very large scale linear programming a case study in combining interior point and simplex methods experience with solving a 12 753 313 variable linear program is described this problem is the linear programming relaxation of a set partitioning problem arising from an airline crew scheduling application a scheme is described that requires successive solutions of small subproblems yielding a procedure that has little growth in solution time in terms of the number of variables experience using the simplex method as implemented in cplex an interior point method as implemented in obi and a hybrid interior point simplex approach is reported the resulting procedure illustrates the power of an interior point simplex combination for solving very large scale linear programs

fractal dimension of higher dimensional chaotic repellors abstract using examples we test formulae previously conjectured to give the fractal information dimension of chaotic repellors and their stable and unstable manifolds in typical dynamical systems in terms of the lyapunov exponents and the characteristic escape time from the repellor our main example a three dimensional chaotic scattering billiard yields a new structure for its invariant manifolds this system also provides an example of a system which is not typical and illustrates how perturbation to the system restores typicality and the applicability of the dimension formulae

the liapunov dimension of strange attractors abstract many papers have been published recently on studies of dynamical processes in which the attracting sets appear quite strange in this paper the question of estimating the dimension of the attractor is addressed while more general conjectures are made here particular attention is paid to the idea that if the jacobian determinant of a map is greater than one and a ball is mapped into itself then generically the attractor will have positive two dimensional measure and most of this paper is devoted to presenting cases with such jacobians for which the attractors are proved to have non empty interior

long range order in the scaling behaviour of hyperbolic dynamical systems abstract detailed statistical analyses of chaotic signals have been so far limited to 2 d maps with one expanding and one contracting direction here by studying filtered signals we provide evidence that the existence of a further stable direction can transform self similarity into self affinity and generate phase transitions according to the thermodynamic formalism of dynamical systems in a hyperbolic case the dimension spectrum is computed exactly as a function of the filter cut off frequency moreover the validity of the kaplan yorke formula and of its generalization are rigorously proven finally the scaling function is shown to satisfy a stochastic recursive relation whose lyapunov exponent allows to control the extension of the range of interactions in the associated hamiltonian

chaotic and non linear dynamic analysis of a two axis rate gyro with feedback control mounted on a space vehicle abstract an analysis is presented in this paper for a two axis rate gyro subjected to linear feedback control mounted on a space vehicle which is spinning with uncertain angular velocity z t about its spin of the gyro for the autonomous case in which z t is steady the stability analysis of the system is studied by routh hurwitz theory for the non autonomous case in which z t is sinusoidal function this system is a strongly non linear damped system subjected to parametric excitation by varying the amplitude of sinusoidal motion periodic and chaotic responses of this parametrically excited non linear system are investigated using the numerical simulation some observations on symmetry breaking bifurcations period doubling bifurcations and chaotic behavior of the system are investigated by various numerical techniques such as phase portraits poincare maps average power spectra and lyapunov exponents in addition some discussions about chaotic motions of this system can be suppressed and changed into regular motions by a suitable constant motor torque are included

two direct methods in linear programming abstract in this paper we introduce two direct methods for solving some classes of linear programming problems the first method produces the extreme vertex or a neighboring vertex with respect to the extreme point the second method is based on the game theory both these methods can be used in the preparation of the starting point for the simplex method the efficiency of the improved simplex method whose starting point is constructed by these introduced methods is compared with the original simplex method and the interior point methods and illustrated by examples also we investigate the elimination of excessive constraints

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

a scaling law how an attractor s volume depends on noise level abstract we investigate the meaning of the dimension of a strange attractor for systems with noise more specifically we investigate the effect of adding noise of magnitude e to a deterministic system with d degrees of freedom if the attractor has dimension d and d d then its volume is zero the addition of noise may be an important physical probe for experimental situations useful for determining how much of the observed phenomena in a system is due to noise already present when the noise is added the attractor a e has positive volume we conjecture that the generalized volume of a e is proportional to e d d for e near 0 and show this relationship is valid in several cases for chaotic attractors there are a variety of ways of defining d and the generalized volume definition must be chosen accordingly

computational experience with an interior point cutting plane algorithm there has been a great deal of success in the last 20 years with the use of cutting plane algorithms to solve specialized integer programming problems generally these algorithms work by solving a sequence of linear programming relaxations of the integer programming problem and they use the simplex algorithm to solve the relaxations in this paper we describe experiments using a predictor corrector interior point method to solve the relaxations for some problems the interior point code requires considerably less time than a simplex based cutting plane algorithm

non linear dynamic analysis and control of chaos for a two degrees of freedom rigid body with vibrating support abstract the dynamic behaviors of a two degrees of freedom rigid body with vibrating support are studied in this paper both analytical and computational results are employed to obtain the characteristics of the system by using the lyapunov direct method the conditions of stability of the relative equilibrium position can be determined the incremental harmonic balance method ihb is used to find the stable and unstable periodic solutions for the strongly non linear system by applying various numerical results such as phase plane poincare map time history and power spectrum analysis a variety of periodic solutions and the phenomena of the chaotic motion is presented the effects of the changes of parameters in the system can be found in the bifurcation diagrams further the chaotic behavior is verified by using lyapunov exponents the modified interpolated cell mapping method micm is used to study the basins of attraction of periodic attractors and the fractal structure besides additions of a constant torque a periodic torque addition of dither signals delayed feedback control adaptive control and bang bang control are used to control the chaos phenomena effectively

liapunov exponents of simple smooth flows an attempt is made to introduce the notion of a simple dynamical system as one where liapunov exponents may be obtained by purely algebraic methods specifically by exploiting the lie algebra relations between vector fields thus in a simple system one need not solve the dynamical equations but is often faced with an equally difficult task of unravelling the algebraic structure the theory is presented within the framework of differential geometry several examples illustrate the usefulness of the proposed concept

construction of chaotic regions a new method of numerical simulation is given in this chapter to describe the characteristics of the solutions of dynamical systems the characteristics of the solutions such as the number of solutions the type and periodicity of the solutions and more importantly the existence of chaotic solutions are of great interest in a physical parametric space the boundaries separating qualitatively different solutions in a physical parametric space constituting a characteristic diagram are constructed below the critical points in the initial bifurcation graph are used as initial approximations depending on the nature of the critical points additional constraints are used to trace the neighbouring critical points by the method of parametric unfolding as a result the characteristics of the steady state solutions can be read directly from the characteristic diagram non linear governing differential equations arise from various types of physical and engineering problems owing to the presence of non linearities analytical solutions are rarely obtained apart from their deterministic nature random like solutions are observed for certain parameters and initial conditions the occurrence of these chaotic motions has been studied by many authors

experiments and analysis on chaotic vibrations of a shallow cylindrical shell panel abstract detailed experimental results and analytical results are presented on chaotic vibrations of a shallow cylindrical shell panel subjected to gravity and periodic excitation the shallow shell panel with square boundary is simply supported for deflection in plane displacement at the boundary is elastically constrained by in plain springs in the experiment the cylindrical shallow shell panel with thickness 0 24 mm square form of length 140 mm and mean radius 5150 mm is used for the test specimen all edges around the shell boundary are simply supported by adhesive flexible films first to find fundamental properties of the shell panel linear natural frequencies and characteristics of restoring force of the shell panel are measured these results are compared with the relevant analytical results then geometrical parameters of the shell panel are identified exciting the shell panel with lateral periodic acceleration nonlinear frequency responses of the shell panel are obtained by sweeping the frequency of periodic acceleration in typical ranges of the exciting frequency predominant chaotic responses are generated time histories of the responses are recorded for inspection of the chaos in the analysis the donnell equation with lateral inertia force is introduced assuming mode functions the governing equation is reduced to a set of nonlinear ordinary differential equations by the galerkin procedure periodic responses are calculated by the harmonic balance method chaotic responses are integrated numerically by the runge kutta gill method the chaotic responses which are obtained by the experiment and the analysis are inspected with the fourier spectra the poincare projections the maximum lyapunov exponents and the lyapunov dimension it is found that the dominant chaotic responses of the shell panel are generated from the responses of the sub harmonic resonance of 1 2 order and of the ultra sub harmonic resonance of 2 3 order by the convergence of the maximum lyapunov exponent to the embedding dimension the number of predominant vibration modes which contribute to the chaos is found to be three or four fairly good agreements are obtained between the experimental results and the analytical results

constraint optimal selection techniques costs for nonnegative linear programming problems we describe an active set cutting plane approach called constraint optimal selection techniques costs and develop an efficient new cost for solving nonnegative linear programming problems we give a geometric interpretation of the new selection rule and provide computational comparisons of the new cost with existing linear programming algorithms for some large scale sample problems

bifurcation behavior of a rotor supported by active magnetic bearings abstract the non linear dynamics of a rigid rotor levitated by active magnetic bearings is investigated the vibrations in the horizontal and vertical directions are analyzed on the center manifold near the double zero degenerate point by using normal form method the resulting normal forms in the horizontal and vertical directions are different due to the effect of rotor weight it is shown that the vibratory behavior in the vertical direction can be reduced on the center manifold to the bogdanov takens form for the autonomous case there exist saddle node bifurcation and hopf bifurcation for local analysis and a saddle connection bifurcation for global analysis for non autonomous case the melnikov technique is used to determine the critical parameter at which the homoclinic orbits intersect transversally for the vibrations in the horizontal direction the essential non linear terms of the truncated normal form are third order the behaviors of zero solutions are given finally numerical simulations are performed to verify the analytical predictions

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

chaos control of new mathieu van der pol systems with new mathieu duffing systems as functional system by gyc partial region stability theory abstract in this paper a new strategy by using gyc partial region stability theory is proposed to achieve chaos control using the gyc partial region stability theory the new lyapunov function used is a simple linear homogeneous function of error states and the lower order controllers are much more simple and introduce less simulation error numerical simulations are given for new mathieu van der pol system and new mathieu duffing system to show the effectiveness of this strategy

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 metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

tuning of a pid controlled gyro by using the bifurcation theory this paper concerns the control design of a pid controlled gimbals suspension gyro whose parameters are determined by using bifurcation theory the non linear mathematical model of the gyro is deduced by using the nutation theory of gyroscopes considering a pid controller with constrained integral action it is shown that depending on different values of the maximum allowed integral action a poincare andronov hopf bifurcation may appear the analysis of the stability or instability of this bifurcation from the first lyapunov value gives a procedure to adjust the parameters of the pid controller the developed control methodology is evaluated through numerical simulations 2007 elsevier b v all rights reserved

generalizations of srb measures to nonautonomous random and infinite dimensional systems we review some developments that are direct outgrowths of or closely related to the idea of srb measures as introduced by sinai ruelle and bowen in the 1970s these new directions of research include the emergence of strange attractors in periodically forced dynamical systems random attractors in systems defined by stochastic differential equations srb measures for infinite dimensional systems including those defined by large classes of dissipative pdes quasi static distributions for slowly varying time dependent systems and surviving distributions in leaky dynamical systems

ising type and other transitions in one dimensional coupled map lattices with sign symmetry we consider a one dimensional lattice of expanding antisymmetric maps 1 1 1 1 with nearest neighbor diffusive coupling for such systems it is known that if the coupling parameter e is small there is unique stationary in time state which is chaotic in space time a disputed question is whether such systems can exhibit ising type phase transitions as e grows beyond some critical value ec we present results from computer experiments which give definite indication that such a transition takes place the mean square magnetization appears to diverge as e approaches some critical value with a critical exponent around 0 9 we also study other properties of the coupled map system

regular and chaotic dynamic analysis and control of chaos of an elliptical pendulum on a vibrating basement the dynamic behavior of an elliptical pendulum subjected to external disturbance is studied in this paper the lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system by applying numerical results phase diagrams power spectrum period t maps and lyapunov exponents are presented to observe periodic and chaotic motions the effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams for global analysis the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping micm method finally several methods the delayed feedback control the addition of constant torque the addition of periodic force adaptive control algorithm and bang bang control are used to control chaos effectively

double degeneracy and chaos in a rate gyro with feedback control the analysis of a single axis rate gyro subjected to feedback control mounted on a space vehicle that is spinning with uncertain angular velocity zabout its spin of the gyro is presented for the autonomous case in which zis steady we examine the dynamics of the resulting system on the center manifold near the double zero degenerate point by using center manifold and normal form methods there exist a few kinds of bifurcations in the autonomous case such as pitchfork and hopf bifurcations for local bifurcation analyses and a saddle connection bifurcation for global analyses as singular velocity zof the space vehicle is harmonic the melnikov technique was used to give criteria for the existence of chaos in the gyro motion the numerical simulations are performed to verify the analytical results in the form of phase portraits bifurcation diagrams and lyapunov exponents in addition chaotic motions of this system can be changed into regular motions by a small parametric perturbation with lyapunov exponent calculations

a family of simplex variants solving an m d linear program in expected number of pivot steps depending on d only we present a family of variants of the simplex method which are based on a constraint by constraint procedure the solution to a linear program is obtained by solving a sequence of subproblems with an increasing number of constraints we discuss several probabilistic models for generating linear programs in all of them the underlying distribution is assumed to be invariant under changing the signs of rows or columns in the problem data a weak regularity condition is also assumed under these models for linear programs with d variables and m d inequality constraints the expected number of pivots required by these algorithms is bounded by a function of minm d only in particular this means that for a fixed number of variables the expected number of pivots is bounded by a constant when the number of constraints tends to infinity since smale s original model smale s 1983 on the average speed of the simplex method of linear programming math programming27 satisfies our probabilistic assumptions the same results apply to his model although not to the particular algorithm he analyzes we also present some results for models generating only feasible linear programs and for bland s pivoting rule we conclude with a discussion of our probabilistic models and show why they are inadequate for obtaining meaningful results unless d and m are of the same order of magnitude

strange attractors and asymptotic measures of discrete time dissipative systems we investigate asymptotic properties of certain discrete time dynamical systems in two and three dimensions with solenoidal attractor it is proved that the asymptotic measures relevant for the generalized version of the ergodic theorem all derive from one haar measure

bifurcations and chaos of a particular van der pol duffing oscillator abstract the paper presents chaotic dynamics of a particular non linear oscillator having duffing type stiffness van der pol damping and dry friction we first utilize an averaging technique to obtain informations regarding the bifurcation behaviour of the vibrating system and then we analyze numerically the chaotic behaviour of the oscillator for parameters near bifurcation curves we also discuss and illustrate the influence of the dry friction on the behaviour of a strange chaotic attractor

a fuzzy approach to quantum logical computation the theory of logical gates in quantum computation has inspired the development of new forms of quantum logic called quantum computational logics the basic semantic idea is the following the meaning of a formula is identified with a quantum information quantity represented by a density operator whose dimension depends on the logical complexity of the formula at the same time the logical connectives are interpreted as operations defined in terms of quantum gates in this framework some possible relations between fuzzy representations based on continuous t norms for quantum gates and the probabilistic behavior of quantum computational finite valued connectives are investigated

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

quantum computer with mixed states and four valued logic in this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations not necessarily unitary a mixed state operator of density matrix of n twolevel quantum systems is considered as an element of 4 n dimensional operator hilbert space liouville space it allows us to use a quantum computer model with four valued logic the gates of this model are general superoperators which act on n ququat state ququat is a quantum state in a four dimensional operator hilbert space unitary two valued logic gates and quantum operations for an n qubit open system are considered as four valued logic gates acting on n ququats we discuss properties of quantum four valued logic gates in the paper we study universality for quantum four valued logic gates

detection of synchronization between chaotic signals an adaptive similarity based approach we present an adaptive similarity based approach to detect generalized synchronization gs with n m phase synchronization ps where n and m are integers and one of them is 1 this approach is based on the similarity index si and gaussian mixture model with the minimum description length criterion the clustering method which is shown to be superior to the closeness and connectivity of a continuous function is employed in this study to detect the existence of gs with n m ps we conducted a computer simulation and a finger lifting experiment to illustrate the effectiveness of the proposed method in the simulation of a rossler lorenz system our method outperformed the conventional si and gs with 2 1 ps within the coupled system was found in the experiment of self paced finger lifting movement cortico muscular gs with 1 2 and 1 3 ps was found between the surface electromyogram signals on the first dorsal interossei muscle and the magnetoencephalographic data in the motor area the gs with n m ps n or m 1 has been simultaneously resolved from both simulation and experiment the proposed approach thereby provides a promising means for advancing research into both nonlinear dynamics and brain science

artificial free simplex algorithm based on the non acute constraint relaxation solving a general linear programming problem using the simplex algorithm relies on introducing artificial variables that creates a large search space this paper presents the non acute constraint relaxation technique that not only eliminates the need for artificial variables but also reduces the start up time to solve the initial relaxation problem to guarantee the optimal solution or infeasibility or unboundedness of a linear programming problem the algorithm reinserts the non acute constraints back to the relaxation problem the results of this algorithm are superior than the original simplex algorithm with artificial variables for a linear programming problem with a large number of acute constraints

on rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions we consider different definitions of the correlation dimension and find some relationships between them and other characteristics of dimension type such as hausdorff dimension box dimension etc we also introduce different ways to define and study the generalized spectrum for dimensions a one parameter family of characteristics of dimension type

dimension of the attractors associated to the ginzburg landau partial differential equation abstract we study the long time behavior of solutions to the ginzburg landau partial differential equation it is shown that a finite dimensional attractor captures all the solutions an upper bound on this dimension is given in terms of physical quantities by estimating the lyapunov exponents on the trajectories finally using the well known side band instabilities of an exact time dependent solution stokes solution we derive lower bounds on the dimension of the universal attractor moreover the lower and upper bounds agree

