difference between the front and rear vehicles play a positive part in improving the steadiness of the traffic flow system the nonlinear analysis testifies that the mkdv equation can describe the propagation feature of density wave the results of numerical simulation show that the steadiness of traffic flow can be amenable to improvement effectively by considering these two factors comprehensive analysis demonstrates that the effect of the backward looking and density difference is propitious to improve traffic stability and suppress traffic congestion

on the multiplicative complexity of boolean functions over the basis 1 abstract the multiplicative complexity c f of a boolean function f is the minimum number of and gates in a circuit representing f which employs only and xor and not gates a constructive upper bound c f 2 n 2 1 n 2 2 for any boolean function f on n variables n even is given a counting argument gives a lower bound of c f 2 n 2 o n thus we have shown a separation by an exponential factor between worst case boolean complexity which is known to be 2 n n 1 and worst case multiplicative complexity a construction of circuits for symmetric boolean functions on n variables requiring less than n 3 n and gates is described

kdv cnoidal waves in a traffic flow model with periodic boundaries abstract an optimal velocity ov model describes car motion on a single lane road in particular near to the boundary signifying the onset of traffic jams this model reduces to a perturbed korteweg de vries kdv equation using asymptotic analysis previously the kdv soliton solution has then been found and compared to numerical results see muramatsu and nagatani 1 here we instead apply modulation theory to this perturbed kdv equation to obtain at leading order the modulated cnoidal wave solution at the next order the whitham equations are derived which have been modified due to the equation perturbation terms next from this modulation system a family of spatially periodic cnoidal waves are identified that characterise vehicle headway distance then for this set of solutions we establish the relationship between the wave speed the modulation term and the driver sensitivity this analysis is confirmed with comparisons to numerical solutions of the ov model as well the long time behaviour of these solutions is investigated

the multiplicative complexity of quadratic boolean forms abstract let the multiplicative complexity l f of a boolean function f be the minimal number of gates that are sufficient to evaluate f by circuits over the basis 1 we characterize the multiplicative complexity l f of quadratic boolean forms f it is half the rank of an associated matrix two quadratic boolean forms f g have the same complexity l f l g iff they are isomorphic by a linear isomorphism we characterize computational independence of two quadratic boolean forms f 1 f 2 in the sense that l f 1 f 2 l f 1 l f 2

tdgl and mkdv equations for jamming transition in the lattice models of traffic abstract the lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena they are the lattice versions of the hydrodynamic model of traffic two lattice models are presented one is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other is the difference equation in which both time and space variables are discrete we apply the linear stability theory and the nonlinear analysis to the lattice models it is shown that the time dependent ginzburg landau tdgl equation is derived to describe the traffic flow near the critical point a thermodynamic theory is formulated for describing the phase transitions and critical phenomena it is also shown that the perturbed modified korteweg de vries mkdv equation is derived to describe the traffic jam

two velocity difference model for a car following theory abstract in the light of the optimal velocity model a two velocity difference model for a car following theory is put forward considering navigation in modern traffic to our knowledge the model is an improvement over the previous ones theoretically because it considers more aspects in the car following process than others then we investigate the property of the model using linear and nonlinear analyses the korteweg de vries equation for short the kdv equation near the neutral stability line and the modified korteweg de vries equation for short the mkdv equation around the critical point are derived by applying the reductive perturbation method the traffic jam could be thus described by the kdv soliton and the kink anti kink soliton for the kdv equation and mkdv equation respectively numerical simulations are made to verify the model and good results are obtained with the new model

the transversal homoclinic solutions and chaos for stochastic ordinary differential equations abstract we consider the persistence of a transversal homoclinic solution and chaotic motion for ordinary differential equations with a homoclinic solution to a hyperbolic equilibrium under an unbounded random forcing driven by a brownian force by lyapunov schmidt reduction the persistence of transversal homoclinic solution is reduced to find the zeros of some bifurcation functions defined between two finite spaces it is shown that for almost all sample paths of the brownian motion the perturbed system exhibits chaos

an extended car following model considering driver s sensory memory and the backward looking effect abstract on the basis of full velocity difference model fvdm an extended car following model is proposed to account for the effect of driver s memory and backward looking effect in this paper the stability conditions of the new model are derived by applying the linear stability analysis the time dependent ginzburg lan tdgl equation and the modified korteweg de vries mkdv equation are derived through nonlinear theory moreover the relationship between the two equations is studied numerical simulations show that the stability of traffic flows can be strengthened with the effect of driver s memory and backward looking effect

analysis of car following model considering driver s physical delay in sensing headway abstract an extended car following model is proposed by taking into account the delay of the driver s response in sensing headway the stability condition of this model is obtained by using the linear stability theory the results show that the stability region decreases when the driver s physical delay in sensing headway increases the kdv equation and mkdv equation near the neutral stability line and the critical point are respectively derived by applying the reductive perturbation method the traffic jams could be thus described by soliton solution and kink antikink soliton solution for the kdv equation and mkdv equation respectively the numerical results in the form of the space time evolution of headway show that the stabilization effect is weakened when the driver s physical delay increases it confirms the fact that the delay of driver s response in sensing headway plays an important role in jamming transition and the numerical results are in good agreement with the theoretical analysis

stabilization effect of multiple drivers desired velocities in car following theory abstract in order to reveal the influence of driver s individual behavior on traffic flow more accurately a new car following model is proposed with consideration of multiple drives desired velocities the stability criterion of the new model is derived through linear stability theory and the results show that the current driver s desired velocity can stabilize traffic flow but the preceding driver s desired velocity can damage traffic stability through nonlinear analysis the traffic jamming transition characteristics near the critical point can be described by the kink antikink soliton of the mkdv equation numerical simulation confirms the analytical results which shows that the multiple drivers desired velocities play an important role in traffic evolution

stability analysis of a new lattice hydrodynamic model by considering lattice s self anticipative density effect abstract in this paper a new lattice hydrodynamic model with consideration of the density difference of a lattice s current density and its anticipative density is proposed the influence of lattice s self anticipative density on traffic stability is revealed through linear stability theory and it shows that lattice s self anticipative density can improve the stability of traffic flow to describe the phase transition of traffic flow the mkdv equation near the critical point is derived by using nonlinear analysis method the propagating behavior of density wave in the unstable region can be described by the kink antikink soliton of the mkdv equation numerical simulation validates the analytical results which shows that traffic jam can be suppressed efficiently by considering lattice s self anticipative density in the modified lattice hydrodynamic model

a novel lattice hydrodynamic model accounting for driver s memory effect and the difference of optimal velocity on curved road abstract a novel lattice hydrodynamic model is put forward which takes the effects of driver s memory and difference of optimal velocity into account on curved road linear stability analysis for the novel model is discussed and the stability condition is deduced through nonlinear analysis the mkdv equation is deduced to explore the evolution of jams near the vertex the exact solution of the mkdv equation is also derived the influence of the above two factors on traffic stability are investigated by numerical examples both numerical and analytical results demonstrate that memory effect and the difference of optimal velocity on curved road can ease traffic jams efficiently

kdv and kink antikink solitons in car following models abstract the jams in the congested traffic are related with various density waves which might be governed by the nonlinear wave equations such as the korteweg de vries kdv equation the burgers equation and the modified korteweg de vries mkdv equation three different versions of optimal velocity models are examined the stability conditions of the models are obtained by using the linear stability theory the kdv equation near the neutral stability line and the mkdv equation around the critical point are derived by applying the reductive perturbation method respectively the traffic jams could be thus described by the kdv and kink antikink soliton solutions for the two kinds of equations the general solutions are given for which can lead to specific solutions in previous work moreover they are applied to solve a new model the full velocity difference model and the corresponding kdv and kink antikink soliton solutions could be quickly obtained which demonstrates the general solutions presented herein are useful

modeling and application analysis of car following model with predictive headway variation abstract this work proposes an improved microscopic model by taking the predictive driving behavior of the preceding car into account firstly we use the linear method to investigate performance of the proposed model deduce the critical linear stability conditions and obtain a neutral curve accounting for stability of the new model then using the nonlinear analysis technique we derive the equations of burgers the korteweg de vries kdv and the modified kdv mkdv respectively to describe the triangular shock wave soliton density wave and the kink antikink density wave finally numerical experiments unfold from two aspects one for verifying the theoretical analysis results and another for testing the impact of predictive driving behavior of the preceding car on traffic stability simulation results show that the new model can stabilize traffic flow compared with the fvd model and confirm that the existence of three kinds of density waves in different phase diagram regions

the stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow abstract a modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice the stability condition of the modified model is obtained through the linear stability analysis the results show that considering the density difference leads to the stabilization of the system the burgers equation and mkdv equation are derived to describe the density waves in the stable and unstable regions respectively numerical simulations show that considering the density difference not only could stabilize traffic flow but also makes the lattice hydrodynamic model more realistic

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

lattice hydrodynamic modeling of two lane traffic flow with timid and aggressive driving behavior abstract in this paper a new two lane lattice hydrodynamic traffic flow model is proposed by considering the aggressive or timid characteristics of driver s behavior the effect of driver s characteristic on the stability of traffic flow is examined through linear stability analysis it is shown that for both the cases of lane changing or without lane changing the stability region significantly enlarges reduces as the proportion of aggressive timid drivers increases to describe the propagation behavior of a density wave near the critical point nonlinear analysis is conducted and mkdv equation representing kink antikink soliton is derived the effect of anticipation parameter with more aggressive timid drivers is also investigated and found that it has a positive negative effect on the stability of two lane traffic flow dynamics simulation results are found consistent with the theoretical findings which confirm that the driver s characteristics play a significant role in a two lane traffic system

disproving the single level conjecture we consider the size of monotone circuits for quadratic boolean functions that is disjunctions of length 2 monomials our motivation is that a good linear in the number of variables lower bound on the monotone circuit size for a certain type of quadratic function would imply a good even exponential lower bound on the general nonmonotone circuit size to get more insight into the structure of monotone circuits for quadratic functions we consider the so called single level conjecture posed explicitly in the early 1990s the conjecture claims that monotone single level circuits that is circuits which have only one level of and gates for quadratic functions are not much larger than arbitrary monotone circuits in this paper we disprove the conjecture as follows there exist quadratic functions whose monotone circuits have linear size but whose monotone single level circuits require almost quadratic size

nonlinear analysis of the optimal velocity difference model with reaction time delay abstract we investigate the effect of reaction time delay of drivers upon traffic flow analytically and numerically we extend the optimal velocity difference model by taking reaction time delay of drivers into account the stability condition is obtained the burgers korteweg de vries kdv and modified korteweg de vries mkdv equations are derived in the stable metastable and unstable regions the results show that the increase of reaction time delay of drivers leads to the unrealistic traffic phenomena and unstable traffic flow by adjusting the coefficient of the velocity and optimal velocity difference the unrealistic traffic phenomena and unstable traffic flow can disappear

multiplicative complexity of vector valued boolean functions abstract we consider the multiplicative complexity of boolean functions with multiple bits of output studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity for so called circuits we show that there is a tight connection between error correcting codes and circuits computing functions with high nonlinearity combining this with known coding theory results we show that functions with n inputs and n outputs with the highest possible nonlinearity must have at least 2 32n and gates we further show that one cannot prove stronger lower bounds by only appealing to the nonlinearity of a function we show a bilinear circuit computing a function with almost optimal nonlinearity with the number of and gates being exactly the length of such a shortest code additionally we provide a function which for general circuits has multiplicative complexity at least 2 n 3 finally we study the multiplicative complexity of almost all functions we show that every function with n bits of input and m bits of output can be computed using at most 2 5 1 o 1 m 2 n and gates

a boolean function requiring 3n network size abstract paul 1977 has proved a 2 5 n lower bound for the network complexity of an explicit boolean function we modify the definition of paul s function slightly and prove a 3 n lower bound for the network complexity of that function

jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing abstract a new lattice hydrodynamic model is proposed by considering the interruption probability effect on traffic flow with passing and analyzed both theoretically and numerically from linear and non linear stability analysis the effect of interruption probability on the phase diagram is investigated and the condition of existence for kink antikink soliton solution of mkdv equation is derived the stable region is enhanced with interruption probability and the jamming transition occurs from uniform flow to kink flow through chaotic flow for higher and intermediate values of non interruption effect of passing it is also observed that there exists conventional jamming transition between uniform flow and kink flow for lower values of non interruption effect of passing numerical simulations are carried out and found in accordance with the theoretical findings which confirm that the effect of interruption probability plays an important role in stabilizing traffic flow when passing is allowed

tight bounds for the multiplicative complexity of symmetric functions the multiplicative complexity of a boolean function f is defined as the minimum number of binary conjunction and gates required to construct a circuit representing f when only exclusive or conjunction and negation gates may be used this article explores in detail the multiplicative complexity of symmetric boolean functions new techniques that allow such exploration are introduced they are powerful enough to give exact multiplicative complexities for several classes of symmetric functions in particular the multiplicative complexity of computing the hamming weight of n bits is shown to be exactly n h n n where h n n is the hamming weight of the binary representation of n we also show a close relationship between the complexities of basic symmetric functions and the fractal known as sierpinski s gasket

a novel lattice hydrodynamic model considering the optimal estimation of flux difference effect on two lane highway abstract the optimal estimation of flux difference effect is introduced to construct a new lattice hydrodynamic model for two lane highway through linear stability analysis it is found that the new consideration plays an important influence upon the stability of two lane traffic flow moreover the mkdv equation near the critical point is derived from nonlinear analysis which describes the propagation behavior of traffic jam in two lane traffic system simulation results show that the stability of two lane traffic system can be increased and the emergence of traffic jams are effectively relieved by the optimal estimation of flux difference effect which is in good agreement with theoretical analysis

nonlinear analysis of a new lattice hydrodynamic model with the consideration of honk effect on flux for two lane highway abstract influence of the honk on traffic flux is taken to construct a new lattice model for two lane freeway the linear stability analysis is applied to obtain the stability condition involving the honk effect on traffic flux in two lane system nonlinear analysis is implemented to get the mkdv equation for the phase transition of two lane lattice traffic flow numerical simulation is worked out to authenticate that the impact of honk on traffic flux strengthens the stability of traffic flow and suppresses the traffic congestion effectively under lane changing in two lane lattice traffic flow which is accordance with the analytic results

exact solutions for a discrete system arising in traffic flow this paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by g f newell as a model for car following in traffic flow in particular newell found exact solutions for shock waves and related phenomena here exact solutions representing periodic waves and solitary waves are obtained the method relates travelling wave solutions to the toda and kac van moerbeke discrete systems in this and other ways much of the interest is in the general phenomena possible in discrete systems here including also a time lag rather than in just the specific traffic flow setting

modified kdv equation for jamming transition in the continuum models of traffic abstract continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway they are the simplified versions of the hydrodynamic model of traffic two continuum models are presented one is described by the partial differential equations and the other is the discrete lattice version the linear stability theory and the nonlinear analysis are applied to the continuum models the modified korteweg de vries equation kdv near the critical point is derived using the reduction perturbation method it is shown that the jamming transition and the density wave in the congested traffic flow are described by the modified kdv equation the solutions of the kdv equations obtained from the two models are compared with that of the optimal velocity model car following model

the korteweg de vries soliton in the lattice hydrodynamic model abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but is also closely connected with the microscopic car following model the modified korteweg de vries mkdv equation about the density wave in congested traffic has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail in the car following model so we devote ourselves to obtaining the kdv equation from the lattice hydrodynamic model and obtaining the kdv soliton solution describing the traffic jam numerical simulation is conducted to demonstrate the nonlinear analysis result

stabilization effect of traffic flow in an extended car following model based on an intelligent transportation system application an extended car following model is proposed by incorporating an intelligent transportation system in traffic the stability condition of this model is obtained by using the linear stability theory the results show that anticipating the behavior of more vehicles ahead leads to the stabilization of traffic systems the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by applying the reductive perturbation method the traffic jam could be thus described by the kink antikink soliton solution for the mkdv equation from the simulation of space time evolution of the vehicle headway it is shown that the traffic jam is suppressed efficiently with taking into account the information about the motion of more vehicles in front and the analytical result is consonant with the simulation one

phase transition in a difference equation model of traffic flow a difference equation is presented to describe traffic flow on a highway the difference equation model is derived from the optimal velocity models formulated in terms of the differential equations it is compared with the differential equation models we investigate phase transitions among the freely moving phase the coexisting phase in which jams appear and the uniform congested phase the linear stability theory is applied and the neutral stability line is obtained we find the critical point below which no jams appear to derive the modified korteweg de vries equation near the critical point we apply the reductive perturbation method we also compare the nonlinear analysis result with that of the optimal velocity model it is shown that the critical point and the amplitude of the jam are different from those of the optimal velocity model

a new lattice model accounting for multiple optimal current differences anticipation effect in two lane system abstract this paper extends a two lane lattice hydrodynamic traffic flow model to take into account the driver s anticipation effect in sensing the multiple optimal current differences based on the proposed model we derive analytically the effect of driver s anticipation of multiple optimal current differences on the instability of traffic dynamics the phase diagrams have been plotted and discussed that the stability region enhances with anticipation effect in sensing multiple optimal current differences through simulation it is found that the oscillation of density wave around critical density decreases with an increase in lattice number and anticipation time for transient and steady state the simulation results are in good agreement with the theoretical analysis which show that considering the driver s anticipation of multiple optimal current differences in two lane lattice model stabilizes the traffic flow and suppresses the traffic jam efficiently

traffic jams granular flow and soliton selection the flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow in a certain range of traffic density steady flow becomes unstable against the growth of a cluster or phantom traffic jam which moves at a slower speed than the otherwise homogeneous flow we show that near the onset of this instability traffic flow is described by a perturbed korteweg de vries kdv equation the traffic jam can be identified with a soliton solution of the kdv equation the perturbation terms select a unique member of the continuous family of kdv solitons these results may also apply to the dynamics of granular relaxation

jamming transitions and the modified korteweg de vries equation in a two lane traffic flow abstract the two lattice models are presented to simulate the traffic flow on a two lane highway they are the lattice versions of the hydrodynamic model of traffic the one model a is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other model b is the difference equation in which both time and space variables are discrete the jamming transitions among the freely moving phase the coexisting phase and the uniform congested phase are studied by using the nonlinear analysis and the computer simulation the modified korteweg de vries mkdv equations are derived from the lattice models near the critical point the traffic jam is described by a kink antikink solution obtained from the mkdv equation it is found that the critical point the coexisting curve and the neutral stability line decrease with increasing the rate of lane changing also the computer simulation is performed for the model b it is shown that the coexisting curves obtained from the mkdv equation are consistent with the simulation result

stabilization analysis and modified korteweg de vries equation in a cooperative driving system two lattice traffic models are proposed by incorporating a cooperative driving system the lattice versions of the hydrodynamic model of traffic flow are described by the differential difference equation and difference difference equation respectively the stability conditions for the two models are obtained using the linear stability theory the results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink anti kink soliton solutions obtained from the mkdv equations

the backward looking effect in the lattice hydrodynamic model abstract the novel lattice hydrodynamic model is presented by incorporating the backward looking effect the stability condition for the the model is obtained using the linear stability theory the result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model the korteweg de vries kdv for short equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kdv soliton solution obtained from the kdv equation the simulation result is consistent with the nonlinear analysis

stabilization and enhancement of traffic flow by the next nearest neighbor interaction the car following model of traffic is extended to take into account the car interaction before the next car ahead the next nearest neighbor interaction the traffic behavior of the extended car following model is investigated numerically and analytically it is shown that the next nearest neighbor interaction stabilizes the traffic flow the jamming transition between the freely moving and jammed phases occurs at a higher density than the threshold of the original car following model by increasing the maximal velocity the traffic current is enhanced without jam by the stabilization effect the jamming transition is analyzed with the use of the linear stability and nonlinear perturbation methods the traffic jam is described by the kink solution of the modified korteweg char21 de vries equation the theoretical coexisting curve is in good agreement with the simulation result

solitons and kinks in a general car following model we study a general car following model of traffic flow on an infinitely long single lane road which assumes that a car s acceleration depends on time delayed values of its own speed the headway between it and the car ahead and the rate of change of headway but makes minimal assumptions about the functional form of that dependence we present a detailed characterization of the onset of linear instability in particular we find a specific limit on the delay time below which the marginal wave number at the onset of instability is zero and another specific limit on the delay time above which steady flow is always unstable crucially the threshold of absolute stability generally does not coincide with an inflection point of the steady state velocity function when the marginal perturbation at onset has wave number 0 we show that burgers and korteweg de vries kdv equations can be derived under the usual assumptions and that corrections to the kdv equation select a single member of the one parameter set of its one soliton solutions by driving a slow evolution of the soliton parameter while in previous models this selected soliton has always marked the threshold of a finite amplitude instability of linearly stable steady flow we find that it can alternatively be a stable small amplitude jam that occurs when steady flow is linearly unstable the model reduces to the usual modified korteweg de vries mkdv equation only in the special situation that the threshold of absolute stability coincides with an inflection point of the steady state velocity function in general near the threshold of absolute stability the model reduces instead to a kdv equation in the regime of small solitons while near an inflection point it reduces to a hayakawa nakanishi equation like the mkdv equation the hayakawa nakanishi equation admits a continuous family of kink solutions and the selection criterion arising from the corrections to this equation can be written down explicitly language en

nonlinear analysis for a modified continuum model considering electronic throttle et and backward looking effect abstract in this research a new car following model is developed by considering the influences of electronic throttle et dynamics and backward looking effect the improved car following model is transformed into a new continuum model through the relationship between the microscopic variables and macroscopic variables the linear stability condition of the extended continuum model can be obtained according to the linear stability theory the neutral stability curve shows that backward looking effect will improve the stability of traffic flow the kdv burgers equation is derived by the nonlinear analysis which can be used to describe the spreading behavior of traffic flow density wave in traffic congestion nearby the neutral stability line numerical experiments have been carried out including the shock waves rarefaction waves and energy consumption the numerical simulation results indicate that the traffic flow stability can be enhanced by considering et dynamics and backward looking effect in addition the above two factors can also effectively reduce energy consumption

a new lattice model of traffic flow with the consideration of the traffic interruption probability abstract in this paper we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways the stability condition of the new model is obtained by the linear stability analysis and the modified korteweg de vries kdv equation is derived through nonlinear analysis thus the space will be divided into three regions stable metastable and unstable the simulation results also show that the traffic interruption probability could stabilize traffic flow

a novel car following model considering average speed of preceding vehicles group abstract in this paper a new car following model is presented by considering the average speed effect of preceding vehicles group in cyber physical systems cps environment the effect of this new consideration upon the stability of traffic flow is examined through linear stability analysis a modified korteweg de vries mkdv equation was derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point good agreement between the simulation and the analytical results shows that average speed of preceding vehicles group leads to the stabilization of traffic systems and thus can efficiently suppress the emergence of traffic jamming

bifurcation analysis of traffic flow through an improved car following model considering the time delayed velocity difference abstract in this paper a new car following model with consideration of time delayed velocity difference is proposed to investigate the effect of time delayed velocity on traffic flow via bifurcation analysis based on this model the linear stability analysis is carried out and the corresponding stability condition is obtained then the hopf bifurcation analysis is performed in term of theoretical analysis and numerical simulation the result shows that there exist hopf bifurcation critical points and the position of the critical points is found to be located on the boundary of the instability region finally the influence of the delay time and sensitivity of velocity difference on hopf bifurcation is discussed respectively

influence of the traffic interruption probability on traffic stability in lattice model for two lane freeway abstract in this paper a new lattice model is proposed with the traffic interruption probability term in two lane traffic system the linear stability condition and the mkdv equation are derived from linear stability analysis and nonlinear analysis by introducing the traffic interruption probability of optimal current for two lane traffic freeway respectively numerical simulation shows that the traffic interruption probability corresponding to high reaction coefficient can efficiently improve the stability of two lane traffic flow as traffic interruption occurs with lane changing

time dependent ginzburg landau equation in a car following model considering the driver s physical delay abstract in this paper an extended car following model considering the delay of the driver s response in sensing headway is proposed to describe the traffic jam it is shown that the stability region decreases when the driver s physical delay in sensing headway increases the phase transition among the freely moving phase the coexisting phase and the uniformly congested phase occurs below the critical point by applying the reductive perturbation method we get the time dependent ginzburg landau tdgl equation from the car following model to describe the transition and critical phenomenon in traffic flow we show the connection between the tdgl equation and the mkdv equation describing the traffic jam

numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries abstract the soliton and kink antikink density waves are simulated with periodic boundaries by adding perturbation in the initial condition on single lane road based on a car following model they are reproduced in the form of the space time evolution of headway both of which propagate backwards it is found that the solitons appear only near the neutral stability line regardless of the boundary conditions and they exhibit upward form when the initial headway is smaller than the safety distance otherwise they exhibit downward form comparison is made between the numerical and analytical results about the amplitude of kink antikink wave and the underlying mechanism is analyzed besides it is indicated that the maximal current of traffic flow increases with decreasing safety distance the numerical simulation shows a good agreement with the analytical results

transformations and multi solitonic solutions for a generalized variable coefficient kadomtsev petviashvili equation kadomtsev petviashvili equations with variable coefficients can be used to characterize many nonlinear phenomena in fluid dynamics and plasma physics more realistically than the equations with constant coefficients hereby a generalized variable coefficient kadomtsev petviashvili equation with nonlinearity dispersion and perturbed terms is investigated transformations of which the consistency conditions are exactly the painleve integrability conditions to the korteweg de vries equation cylindrical korteweg de vries equation kadomtsev petviashvili equation and cylindrical kadomtsev petviashvili equation are presented by formal dependent variable transformation assumptions using the hirota bilinear method from the variable coefficient bilinear equation the multi solitonic solution auto backlund transformation and lax pair for the variable coefficient kadomtsev petviashvili equation are obtained moreover the influence of inhomogeneity coefficients on solitonic structures and interaction properties is discussed for physical interest and possible applications

a note on a problem in the theory of grammatical complexity abstract in this note we answer an open question in the theory of grammatical complexity we show that if l is an infinite context free language then l n the set of words in l of length less than or equal to n can be generated by o l n 2 3 context free productions and if l is an infinite linear language then l n can be generated by o l n linear productions we also show that these bounds are the best possible

effect of optimal estimation of flux difference information on the lattice traffic flow model abstract in this paper a new lattice model is proposed by considering the optimal estimation of flux difference information the effect of this new consideration upon the stability of traffic flow is examined through linear stability analysis furthermore a modified korteweg de vries mkdv equation near the critical point is constructed and solved by means of nonlinear analysis method and thus the propagation behavior of traffic jam can be described by the kink antikink soliton solution of the mkdv equation numerical simulation is carried out under periodical condition with results in good agreement with theoretical analysis therefore it is verified that the new consideration can enhance the stability of traffic systems and suppress the emergence of traffic jams effectively

computation of bifurcation manifolds of linearly independent homoclinic orbits abstract regarding the small perturbation as a parameter in an appropriate space of functions we can discuss co existence of homoclinic orbits for non autonomous perturbations of an autonomous system in r n and describe conditions of parameters for such degenerate homoclinic bifurcations with some bifurcation manifolds of infinite dimension since those manifolds determine the relation among parameters for such bifurcations in this paper we give an algorithm to compute approximately those manifolds and concretely obtain their first order approximates

the influence of continuous historical velocity difference information on micro cooperative driving stability abstract in this paper a new micro cooperative driving car following model is proposed to investigate the effect of continuous historical velocity difference information on traffic stability the linear stability criterion of the new model is derived with linear stability theory and the results show that the unstable region in the headway sensitivity space will be shrunk by taking the continuous historical velocity difference information into account through nonlinear analysis the mkdv equation is derived to describe the traffic evolution behavior of the new model near the critical point via numerical simulations the theoretical analysis results are verified and the results indicate that the continuous historical velocity difference information can enhance the stability of traffic flow in the micro cooperative driving process

density waves in a traffic flow model with reaction time delay abstract density waves are investigated analytically and numerically in the optimal velocity model with reaction time delay of drivers the stability condition of this model is obtained by using the linear stability theory the results show that the decrease of reaction time delay of drivers leads to the stabilization of traffic flow the burgers korteweg de vries kdv and modified korteweg de vries mkdv equations are derived to describe the density waves in the stable metastable and unstable regions respectively the triangular shock waves soliton waves and kink antikink waves appearing respectively in the three distinct regions are derived to describe the traffic jams the numerical simulations are given

multiple chaos arising from single parametric perturbation of a degenerate homoclinic orbit abstract in this paper we investigate multiple existence of homoclinic solutions for a periodically perturbed n dimensional autonomous differential equation with a degenerate homoclinic solution of degeneracy degree d known results were obtained with a functional perturbation which is regarded as an infinite dimensional parameter in this paper we consider a single parameter perturbation a special form of former s functional perturbation and prove that the single parameter is enough to unfold all possibilities of linearly independent homoclinic solutions bifurcated from the unperturbed degenerate homoclinic one which actually improves the known results furthermore we prove that those homoclinic solutions are all transversal showing co existence of multiple chaotic motions

full velocity difference model for a car following theory in this paper we present a full velocity difference model for a car following theory based on the previous models in the literature to our knowledge the model is an improvement over the previous ones theoretically because it considers more aspects in car following process than others this point is verified by numerical simulation then we investigate the property of the model using both analytic and numerical methods and find that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion

traffic bottleneck characteristics caused by the reduction of lanes in an optimal velocity model abstract in this paper the lane reduction bottleneck is investigated using the optimal velocity model in which two kinds of vehicles fast and slow are introduced the asymmetric lane changing rules in the slowdown section and the lane squeezing behaviors at the bottleneck are taken into account under the periodic boundary condition the numerical simulations are performed the traffic states change with increasing density and an interesting phenomenon of ratio inversion appears when the current saturates the headway and velocity discontinuously vary with the position in addition traffic patterns and the phase transition points depend greatly on the speed limit and the length of the slowdown section

the theoretical analysis of the lattice hydrodynamic models for traffic flow theory abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but also connected with the microscopic car following model closely the modified korteweg de vries mkdv equation related to the density wave in a congested traffic region has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail for the car following model we devote ourselves to obtaining the kdv equation from the original lattice hydrodynamic models and the kdv soliton solution to describe the traffic jam especially we obtain the general soliton solution of the kdv equation and the mkdv equation we review several lattice hydrodynamic models which were proposed recently we compare the modified models and carry out some analysis numerical simulations are conducted to demonstrate the nonlinear analysis results

effect of looking backward on traffic flow in an extended multiple car following model abstract in this paper a new car following model is proposed by incorporating the backward looking effect under certain conditions and multiple information of preceding cars in traffic flow and the neutral stability condition of this model can be obtained by using the linear stability theory numerical simulation shows that the proposed model is theoretically an improvement over previous ones