aspects of total variation regularized l1 function approximation the total variation based image denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 has been generalized and modified in many ways in the literature one of these modifications is to use the l1 norm as the fidelity term we study the interesting consequences of this modification especially from the point of view of geometric properties of its solutions it turns out to have interesting new implications for data driven scale selection and multiscale image decomposition

bifurcation phenomena in the optimal velocity model for traffic flow in the optimal velocity model with a time lag we show that there appear multiple exact solutions in some ranges of car density describing a metastable uniform flow a metastable congested flow and an unstable congested flow this establishes the presence of subcritical hopf bifurcations our analytical results have implications for continuum traffic flow such as hysteresis phenomena associated with discontinuous transitions between uniform and congested flow

local lyapunov exponents in chaotic systems abstract we define a local lyapunov exponent in chaotic systems so that the lyapunov exponent along a trajectory is the integral over the local exponent thus extending previously used short time lyapunov exponents to a pointwise definition calculations are presented for the dissipative lorenz system the conservative chirikov taylor standard map and a 3d volume preserving flow of interest in magnetohydrodynamics

an extended continuum traffic model with the consideration of the optimal velocity difference abstract in this letter we derived an extended continuum model from a car following model with consideration of the optimal velocity difference called the relative optimal velocity via employing the transformation relation from microscopic variables to macroscopic ones the stability condition of this continuum traffic model is obtained by performing linear stability analysis results show that the optimal velocity difference helps to improve the stability of traffic flow we make use of the upwind finite difference scheme for simulation the effects of the optimal velocity difference the relative optimal velocity and the velocity difference the optimal velocity on local clustering effect and instability are studied and compared each other respectively the spatiotemporal evolution patterns of traffic flow for the different initial density strength of the optimal velocity difference and the velocity difference are obtained their space time diagrams reveal the local clustering effect induced by the instability of traffic flow and generate the stop go traffic jams numerical simulation result indicates the unstable region is shrunken under the effect of the optimal velocity difference the relative optimal velocity and or the velocity difference the optimal velocity

dynamics stability and statistics on lattices and networks these lectures aim at surveying some dynamical models that have been widely explored in the recent scientific literature as case studies of complex dynamical evolution emerging from the spatio temporal organization of several coupled dynamical variables the first message is that a suitable mathematical description of such models needs tools and concepts borrowed from the general theory of dynamical systems and from out of equilibrium statistical mechanics the second message is that the overall scenario is definitely reacher than the standard problems in these fields for instance systems exhibiting complex unpredictable evolution do not necessarily exhibit deterministic chaotic behavior i e lyapunov chaos as it happens for dynamical models made of a few degrees of freedom in fact a very large number of spatially organized dynamical variables may yield unpredictable evolution even in the absence of lyapunov instability such a mechanism may emerge from the combination of spatial extension and non

darboux transformation and explicit solutions for two integrable equations a new n fold darboux transformation for two integrable equations is constructed with the help of a gauge transformation for the spectral problem proposed by qiao z j qiao phys lett a 192 1994 316 322 by the darboux transformation explicit soliton and multi soliton solutions for the two equations are obtained in particular soliton and complexiton solutions are shown through some figures

linear stability and nonlinear analyses of traffic waves for the general nonlinear car following model with multi time delays abstract in this paper the general nonlinear car following model with multi time delays is investigated in order to describe the reactions of vehicle to driving behavior platoon stability and string stability criteria are obtained for the general nonlinear car following model burgers equation and korteweg de vries kdv equation and their solitary wave solutions are derived adopting the reductive perturbation method we investigate the properties of typical optimal velocity model using both analytic and numerical methods which estimates the impact of delays about the evolution of traffic congestion the numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion

some qualitative properties for the total variation flow we prove the existence of a finite extinction time for the solutions of the dirichlet problem for the total variation flow for the neumann problem we prove that the solutions reach the average of its initial datum in finite time the asymptotic profile of the solutions of the dirichlet problem is also studied it is shown that the profiles are nonzero solutions of an eigenvalue type problem that seems to be unexplored in the previous literature the propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p laplacian operator finally the study of the radially symmetric case allows us to point out other qualitative properties that are peculiar of this special class of quasilinear equations

the total variation flow in rn the purpose of this chapter is to prove existence and uniqueness of the minimizing total variation flow in n frac partial u partial t div left frac du left du right right in left 0 infty right times mathbb r n 3 1 coupled with the initial condition u 0 x u 0 x text x in mathbb r n 3 2 when u0 l loc 1 l n

bifurcation analysis of a class of car following traffic models abstract we consider a follow the leader traffic model describing the dynamics of n cars on a circular road where each car driver chooses his acceleration according to a certain law the model is represented by a nonlinear system of ode s this model is known to have a solution with constant velocities and headways which in a certain parameter regime is stable varying the density of the cars we prove that the loss of stability is generally due to a hopf bifurcation also we investigate numerically the global bifurcation diagram for periodic solutions and obtain a complete picture of the dynamics of general optimal velocity models finally some analytical results on the stability of solutions in the case of non equal drivers are given

least squares shadowing sensitivity analysis of chaotic limit cycle oscillations abstract the adjoint method among other sensitivity analysis methods can fail in chaotic dynamical systems the result from these methods can be too large often by orders of magnitude when the result is the derivative of a long time averaged quantity this failure is known to be caused by ill conditioned initial value problems this paper overcomes this failure by replacing the initial value problem with the well conditioned least squares shadowing lss problem the lss problem is then linearized in our sensitivity analysis algorithm which computes a derivative that converges to the derivative of the infinitely long time average we demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations

analysis of optimal velocity model with explicit delay we analyze the optimal velocity model ovm with explicit delay the properties of congestion and the delay time of car motion are investigated by analytical and numerical methods it is shown that the small explicit delay time has almost no effects in the case of the large explicit delay time a new phase of congestion pattern of ovm seems to appear

total variation time flow with quantile regression for image restoration abstract we analyze the time flow of a modification of the standard rudin osher fatemi rof model for image restoration using the bounded variation semi norm the solution of the minimization problem is a restored image in the space of bounded variation bv recovered from a corrupted one and the functional may include a more general term s x u rather than the l 2 penalty term as used in the original rof model these new models were introduced in osher and scherzer 2004 31 in particular we will examine the non differentiable quantile regression penalty we will define an appropriate weak solution of the time flow and in particular prove the existence in l 0 b v and l stability

bifurcations and multiple traffic jams in a car following model with reaction time delay we investigate an optimal velocity car following model for n cars on a circular singlelane road where reaction time delay of drivers is taken into account the stability of the uniform ow equilibrium is studied analytically while bifurcating periodic solutions for difierent wave numbers are investigated with numerical continuation techniques this reveals that the periodic solution with the smallest wave number may be stable and all other periodic solutions are unstable as n is increased periodic solutions develop stop and go fronts that correspond to rapid deceleration and acceleration between regions of uniformly owing and stagnant tra c in terms of the positions of all cars on the ring these fronts are associated with tra c jams all tra c jams form a tra c pattern that evolves under time due to slow motion of the fronts the tra c pattern corresponding to the stable periodic motion of cars is the only stable one however we flnd that other periodic orbits may be unstable only so weakly that they give rise to transient tra c jams that may persist for long times eventually such tra c jams either merge with one another or disperse until the stable tra c pattern is reached

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

decomposition of images by the anisotropic rudin osher fatemi model the total variation based image denoising model of rudin osher and fatemi can be generalized in a natural way to favor certain edge directions we consider the resulting anisotropic energies and study properties of their minimizers 2004 wiley periodicals inc

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

ergodic properties of the lozi mappings in this paper we construct the bowen ruelle measure for the lozi mapping an almost everywhere hyperbolic diffeomorphism of the plane we also derive some of its properties which are similar to those of an axiom a system

one dimensional unstable eigenfunction and manifold computations in delay differential equations in this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation this is used to obtain the necessary starting data for an established algorithm for computing one dimensional 1d unstable manifolds of an associated saddle fixed point of a suitable poincare map to illustrate our method we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase conjugate feedback

anomalous lyapunov spectrum in globally coupled oscillators abstract numerical experiments of a globally coupled oscillator system show that one type of collective chaos of high dimension has discrete and continuous parts in its lyapunov spectrum this occurs in a scattered state i e a state in which no two oscillators behave identically it is argued from a consideration of the phase space structure that the discrete exponents are related to in a sense the macroscopic dynamics while the continuous part reflects the microscopic dynamics this type of high dimensional chaos is compared to a second type possessing an apparently continuous part only preceding the appearance of the first type we found a sequence of bifurcations of collective low dimensional behavior in scattered states and their investigation reveals the route to the first type of the high dimensional chaos

hydrodynamic lyapunov modes in coupled map lattices in this paper numerical and analytical results are presented which indicate that hydrodynamic lyapunov modes hlms also exist for coupled map lattices cmls the dispersion relations for the hlms of cmls are found to fall into two different universality classes it is characterized by lambda approximately k for coupled standard maps and lambda approximately k2 for coupled circle maps the conditions under which hlms can be observed are discussed the role of the hamiltonian structure conservation laws translational invariance and damping is elaborated our results are as follows 1 the hamiltonian structure is not a necessary condition for the existence of hlms 2 conservation laws or the translational invariance alone cannot guarantee the existence of hlms 3 including a damping term in the system of coupled hamiltonian maps does not destroy the hlms the lambda k dispersion relation of hlms however changes to the universality class with lambda k2 under damping in contrast no hlms survives in the system of coupled circle maps under damping 4 an on site potential destroys the hlms 5 the study of zero value lyapunov exponents les and associated lyapunov vectors lvs shows that translational invariance and conservation laws play different roles in the tangent space dynamics 6 the dynamics of the coordinate and momentum parts of lvs in hamiltonian systems are related but different furthermore numerical results for a two dimensional system show that the appearance of hlms in cmls is not restricted to the one dimensional case

numerical stability analysis of a large scale delay system modeling a lateral semiconductor laser subject to optical feedback this paper highlights the use of advanced numerical tools to study the stability of large scale systems of delay differential equations ddes specifically we consider a model describing a semiconductor laser subject to conventional optical feedback and lateral carrier diffusion the symmetry of the governing rate equations allows external cavity mode solutions ecms to be computed as steady state solutions using the software package dde biftool branches of ecms are computed as a function of varying feedback strength the stability along these branches is computed by solving eigenvalue problems the size of which is governed by a step length heuristic in this paper we employ an improved heuristic which substantially reduces the size of these eigenvalue problems this approach makes the stability analysis of large scale systems of ddes computationally feasible

lyapunov modes in hard disk systems we consider simulations of a two dimensional gas of hard disks in a rectangular container and study the lyapunov spectrum near the vanishing lyapunov exponents to this spectrum are associated eigen directions called lyapunov modes we carefully analyze these modes and show how they are naturally associated with vector fields over the container we also show that the lyapunov exponents and the coupled dynamics of the modes where it exists follow linear laws whose coefficients only depend on the density of the gas but not on aspect ratio and very little on the boundary conditions

digital filters as absolute norm regularizers a variational formulation of the digital filtering problem based on a certain regularizing functional is presented in particular the special case where the regularizing functional is defined by means of l sub 1 norm is considered and a characterization of its minima is presented it is shown that for a certain class of signals one solution to the regularization problem can be obtained by means of a suitable recursive median filter some examples and a possible extension of the variational approach are also discussed

a property of the minimum vectors of a regularizing functional defined by means of the absolute norm we consider a regularizing functional defined by means of the l sub 1 norm where the regularization is obtained using first differences as is well known such a functional can be put in relation with recursive median filters of appropriate window length we show that at least one of the minima is reached at a vector whose components have values over the same discrete set of the given signal this suggests a simple method to refine the approximate solution to the regularization problem which can be obtained with recursive median filters of increasing order we also report an example of application where the refinement method is employed for a signal detection problem

quasi periodic solution of the 2 1 dimensional boussinesq burgers soliton equation abstract a 2 1 dimensional bossinesq burgers soliton equation is proposed which has a affinitive connection with the boussinesq burgers soliton hierarchy through a natural nonlinearization of the boussinesq burgers s eigenvalue problems a finite dimensional hamiltonian system is obtained and is proved to be completely integrable in liouville sense the abel jacobi coordinates are constructed to straighten out the hamiltonian flows from which the quasi periodic solutions of the 2 1 dimensional boussinesq burgers equation are derived by resorting to the riemann theta functions

characterizing dynamics with covariant lyapunov vectors a general method to determine covariant lyapunov vectors in both discrete and continuous time dynamical systems is introduced this allows us to address fundamental questions such as the degree of hyperbolicity which can be quantified in terms of the transversality of these intrinsic vectors for spatially extended systems the covariant lyapunov vectors have localization properties and spatial fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the lyapunov exponents

quasi periodic solution of a new 2 1 dimensional coupled soliton equation a new 2 1 dimensional integrable soliton equation is proposed which has a close connection with the levi soliton hierarchy through the nonlinearization of the levi eigenvalue problems we obtain a finite dimensional integrable system the abel jacobi coordinates are constructed to straighten out the hamiltonian flows by which the solutions of both the 1 1 and 2 1 levi equations are obtained through linear superpositions an inversion procedure gives the quasi periodic solution in the original coordinates in terms of the riemann theta functions

estimation of lyapunov exponents of dynamical systems using a spatial average we present an unconventional method of estimating all of the lyapunov exponents of a dynamical system from either a known map or a set of experimental data rather than averaging exponents along a single trajectory we instead represent each exponent as an integral over all of phase space the contribution to each exponent calculated at each point in phase space is averaged spatially by weighting areas of high density more heavily than areas of low density according to the invariant measure of the system explicit formulas for approximating both the contributions to the exponents and the invariant measure are given and convergence results stated the techniques are illustrated in detail for the henon system

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

restricted flows of soliton hierarchies coupled kdv and harry dym case restricted flows of soliton hierarchies associated with the energy dependent schrodinger spectral problem are determined explicitly a remarkable connection with separable potentials is used for proving complete integrability of the restricted flows a previously unknown lagrangian and hamiltonian formulation of the neumann system is found whole families of generalizations of the neumann and garnier systems are given

updated semi discretization method for periodic delay differential equations with discrete delay an updated version of the semi discretization method is presented for periodic systems with a single discrete time delay the delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined stability charts are constructed for the damped and delayed mathieu equation for different time period time delay ratios the convergence of the method is investigated by examples stability charts are constructed for 1 and 2 degree of freedom milling models the codes of the algorithm are also attached in the appendix copyright 2004 john wiley sons ltd

metastable patterns in solutions of ut ϵ2uxx f u we consider the equation in question on the interval 0 x 1 having neumann boundary conditions with f u f u where f is a double well energy density with equal minima at u 1 the only stable states of the system are patternless constant solutions but given two phase initial data a pattern of interfacial layers typically forms far out of equilibrium the ensuing nonlinear relaxation process is extremely slow patterns persist for exponentially long times proportional to exp a l where a f 1 and l is the minimum distance between layers physically a tiny potential jump across a layer drives its motion we prove the existence and persistence of these metastable patterns and characterise accurately the equations governing their motion the point of view is reminiscent of center manifold theory a manifold parametrising slowly evolving states is introduced a neighbourhood is shown to be normally attracting and the parallel flow is characterised to high relative accuracy proofs involve a detailed study of the dirichlet problem spectral gap analysis and energy estimates

numerical bifurcation analysis of delay differential equations numerical methods for the bifurcation analysis of delay differential equations ddes have only recently received much attention partially because the theory of ddes smoothness boundedness stability of solutions is more complicated and less established than the corresponding theory of ordinary differential equations as a consequence no established software packages exist at present for the bifurcation analysis of ddes we outline existing numerical methods for the computation and stability analysis of steady state solutions and periodic solutions of systems of ddes with several constant delays

global bifurcation investigation of an optimal velocity traffic model with driver reaction time we investigate an optimal velocity model which includes the reflex time of drivers after an analytical study of the stability and local bifurcations of the steady state solution we apply numerical continuation techniques to investigate the global behavior of the system specifically we find branches of oscillating solutions connecting hopf bifurcation points which may be super or subcritical depending on parameters this analysis reveals several regions of multistability

quasi periodic solutions for some 2 1 dimensional integrable models generated by the jaulent miodek hierarchy some 2 1 dimensional integrable models including the modified kadomtsev petviashvili equation generated by the jaulent miodek hierarchy are investigated with the help of the jaulent miodek eigenvalue problem these 2 1 dimensional integrable models are separated into compatible hamiltonian systems of ordinary differential equations using the generating function flow method the involutivity and the functional independence of the integrals are proved the abel jacobi coordinates are introduced from which the quasi periodic solutions for these 2 1 dimensional integrable models are derived by resorting to the riemann theta functions pacs number 0230j

the problem of spurious lyapunov exponents in time series analysis and its solution by covariant lyapunov vectors we briefly recall the methods for the determination of lyapunov exponents from time series data and their limitations one particular problem is given by the fact that reconstructed phase spaces have usually extra dimensions compared to the true phase space of a dynamical system leading to extra so called spurious lyapunov exponents several methods to identify the true ones have been proposed which do not give satisfactory results we show that the geometric information contained in covariant lyapunov vectors can be used to identify the true exponents we illustrate its use and its limitations by applying it to experimental nmr laser data this article is part of a special issue of journal of physics a mathematical and theoretical devoted to lyapunov analysis from dynamical systems theory to applications

new finite dimensional integrable systems and explicit solutions of hirota satsuma coupled kortweg de vries equation the nonlinearization approach is extended to the hirota satsuma coupled kortweg de vries kdv equation associated with a 4 4 matrix spectral problem from which two new finite dimensional integrable hamiltonian systems are obtained in the liouville sense it is shown that the solutions of this coupled kdv equation are reduced to solving a compatible system of ordinary differential equations the reductions of the two hamiltonian systems and their separability are discussed an interesting connection between the two reduced hamiltonian systems in the case of one parameter and known two dimensional integrable systems is revealed as application some explicit solutions of the hirota satsuma coupled kdv equation are derived

invariant manifolds for metastable patterns in ut e2uxx f u we consider the above equation on the interval 0 x 1 subject to neumann boundary conditions with f u f u where f is a double well energy density function with equal minima our previous work 3 proved the existence and persistence of very slowly evolving patterns metastable states in solutions with two phase initial data here we characterise these metastable states in terms of the global unstable manifolds of equilibria as conjectured by fusco and hale 6

recursive median filters of increasing order a variational approach for a certain class of signals it is known that the recursive median filters provide a minimum of a related regularizing functional defined by means of the l sub 1 norm we generalize such results and we show that a good approximation to the minima of such a functional can be obtained for any signal by means of successive applications of recursive median filters of increasing order

weak dissipative effects on trajectories from the edge of basins of attraction abstract the purpose of this work is to present convergence properties of regular and chaotic conservative trajectories under small dissipation it is known that when subjected to dissipation stable periodic points become sinks attracting the surrounding trajectories which belong to rational irrational tori while chaotic trajectories converge to a chaotic attractor if it exists using the standard map and a mixed plot we show that this simple scenario can be rather complicated and strongly depends on the dissipation intensity for small dissipations the huge amount of attractors of the phase space generates a complicated and intricate dynamics where trajectories are steered to their attractors based on the local non hyperbolicity measured by the lyapunov vectors dissipation creates holes or attracting channels on the torus from the conservative limit and allows trajectories to penetrate it these holes are regions of large local hyperbolicity and are related to sticky channels reported recently for stronger dissipation sinks tend to attract all trajectories prevailing over the chaotic attractor

on the concept of stationary lyapunov basis we propose the concept of stationary lyapunov basis the basis of tangent vectors e i x defined at every point x of the attractor of the dynamical system and show that one can reformulate some algorithms for calculation of lyapunov exponents i so that eachi can be treated as the average of a function si x this enables one to use measure averaging in theoretical arguments thus proposing the rigorous basis for a number of ideas for calculation of lyapunov exponents from time series we also study how the lyapunov vectors in benettin s algorithm converge to the stationary basis and show that this convergence rate determines continuity of the field of stationary lyapunov vectors 1998 elsevier science b v

lyapunov vectors and assimilation in the unstable subspace theory and applications based on a limited number of noisy observations estimation algorithms provide a complete description of the state of a system at current time estimation algorithms that go under the name of assimilation in the unstable subspace aus exploit the nonlinear stability properties of the forecasting model in their formulation errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system the subspace spanned by lyapunov vectors with positive and zero exponents while the observational noise does not disturb the system along the stable directions the formulation of the aus approach in the context of four dimensional variational assimilation 4dvar aus and the extended kalman filter ekf aus and its application to chaotic models is reviewed in both instances the aus algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts as predicted by the theory when error dynamics is linear the optimal subspace dimension for 4dvar aus is given by the number of positive and null lyapunov exponents while the ekf aus algorithm using the same unstable and neutral subspace recovers the solution of the full ekf algorithm but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given this article is part of a special issue of journal of physics a mathematical and theoretical devoted to lyapunov analysis from dynamical systems theory to applications

the finite band solution of the jaulent miodek equation a method to construct the finite band solution to the soliton equation is presented we take the jaulent miodek equation as an example with the use of the nonlinearization of lax pair the jaulent miodek equation is decomposed into two finite dimensional integrable systems whose properties are studied from the view of an r matrix then through solving these finite dimensional integrable systems the finite band solution of the jaulent miodek equation is obtained

distribution of characteristic exponents in the thermodynamic limit the existence of the thermodynamic limit for the spectrum of the lyapunov characteristic exponents is numerically investigated for the fermi pasta ulam p model we show that the shape of the spectrum for energy density well above the equipartition threshold e allows the kolmogorov sinai entropy to be expressed simply in terms of the maximum exponent i the presence of a power law behaviour e is investigated the analogies with similar results obtained from the dynamics of symplectic random matrices seem to indicate the possibility of interpreting chaotic dynamics in terms of some universal properties

subcritical hopf bifurcations in a car following model with reaction time delay a nonlinear car following model of highway traffic is considered which includes the reaction time delay of drivers linear stability analysis shows that the uniform flow equilibrium of the system loses its stability via hopf bifurcations and thus oscillations can appear the stability and amplitudes of the oscillations are determined with the help of normal form calculations of the hopf bifurcation that also handles the essential translational symmetry of the system we show that the subcritical case of the hopf bifurcation occurs robustly which indicates the possibility of bistability we also show how these oscillations lead to spatial wave formation as can be observed in real world traffic flows

consensus problems with distributed delays with application to traffic flow models this paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics in the application problems the distributed delay whose kernel is a gamma distribution with a gap represents the human drivers behavior in the average the aim of the paper is to give a characterization of the regions in the corresponding delay parameter space where a consensus is reached for all initial conditions the structure and properties of the system are fully exploited which leads to explicit and computationally tractable expressions as a by product a stability theory for distributed delay systems with a gamma distribution kernel is developed also explicit expressions for the consensus function al of time delay systems with constant and distributed delays that solve a consensus problem are provided several illustrative examples complete the presentation

time series forecasting using a system of ordinary differential equations this paper presents a hybrid evolutionary method for identifying a system of ordinary differential equations odes to predict the small time scale traffic measurements data we used the tree structure based evolutionary algorithm to evolve the architecture and a particle swarm optimization pso algorithm to fine tune the parameters of the additive tree models for the system of ordinary differential equations we also illustrate some experimental comparisons with genetic programming gene expression programming and a feedforward neural network optimized using pso algorithm experimental results reveal that the proposed method is feasible and efficient for forecasting the small scale traffic measurements data

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

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

from synchronization to lyapunov exponents and back the goal of this paper is twofold in the first part we discuss a general approach to determine lyapunov exponents from ensemble rather than time averages the approach passes through the identification of locally stable and unstable manifolds the lyapunov vectors thereby revealing an analogy with generalized synchronization the method is then applied to a periodically forced chaotic oscillator to show that the modulus of the lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase synchronization the analytical calculations are carried out for a model the generalized special flow that we construct as a simplified version of the periodically forced rossler oscillator

on time flows of minimizers of general convex functionals of linear growth with variable exponent in bv space and stability of pseudosolutions here we examine a method of selective smoothing in image restoration in bv space using a variable exponent functional of linear growth variable exponent growth was suggested in p blomgren et al 1997 6 and in y chen et al 2006 8 the notion of a pseudosolution of the minimization problem is discussed as well as the proof of existence and uniqueness of the solution of the time flow for the associated time dependent pde here we prove stability for pseudosolutions while also discussing the case for more general convex functionals of linear growth and variable exponent for use as an approximation for the time flow other than that which is used in y chen et al 2006 8

asymptotic properties of linear filter for deterministic processes abstract it is known that kalman bucy filter is stable with respect to initial conditions under the assumptions of uniform complete controllability and uniform complete observability in this paper we prove the stability of kalman bucy filter for the case of noise free dynamical system i e for deterministic processes the earlier stability results cannot be applied for this case as the system is not controllable we further show that the optimal linear filter for a general class of non gaussian initial conditions is asymptotically proximal to kalman bucy filter it is also shown that the filter corresponding to non zero system noise in the limit of small system noise approaches the filter corresponding to zero system noise in the case of gaussian initial conditions