a computation of the limit capacity of the lorenz attractor abstract attempts to compute directly the limit capacity or fractal dimension of the lorenz attractor using the box counting algorithm suggested by takens encounter a convergence problem this convergence problem is discussed leading to an extrapolation procedure that resolves it and yields a fractal dimension that is accurate to the resolution of the smallest boxes used

global chaos control of non autonomous systems this study describes a global approach of controlling chaos to reduce tedious waiting time caused by using conventional local controllers with euler s method a non autonomous system is approximated by a non linear difference system and then an approximate global poincare map function is derived from the difference system by iterating one or more periods of a periodic excitation based on the map function unstable periodic orbits embedded in a chaotic motion can be detected and a global controller for a targeted unstable periodic orbit is designed the global controller makes all the unstable periodic orbits vanish except a targeted periodic orbit furthermore a lyapunov s direct method is applied to confirm that the global controller can asymptotically stabilize the unique periodic orbit for practical applications system models are usually unknown to obtain a mathematical model non linear system identification based on the harmonic balance principle is applied to an unknown chaotic system of a noisy environment simulation results demonstrate that the global controller successfully regularizes a chaotic motion even if the chaotic trajectory is far from the targeted periodic orbit

the hopf bifurcation and limit cycle by the incremental harmonic balance method abstract it is well recognized that periodic solutions and their stabilities under small perturbations play a very important role in the study of nonlinear dynamic systems these problems have been investigated by various perturbation methods which are however subjected to the limitation of weak nonlinearity moreover a perturbation method cannot define the parameter range within which a correct solution or a satisfactory approximation can be obtained by the method this situation may lead to totally incorrect results when the parameter is out of a certain range by introducing a variable parameter the incremental harmonic balance method which can treat strongly nonlinear dynamic problems can be used to perform parametric studies on the hopf bifurcation and limit cycle problems this method is ideally suited for parametric studies giving solution diagrams in this paper it is applied to study the van der pol oscillator and coupled oscillators examples show that beyond a certain limit the standard perturbation methods will give incorrect results

dimension theory for invariant measures of endomorphisms we establish the exact dimensional property of an ergodic hyperbolic measure for a c 2 non invertible but non degenerate endomorphism on a compact riemannian manifold without boundary based on this we give a new formula of lyapunov dimension of ergodic measures and show it coincides with the dimension of hyperbolic ergodic measures in a setting of random endomorphisms our results extend several well known theorems of barreira et al ann math 149 755 783 1999 and ledrappier and young commun math phys 117 4 529 548 1988 for diffeomorphisms to the case of endomorphisms

a p ge semiconductor experiment showing chaos and hyperchaos abstract a p ge semiconductor experiment is investigated by the help of both probabilistic and dynamical characterization methods dimensions lyapunov exponents and the corresponding scaling functions are calculated two exemplary files of data from the p ge semiconductor experiment exhibiting spontaneous i e undriven resistance oscillations in the low temperature avalanche breakdown are shown to be chaotic and hyperchaotic respectively for the first file we obtained a fractal dimension between two and three and one positive lyapunov exponent whereas for the second file we found a fractal dimension between three and four and two positive lyapunov exponents adopting the terminology introduced by rossler the behavior corresponding to the latter file is called hyperchaotic furthermore using the language of the thermodynamical formalism the probabilistic scaling function evaluated for the hyperchaotic state indicates a phase transition like behavior

representing continuous t norms in quantum computation with mixed states a model of quantum computation is discussed in aharanov et al 1997 proc 13th annual acm symp on theory of computation stoc pp 20 30 and tarasov 2002 j phys a math gen 35 5207 35 in which quantum gates are represented by quantum operations acting on mixed states it allows one to use a quantum computational model in which connectives of a four valued logic can be realized as quantum gates in this model we give a representation of certain functions known as t norms menger 1942 proc natl acad sci usa 37 57 60 that generalize the triangle inequality for the probability distribution valued metrics as a consequence an interpretation of the standard operations associated with the basic fuzzy logic hajek 1998 metamathematics of fuzzy logic trends in logic vol 4 dordrecht kluwer is provided in the frame of quantum computation

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

the many facets of linear programming we examine the history of linear programming from computational geometric and complexity points of view looking at simplex ellipsoid interior point and other methods

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow