a rational spectral collocation method for solving a class of parameterized singular perturbation problems a new kind of numerical method based on rational spectral collocation with the sinh transformation is presented for solving parameterized singularly perturbed two point boundary value problems with one boundary layer by means of the sinh transformation the original chebyshev points are mapped onto the transformed ones clustered near the singular points of the problem the results from asymptotic analysis as regards the singularity of the solution are employed to determine the parameters in the transformation numerical experiments including several nonlinear cases illustrate the high accuracy and efficiency of our method

multiple paths extraction in images using a constrained expanded trellis single shortest path extraction algorithms have been used in a number of areas such as network flow and image analysis in image analysis shortest path techniques can be used for object boundary detection crack detection or stereo disparity estimation sometimes one needs to find multiple paths as opposed to a single path in a network or an image where the paths must satisfy certain constraints in this paper we propose a new algorithm to extract multiple paths simultaneously within an image using a constrained expanded trellis cet for feature extraction and object segmentation we also give a number of application examples for our multiple paths extraction algorithm

measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

singular perturbations for third order nonlinear multi point boundary value problem abstract this paper is devoted to study the following third order multi point singularly perturbed boundary value problem x t f t x t x t x t 0 0 t 1 0 1 x 0 0 ax 0 bx 0 i 1 n 2 i x i a cx 1 dx 1 i 1 n 2 i x i b where a b c d 0 a b r a b 0 c d 0 i 0 i 0 i 1 2 n 2 0 1 2 n 2 1 and 0 1 2 n 2 1 the existence uniqueness and asymptotic estimates of solutions of the boundary value problem are give by using priori estimates differential inequalities technique and leray schauder degree theory

automatic finding of main roads in aerial images by using geometric stochastic models and estimation this paper presents an automated approach to finding main roads in aerial images the approach is to build geometric probabilistic models for road image generation we use gibbs distributions then given an image roads are found by map maximum a posteriori probability estimation the map estimation is handled by partitioning an image into windows realizing the estimation in each window through the use of dynamic programming and then starting with the windows containing high confidence estimates using dynamic programming again to obtain optimal global estimates of the roads present the approach is model based from the outset and is completely different than those appearing in the published literature it produces two boundaries for each road or four boundaries when a mid road barrier is present

least squares spectral collocation for discontinuous and singular perturbation problems a least squares spectral collocation scheme for discontinuous problems is proposed for the first derivative operator the domain is decomposed in subintervals where the jumps are imposed at the discontinuities equal order polynomials are used on all subdomains for the discretization spectral collocation with chebyshev polynomials is employed fast fourier transforms are now available the collocation conditions and the interface conditions lead to an overdetermined system which can be efficiently solved by least squares the solution technique will only involve symmetric positive definite linear systems this approach is further extended to singular perturbation problems where least squares are used for stabilization by a suitable decomposition of the domain the boundary layer is well resolved numerical simulations confirm the high accuracy of our spectral least squares scheme

fractal properties of robust strange nonchaotic attractors in maps of two or more dimensions we consider the existence of robust strange nonchaotic attractors in a simple class of quasiperiodically forced systems rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box counting dimension d 0 is larger than their information dimension d 1 by 1 i e d 0 d 1 1 we also show how this property is manifested in numerical experiments

the pseudospectral method for third order differential equations generalized quadrature rules are derived which assist in the selection of collocation points for the pseudospectral solution of differential equations in particular it is shown that for an nth order differential equation in one space dimension with two point derivative boundary conditions an ideal choice of interior collocation points is the set of zeros of a jacobi polynomial the pseudospectral solution of a third order initial boundary value problem is considered and accuracy is assessed by examining how well the discrete eigenproblem approximates the continuous one convergence is established for a special choice of collocation points and numerical results are included to demonstrate the viability of the approach

fast structured direct spectral methods for differential equations with variable coefficients i the one dimensional case we study the rank structures of the matrices in fourier and chebyshev spectral methods for differential equations with variable coefficients in one dimension we show analytically that these matrices have a so called low rank property not only for constant or smooth variable coefficients but also for coefficients with steep gradients and or high variations large ratios in their maximum minimum function values we develop a matrix free direct spectral solver which uses only a small number of matrix vector products to construct a structured approximation to the original discretized matrix a without the need to explicitly form a this is followed by fast structured matrix factorizations and solutions the overall direct spectral solver has o n log 2 n complexity and o n memory requirement numerical tests for several important but notoriously difficult problems show the superior efficiency and accuracy of our direct spectral solver especially when iterative methods have severe difficulties

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

fractal distribution of floaters on a fluid surface and the transition to chaos for random maps abstract the long time spatial distribution of particles floating on the surface of a confined fluid whose flow velocity has complicated time dependence is considered it is shown that this distribution can be either a fractal or else can clump at several or one discrete points the transition from the latter type of distribution to the former occurs when the lyapunov exponent characterizing the particle motion passes through zero from negative values to positive values the characteristic features of this type of transition are investigated using random maps it is shown that near the transition there are extremely intermittent temporal fluctuations in the particle cloud and their scaling with a parameter is elucidated

intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven duffing oscillator different mechanisms for the creation of strange nonchaotic attractors snas are studied in a two frequency parametrically driven duffing oscillator we focus on intermittency transitions in particular and show that snas in this system are created through quasiperiodic saddle node bifurcations type i intermittency as well as through a quasiperiodic subharmonic bifurcation type iii intermittency the intermittent attractors are characterized via a number of lyapunov measures including the behavior of the largest nontrivial lyapunov exponent and its variance as well as through distributions of finite time lyapunov exponents these attractors are ubiquitous in quasiperiodically driven systems the regions of occurrence of various snas are identified in a phase diagram of the duffing system

simple approach to the creation of a strange nonchaotic attractor in any chaotic system a simple approach to the creation of a strange nonchaotic attractor in any chaotic system is described the main idea is to control the parameter of the system in such a manner that the system dynamics is expanding at some times but converging at others with this approach a strange nonchaotic attractor can be found in a large region in the parameter space near the boundaries between chaotic and regular phases or within the chaotic region far from the regular one the maximum nontrivial lyapunov exponent of the system can pass through zero nonsmoothly and cannot be fitted by a linear function

a computational method for solving third order singularly perturbed boundary value problems in this paper a new computational method is presented for solving a class of third order singularly perturbed boundary value problems with a boundary layer at the left of the underlying interval in this method first the given third order singularly perturbed boundary value problem is transformed into a system of two odes subject to suitable initial and boundary conditions and a zeroth order asymptotic expansion for the solution of the given problem is constructed then the reduced terminal value problem is solved analytically in the reproducing kernel space this method is effective and easy to implement a numerical examples is studied to demonstrate the accuracy of the present method results obtained by the method are found to be in good agreement with the exact solution not only in the boundary layer but also away from the layer

boundary layer resolving pseudospectral methods for singular perturbation problems pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary differential equations odes which possess boundary layers it is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions we introduce here a new effective procedure based on coordinate stretching and the chebyshev pseudospectral method to resolve the boundary layers stable and accurate results are obtained for very thin boundary layers with a fairly small number of spectral collocation points

some relations between dimension and lyapounov exponents we consider differentiable maps and compact invariant sets we introduce dimensional quantities related to the ergodic invariant measures and prove some simple relations

the calculation of lyapunov spectra abstract linearization around the chaotic orbits of dynamical systems offers good prospects for understanding complex systems the naturally available information that can be obtained from such studies are the magnitudes and directions in phase space of stretching and shrinking of an initial small sphere of realizations this information is a property of a time displacement matrix that relates the initial bundle of realizations to its later configuration in this paper we extract information from this matrix through its singular values and the associated orthogonal matrices this given an algebraic foundation to the geometric methods that have been used previously the equations of the orthogonal principal stretching and contraction directions show that asymptotically after a long time they depend only on the location in phase space and not on the orbit as an example we show that these directions sketch out the attractor of the lorenz model

strange nonchaotic attractors in the quasiperiodically forced logistic map different mechanisms for the creation of strange nonchaotic dynamics in the quasiperiodically forced logistic map are studied these routes to strange nonchaos are characterized through the behavior of the largest nontrivial lyapunov exponent as well as through the characteristic distributions of finite time lyapunov exponents strange nonchaotic attractors can be created at a saddle node bifurcation when the dynamics shows type i intermittency this intermittent transition which is studied in detail is characterized through scaling exponents band merging crises through which dynamics remains nonchaotic are also studied and correspondence is made with analogous behavior in the unforced logistic map robustness of these phenomena with respect to additive noise is investigated s1063 651x 98 10302 1

on coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term in this paper we prove the existence of the solution to the mixed problem for coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of the solution

experimental observation of dynamics near the torus doubling terminal critical point a nonlinear electronic circuit driven by two signals with golden mean frequency ratio is studied we have observed different dynamical regimes including tori doubled tori strange nonchaotic attractors and chaos which all meet together at the critical point terminating the torus doubling bifurcation curve tdt point in the parameter plane of the system the parameter plane arrangement spectra and portraits of attractors observed in the experiment are in reasonable coincidence with numerical computations for a quasiperiodically forced logistic map where the tdt critical point originally has been found and studied theoretically s kuznetsov a pikovsky and u feudel phys rev e 57 1585 1998

singular continuous spectra in dissipative dynamics we demonstrate the occurrence of regimes with singular continuous fractal fourier spectra in autonomous dissipative dynamical systems the particular example is an ordinary differential equation system at the accumulation points of bifurcation sequences associated with the creation of complicated homoclinic orbits two different mechanisms responsible for the appearance of such spectra are proposed in the first case when the geometry of the attractor is symbolically represented by the thue morse sequence both the continuous time process and its discrete poincar e map have singular power spectra the other mechanism is due to the logarithmic divergence of the first return times near the saddle point here the poincar e map possesses the discrete spectrum while the continuous time process displays the singular one a method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual fourier analysis technique

the birth of strange nonchaotic attractors abstract a mechanism is described for the development of strange nonchaotic attractors from two frequency quasiperiodic attractors in quasiperiodically driven maps this mechanism is intimately tied to the phenomenon of torus doubling the transition to strange nonchaotic behavior occurs when a period doubled torus collides with its unstable parent torus as the collision is approached the period doubled torus becomes extremely wrinkled ultimately becoming fractal at the collision the lyapunov exponent remains negative through the collision these collisions are shown to be a new type of attractor merging crisis the new feature is the possibility of nonchaotic attractors taking part in the crisis this mechanism is illustrated via numerical and analytical studies of a quasiperiodically driven logistic map

reduction of the synchronization time in random logistic maps we report on the effects of additive noises in a nonchaotic logistic map in this system the lyapunov exponent changes from negative to positive as the noise intensity is increased when the lyapunov exponent is negative the synchronization of orbits with different initial conditions occurs we find that the synchronization time cannot be determined solely by the lyapunov exponent when the noise intensity is greater than a point at which the lyapunov exponent is minimum we show that this reduction of the synchronization time is attributed to initial nonstationary behaviors where the critical point of the logistic map plays an important role

circular shortest path in images abstract shortest path algorithms have been used in a number of applications such as crack detection road or linear feature extraction in images there are applications where the starting and ending positions of the shortest path need to be constrained in this paper we present several new algorithms for the extraction of a circular shortest path in an image such that the starting and ending positions coincide the new algorithms we developed include multiple search algorithm image patching algorithm multiple backtracking algorithm the combination of image patching and multiple back tracking algorithm and approximate algorithm the typical running time of our circular shortest path extraction algorithm on a 256 256 image is about 0 3 s on a rather slow 85 mhz sun sparc computer a variety of real images for crack detection in borehole data and object boundary extraction have been tested and good results have been obtained

asymptotic and numerical analysis of singular perturbation problems a survey this paper is intended to be a brief survey of the asymptotic and numerical analysis of singular perturbation problems the purpose is to find out what problems are treated and what numerical asymptotic methods are employed with an eye toward the goal of developing general methods to solve such problems a summary of the results of some recent methods is presented and this leads to conclusions and recommendations about what methods to use on singular perturbation problems finally some areas of current research are indicated a bibliography of about 130 items is provided

pseudospectral solution of near singular problems using numerical coordinate transformations based on adaptivity the work presented here describes a method of coordinate transformation that enables spectral methods to be applied efficiently to differential problems with steep solutions the approach makes use of the adaptive finite difference method presented by huang and sloan siam j sci comput 15 1994 pp 776 797 this method is applied on a coarse grid to obtain a rough approximation of the solution and a suitable adapted mesh the adaptive finite difference solution permits the construction of a smooth coordinate transformation that relates the computational space to the physical space the map between the spaces is based on chebyshev polynomial interpolation finally the standard pseudospectral ps method is applied to the transformed differential problem to obtain highly accurate nonoscillatory numerical solutions numerical results are presented for steady problems in one and two space dimensions

a computational method for solving boundary value problems for third order singularly perturbed ordinary differential equations singularly perturbed two point boundary value problems spbvps for third order ordinary differential equations odes with a small parameter multiplying the highest derivative are considered a numerical method is suggested in this paper to solve such problems in this method the given bvp is transformed into a system of two odes subject to suitable initial and boundary conditions then the domain of definition of the differential equation a closed interval is divided into two sub intervals which we call the inner region boundary layer and the outer region then the de is solved in these intervals separately the solutions obtained in these intervals are combined to give the solution in the whole interval to obtain boundary conditions at the transition points boundary values inside this interval we use mostly the zeroth order asymptotic expansion of the solution of the bvp or a suitable asymptotic expansion solution first the linear equations are considered and then the semi linear equations to solve semi linear equations newton s method of quasi linearisation is applied examples are provided to illustrate the method the method is easy to implement and suitable for parallel computing

mappings and accuracy for chebyshev pseudo spectral approximations abstract the effect of mappings on the approximation by chebyshev collocation of functions which exhibit localized regions of rapid variation is studied a general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials a particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in applications it is shown that the mapped function can be approximated much more accurately by chebyshev polynomial approximations than the original function the effect on the approximation of introducing subdomains is also studied the accuracy of the pseudo spectral approximation is very sensitive to the location of the interface although this sensitivity is reduced when mappings are employed within the subdomains

an asymptotic numerical fitted mesh method for singularly perturbed third order ordinary differential equations of reaction diffusion type singularly perturbed boundary value problems spbvps for third order ordinary differential equations odes with a small parameter multiplying the highest derivative of the form ey x b x y x c x y x f x y 0 p y 0 q y 1 r where b x c x and f x are sufficiently smooth functions satisfying certain conditions are considered firstly this third order singularly perturbed boundary value problem spbvp is transformed into equivalent problem of weakly coupled system of one first order and one second order ode with a small parameter multiplying the highest derivative of the second order ode subject to initial and boundary conditions respectively a computational method is suggested in this paper to solve this system in this method we first find the zero order asymptotic expansion approximation of the solution of the weakly coupled system then this system is decoupled by approximating the first component of the solution by its zero order asymptotic expansion approximation in the second equation finally the second equation is solved by the fitted mesh method j j h miller e o riordan g i shishkin in error estimates in the maximum norm for linear problems in one and two dimensions world scientific singapore 1996 numerical experiments are conducted

an asymptotic numerical method for singularly perturbed third order ordinary differential equations of convection diffusion type abstract singularly perturbed two point boundary value problems spbvps for third order ordinary differential equations odes with a small parameter multiplying the highest derivative are considered a numerical method is suggested in this paper to solve such problems in this method the given bvp is transformed into a weakly coupled system of two odes subject to suitable initial and boundary conditions then the computational method presented in this paper is applied to this system in this method we reduce the weakly coupled system into a decoupled system then to solve this decoupled system numerically we apply a boundary value technique bvt in which the domain of definition of the differential equation is divided into two nonoverlapping subintervals called inner and outer regions then we solve the decoupled system over these regions as two point boundary value problems an exponentially fitted finite difference scheme is used in the inner region and a classical finite difference scheme in the outer region the boundary conditions at the transition point are obtained using the zero order asymptotic expansion approximation of the solution of the problem this computational method is distinguished by the facts that the decoupling reduces the computational time very much and it is well suited for parallel computing this method can be extended to a system of two ordinary differential equations of which one is of first order and the other is of second order numerical examples are given to illustrate the method

characterization of noise induced strange nonchaotic attractors received 17 january 2006 revised manuscript received 30 march 2006 published 17 july 2006strange nonchaotic attractors snas were previously thought to arise exclusively in quasiperiodic dynami cal systems a recent study has revealed however that such attractors can be induced by noise in nonquasi periodic discrete time maps or in periodically driven ows in particular in a periodic window of such asystem where a periodic attractor coexists with a chaotic saddle nonattracting chaotic invariant set none ofthe lyapunov exponents of the asymptotic attractor is positive small random noise is incapable of causingcharacteristic changes in the lyapunov spectrum but it can make the attractor geometrically strange bydynamically connecting the original periodic attractor with the chaotic saddle here we present a detailed studyof noise induced snas and the characterization of their properties numerical calculations reveal that thefractal dimensions of noise induced snas typically assume fractional values in contrast to snas in quasip eriodically driven systems whose dimensions are integers an interesting nding is that the uctuations of the nite time lyapunov exponents away from their asymptotic values obey an exponential distribution thegenerality of which we are able to establish by a theoretical analysis using random matrices we suggest apossible experimental test we expect noise induced snas to be general doi 10 1103 physreve 74 016203 pacs number s 05 45 gg

strange attractors that are not chaotic abstract it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic here we use the word strange to refer to the geometry or shape of the attracting set while the word chaotic refers to the dynamics of orbits on the attractor in particular the exponential divergence of nearby trajectories we first give examples for which it can be demonstrated that there is a strange nonchaotic attractor these examples apply to a class of maps which model nonlinear oscillators continuous time which are externally driven at two incommensurate frequencies it is then shown that such attractore are persistent under perturbations which preserve the original system type i e there are two incommensurate external driving frequencies this suggests that for systems of the typw which we have considered nonchaotic strange attractors may be expected to occur for a finite interval of parameter values on the other hand when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit thus we conjecture that in general continuous time systems flows which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space

synchronization of strange nonchaotic attractors strange nonchaotic attractors snas which are realized in many quasiperiodically driven nonlinear systems are strange geometrically fractal but nonchaotic the largest nontrivial lyapunov exponent is negative two such identical independent systems can be synchronized by in phase driving because of the negative lyapunov exponent the systems converge to a common dynamics which because of the strangeness of the underlying attractor is aperiodic this feature which is robust to external noise can be used for applications such as secure communication a possible implementation is discussed and its performance is evaluated the use of snas rather than chaotic attractors can offer some advantages in experiments involving synchronization with aperiodic dynamics

the asymptotic solution of a class of third order boundary value problems arising in the theory of thin film flows this paper studies boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third order boundary value problems which govern the motion of thin liquid films subject to viscous capillary and gravitational forces precise conditions specifying where and when the third order derivative terms in the differential equations can be neglected are derived and improved estimates for the actual solutions in terms of solutions of the lower order models are constructed the paper also contains a technique for replacing a third order problem with an asymptotically equivalent second order one that may have wider applicability

rational spectral collocation and differential evolution algorithms for singularly perturbed problems with an interior layer abstract we are concerned with using high accuracy numerical methods for solving singularly perturbed problems whose solutions exhibit an interior layer a rational spectral collocation method in barycentric form with sinh transformation is firstly applied to find the approximate solution to the given problem the sinh transformation consists of two parameters the location and the width of the interior layer with the tool of the asymptotic analysis the interior layer can be easily located then in determining the width of the interior layer we design a nonlinear unconstrained optimization problem which is solved by using the basic differential evolution de algorithm the feasibility and effectiveness of the proposed method is verified by numerical results the proposed method can also be applied to other singularly perturbed problems

a survey of numerical techniques for solving singularly perturbed ordinary differential equations this survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of the ideas and methods of singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the numerical methods developed by numerous researchers after 1984 2000 the work done in this area during the period 1905 1984 has already been surveyed by the first author of this paper see appl math comput 30 1989 223 for details due to the space constraints we have covered only singularly perturbed one dimensional problems

birth of strange nonchaotic attractors due to interior crisis abstract we study the interior crisis in the period 3 window of the quasiperiodically forced logistic map two routes from quasiperiodicity to chaos involving strange nonchaotic attractors sna are discovered along one route we observe a sudden widening of the sna this is similar to the interior crisis in chaotic systems along the other route we find a direct transition from an invariant curve to a strange nonchaotic attractor exactly at the interior crisis point this is a new mechanism of the appearance of strange nonchaotic attractors beyond the interior crisis the temporal behavior can be described as a crisis induced intermittency whose scaling behavior is discussed

comment on strange nonchaotic attractors in autonomous and periodically driven systems the problem of the existence of strange nonchaotic attractors sna s in autonomous systems is discussed it is demonstrated that the recently reported example of a sna in an autonomous system v s anishchenko et al phys rev e 54 3231 1996 is in fact a chaotic attractor with positive largest lyapunov exponent

membrane boundary extraction using circular multiple paths membrane proteins represent over 50 of known drug targets accordingly several widely used assays in the high content analysis area rely on quantitative measures of the translocation of proteins between intracellular organelles and the cell surface in order to increase the sensitivity of these assays one needs to measure the signal specifically along the membrane requiring a precise segmentation of this compartment manual tracing of membrane boundary is very time consuming and confronts us with issues of objectivity and reproducibility in this paper we present an approach based on a circular multiple paths technique on transformed images that enables us to segment the membrane compartment accurately and rapidly we have presented three approaches for image transformation the circular property of the multiple paths ensures that we are obtaining closed contours for the membrane boundary the position of the multiple paths provides the edges of the membrane boundary the effectiveness of our algorithm is illustrated using cells expressing epitope tagged membrane proteins

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

interactive segmentation of non star shaped contours by dynamic programming in this paper we present the rack algorithm for the detection of optimal non star shaped contours in images it is based on the combination of a user driven image transformation and dynamic programming the fundamental idea is to interactively specify and edit the general shape of the desired object by using a rack this rack is used to model the image as a directed acyclic weighted graph that contains a path corresponding to the expected contour in this graph the shortest path with respect to an adequate cost function can be calculated efficiently via dynamic programming the experimental results indicate the algorithm s ability of combining an acceptable amount of user interaction with generally good segmentation results

interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map mechanisms and their characterizations a simple quasiperiodically forced one dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors snas in a two parameter a ensuremath f space the routes include transitions to chaos via snas from both a one frequency torus and a period doubled torus in the former case we identify the fractalization and type i intermittency routes in the latter case we point out that at least four distinct routes for the truncation of the torus doubling bifurcation and the creation of snas occur in this model in particular the formation of snas through heagy hammel fractalization and type iii intermittent mechanisms is described in addition it has been found that in this system there are some regions in the parameter space where a dynamics involving a sudden expansion of the attractor which tames the growth of period doubling bifurcation takes place creating the sna the snas created through different mechanisms are characterized by the behavior of the lyapunov exponents and their variance by the estimation of the phase sensitivity exponent and through the distribution of finite time lyapunov exponents

singularly perturbed third order boundary value problem for nonlinear systems abstract this paper deals with the existence of solutions to a singularly perturbed boundary value problem for third order nonlinear differential systems the authors construct an appropriate generalized lower solution upper solution pair a concept that is defined in this paper and employ the method of descent nagumo conditions algebraic boundary layer functions and volterra type integral operator to guarantee the existence of solutions of the problem the uniformly valid asymptotic estimate of the solutions is given as well the differential systems has nonlinear dependence on all over order derivatives of the unknown

circular shortest paths by branch and bound shortest path algorithms are used for a large variety of optimisation problems in network and transportation analysis they are also used in image analysis for object segmentation disparity estimation path finding and crack detection sometimes the topology of the problem demands that the path be circular such circular path constraints occur in polar object segmentation disparity estimation for panoramic stereo images and in shortest paths around a cylinder in this paper we present a new efficient algorithm for circular shortest path determination on a u by v trellis in o u 1 6 v average time we impose a binary search tree on the set of path endpoints and use a best first branch and bound search technique to efficiently obtain the global minimum circular path the typical running time of our circular shortest path algorithm on a 256 times 256 image is in the order of 0 1 seconds on a 1ghz dell p3 workstation under the linux operating system applications to crack detection and object segmentation are presented

pole condition for singular problems the pseudospectral approximation abstract this paper deals with the pseudospectral solution of differential equations with coordinate singularities such as those which describe situations in spherical or cylindrical geometries we use the differential equation together with a smoothness assumption on the solution to construct pole conditions the pole conditions which are straightforward and easily implemented serve as numerical boundary conditions at the coordinate singularity standard pseudospectral methods including fast transformation techniques can then be applied to the singular problem the method is illustrated using the eigenvalue problem of bessel s equation and a poisson equation on the unit disk numerical results show that spectral convergence is achieved

noise induced unstable dimension variability and transition to chaos in random dynamical systems results are reported concerning the transition to chaos in random dynamical systems in particular situations are considered where a periodic attractor coexists with a nonattracting chaotic saddle which can be expected in any periodic window of a nonlinear dynamical system under noise the asymptotic attractor of the system can become chaotic as characterized by the appearance of a positive lyapunov exponent generic features of the transition include the following 1 the noisy chaotic attractor is necessarily nonhyperbolic as there are periodic orbits embedded in it with distinct numbers of unstable directions unstable dimension variability and this nonhyperbolicity develops as soon as the attractor becomes chaotic 2 for systems described by differential equations the unstable dimension variability destroys the neutral direction of the flow in the sense that there is no longer a zero lyapunov exponent after the noisy attractor becomes chaotic and 3 the largest lyapunov exponent becomes positive from zero in a continuous manner and its scaling with the variation of the noise amplitude is algebraic formulas for the scaling exponent are derived in all dimensions numerical support using both low and high dimensional systems is provided

invariant graphs for forced systems abstract many applications of nonlinear dynamics involve forced systems we consider the case where for a fixed input the driven system is contracting this is for instance the situation in certain classes of filters and in the study of synchronization when such contraction is uniform it is well known that there exists a globally attracting invariant set which is the graph of a function from the driving state space to the driven state space if the contraction is sufficiently strong then is smooth we describe the theoretical framework for such results and discuss a number of applications to the filtering of time series to synchronization and to quasiperiodically forced systems we go on to give recent generalizations to the case of non uniform contraction that is contraction measured by lyapunov exponent like quantities we conclude with a number of new results for quasiperiodic forcing a corollary of these is that a strange non chaotic attractor for such a system cannot be the graph of a continuous function nor roughly speaking can it have as open attracting neighbourhood in other words its closure must contain some repelling orbits

fractalization of a torus as a strange nonchaotic attractor fractalization of a torus and its transition to chaos in a quasiperiodically forced logistic map is reinvestigated in relation to a strange nonchaotic attractor with the aid of a functional equation for the invariant curve the existence of a fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor as well as the fourier mode analysis mechanisms of the onset of a fractal torus and the transition to chaos are studied in connection with the intermittency

intermittency route to strange nonchaotic attractors in a non skew product map whether strange nonchaotic attractors snas can typically arise in non skew product maps has been a crucial question for more than two decades recently it was shown that snas arise in a particular non skew product map related to quasiperiodically driven continuous dynamical systems r badard chaos solitons fractals 28 1327 2006 chaos 18 023127 2008 in the present paper we derive badard s non skew product map from a periodically driven continuous dynamical system with spatially quasiperiodic potential and investigate onset mechanisms of snas in the map in particular we focus on a transition route to intermittent snas where snas appear after pair annihilations of stable and unstable fixed points located on a ring shaped invariant curve then the mean residence time and rotation numbers have a logarithmic singularity finally we discuss the existence of snas in a special class of non skew product maps

further examples of the boundary value technique in singular perturbation problems illustration de la technique des valeurs frontieres dans les problemes a perturbations singulieres par des exemples varies

singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations abstract this article shows the existence uniqueness and asymptotic estimates of solutions of the singularly perturbed boundary value problems for a class of the third order nonlinear ordinary differential equations with a small parameter e 0 ey x y y e satisfying the condition y 0 0 y 1 0 y 1 0 or y 0 0 y 1 0 y 1 0

singularly perturbed problems in partial differential equations a survey this survey paper contains a surprisingly large amount of material on singularly perturbed partial differential equations and indeed can serve as an introduction to some of the ideas and methods of the singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the methods developed by numerous researchers after 1980 2000 in this review we have covered singularly perturbed partial differential equations about odes the survey has already been done by us see m k kadalbajoo k c patidar appl math comput 130 2002 457 510

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

a rational spectral collocation method for third order singularly perturbed problems a new numerical method is developed for solving a class of third order singularly perturbed boundary value problems first of all the given problem is transformed into a system of two ordinary differential equations odes subject to suitable initial and boundary conditions then the rational spectral collocation method in barycentric form with sinh transformation is applied to solve the system of odes according to the asymptotic analysis the location and width of boundary layer of the given problem which are chosen as parameters in the sinh transformation can be determined ample numerical experiments are presented to illustrate the computational efficiency and accuracy of the our method

on the characterization of non stationary chaotic systems autonomous and non autonomous cases abstract properties of non stationary dynamical systems are studied using the concept of a snapshot attractor which takes into account a large number of initial conditions within the basin of attraction in this paper both autonomous and non autonomous systems are considered we have discussed three different ways of inducing non stationarity in a chaotic system a when the parameter changes in a linear fashion b when the parameter changes in a random fashion and c when it is governed by an equation inducing a chaotic change in it here all the variations are with respect to time though the first and second situations have already been considered in romeiras et al 1990 1 and serquina et al 2008 2 the last one has never been considered before in each case the basic fractal properties and the famous pesin identity are proved numerically the lyapunov exponents which are calculated via an averaging procedure lead to the expected values

a rational spectral collocation method with adaptively transformed chebyshev grid points a spectral collocation method based on rational interpolants and adaptive grid points is presented the rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed chebyshev points the locations of the grid points are adapted to singularities of the underlying solution and the locations of these singularities are approximated by the locations of poles of chebyshev pade approximants numerical experiments on two time dependent problems one with finite time blow up and one with a moving front indicate that the method far outperforms the standard chebyshev spectral collocation method for problems whose solutions have singularities in the complex plane close to 1 1

dynamic refinement algorithms for spectral element methods abstract a numerical method is presented that combines high order domain decomposition and adaptive mesh refinement the spatial discretization is based on a nonconforming spectral element method meshes are generated by adaptive refinement of a quadtree using either local solution gradients or the local polynomial spectrum as a refinement criteria the method is applied to solve scalar test problems and to simulate the flow in a lid driven cavity at moderate reynolds numbers

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed