computing two dimensional poincar maps for hyperchaotic dynamics poincar map pm is one of the felicitous discrete approximation of the continuous dynamics to compute pm the discrete relation s between the successive point of interactions of the trajectories on the suitable poincar section ps are found out these discrete relations act as an amanuensis of the nature of the continuous dynamics in this article we propose a computational scheme to find a hyperchaotic pm hpm from an equivalent three dimensional 3d subsystem of a 4d or higher hyperchaotic model for the experimental purpose a standard four dimensional 4d hyperchaotic lorenz stenflo system hlss and a five dimensional 5d hyperchaotic laser model hlm is considered equivalent 3d subsystem is obtained by comparing the movements of the trajectories of the original hyperchaotic systems with all of their 3d subsystems the quantitative measurement of this comparison is made promising by recurrence quantification analysis rqa various two dimensional 2d poincar mas are computed for several suitable poincar sections for both the systems but only some of them are hyperchaotic in nature the hyperchaotic behavior is verified by positive values of both one dimensional 1d lyapunov exponent le i and 2d lyapunov exponent le ii at the end similarity of the dynamics between the hyperchaotic systems and their 2d hyperchaotic poincar maps hpm has been established through mean recurrence time mrt statistics for both of 4d hlss and 5d hlm and the best approximated discrete dynamics for both the hyperchaotic systems are found out

an accelerated poincare map method for autonomous oscillators a novel time domain method for finding the periodic steady state of a free running electrical oscillator is introduced the method is based on the extrapolation technique mpe the new method is applied to a family of artificial benchmark problems and to a real circuit colpitt s oscillator it turns out to have super linearly convergence properties in both cases full implementational details are provided

vibrations and stability of axially traveling laminated beams abstract in this paper vibrations and stability of an axially traveling laminated composite beam are investigated analytically via the method of multiple scales based on classical laminated beam theory the governing equations of motion for a time variant axial speed are obtained using newton s second law of motion and constitutive relations the method of multiple scales an approximate analytical method is applied directly to the gyroscopic governing equations of motion and complex eigenfunctions and natural frequencies of the system are obtained the stability boundaries of the system near resonance are determined via the routh hurwitz criterion finally a parametric study is conducted which considers the effects of laminate type and configuration as well as the mean speed and amplitude of speed fluctuations on the vibration response natural frequencies and stability boundaries of the system

supercritical speed stability of the trivial equilibrium of an axially moving string on an elastic foundation the stability of an axially moving string supported by a discrete or distributed elastic foundation is examined analytically particular attention is directed at the distribution of the critical speeds and identifying the divergence instability of the trivial equilibrium the elastically supported string shows unique stability behavior that is considerably different from unsupported axially moving string in particular any elastic foundation discrete or distributed leads to multiple critical speeds and a single region of divergence instability above the first critical speed whereas the unsupported string has one critical speed and is stable at all supercritical speeds additionally the elastically supported string critical speeds are bounded above and the maximum critical speed is the upper bound of the divergent speed region the analysis draws on the self adjoint eigenvalue problem for the critical speeds and a perturbation analysis about the critical speeds neither numerical solution nor spatial discretization which can produce substantially incorrect results are required the system falls in the class of dispersive gyroscopic continua and its behavior provides a useful comparison for general gyroscopic systems the analytical findings also serve as a benchmark for approximate methods applied to gyroscopic continua

some considerations on poincare maps for chaotic flows the standard way to reduce a flow to a time discrete dynamical system is by the technique of the poincaresurface of section we discuss the relationship between poincaremaps obtained from different surfaces of section and give some considerations for practical application for this method

nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide abstract in this paper transversal nonlinear vibration of an axially moving viscoelastic string supported by a partial viscoelastic guide is analytically investigated the string is traveling under time variant velocity which includes a mean velocity along with small harmonic fluctuations the model of the viscoelastic guide is also a parallel combination of springs and viscous dampers the governing partial differential equation is derived from hamilton s principle and geometrical relations the method of multiple scales is applied to the governing partial differential equation to obtain solvability conditions for both non resonance and principal parametric resonance cases additionally in the case of principal parametric resonance the stability and bifurcation of trivial and non trivial steady state responses are analyzed through the routh hurwitz criterion eventually numerical simulations are presented to highlight the effects of mean velocity guide length stiffness and damping coefficient of the guide and viscosity coefficient of the string on the natural frequencies stability frequency response curves and bifurcation points of the system

stability analysis of an axially accelerating string the dynamic response of an axially accelerating string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity approximate analytical solutions are sought using two different approaches in the first approach the equations are discretized first and then the method of multiple scales is applied to the resulting equations in the second approach the method of multiple scales is applied directly to the partial differential system principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for a band saw and a threadline problem

vibrations of an axially accelerating beam with small flexural stiffness transverse vibrations of an axially moving beam are considered the axial velocity is harmonically varying about a mean velocity the equation of motion is expressed in terms of dimensionless quantities the beam effects are assumed to be small since in this case the fourth order spatial derivative multiplies a small parameter the mathematical model becomes a boundary layer type of problem approximate solutions are searched using the method of multiple scales and the method of matched asymptotic expansions results of both methods are contrasted with the outer solution

test your surrogate data before you test for nonlinearity the schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis in particular we pinpoint some important caveats of the prominent algorithm of amplitude adjusted fourier transform surrogates aaft and compare it to the iterated aaft which is more consistent in representing the null hypothesis it turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be reinvestigated taking into account the inaccuracies in the aaft algorithm mainly concerning the mismatching of the linear correlations in order to deal with such inaccuracies we propose the use of linear together with nonlinear polynomials as discriminating statistics the application of this setup to some well known real data sets cautions against the use of the aaft algorithm

non linear parametric vibration and stability of axially moving visco elastic rayleigh beams abstract an axially moving visco elastic rayleigh beam with cubic non linearity is considered and the governing partial differential equation of motion for large amplitude vibration is derived through geometrical constitutive and dynamical relations by directly applying the method of multiple scales to the governing equations of motion and considering the solvability condition the linear and non linear frequencies and mode shapes of the system are analytically formulated in the presence of damping terms it can be seen that the amplitude is exponentially time dependent and as a result the non linear natural frequencies of the system will be time dependent for the resonance case through considering the solvability condition and routh hurwitz criterion the stability conditions are developed analytically eventually the effects of system parameters on the vibrational behavior stability and bifurcation points of the system are investigated through parametric studies

coupled longitudinal transverse dynamics of an axially accelerating beam abstract the coupled longitudinal transverse nonlinear dynamics of an axially accelerating beam is numerically investigated this problem is classified as a parametrically excited gyroscopic system the axial speed is assumed to be comprised of a constant mean value along with harmonic fluctuations hamilton s principle is employed to derive the equations of motion of the system which are in the form of two coupled partial differential equations the equations are discretized using the galerkin method which yields a set of coupled second order nonlinear ordinary differential equations with time dependent coefficients the sub critical dynamics of the system is examined via the pseudo arclength continuation technique while the global dynamics is investigated using direct time integration the mean axial speed and the amplitude of the speed variations are varied so as to construct the bifurcation diagrams of poincare maps the vibration specifications of the system are investigated more detailed via plotting time histories phase plane portraits and fast fourier transforms ffts

vibrational responses of antisymmetric angle ply laminated conical shell by the methods of polynomial based differential quadrature and fourier expansion based differential quadrature abstract vibrational response of antisymmetric angle ply laminated conical shell based on transverse shear deformation theory is analyzed in this research the equilibrium and corresponding boundary equations including the extension coupling terms are derived in terms of displacement and rotational components two types of differential quadrature methods dqm including polynomial based differential quadrature pdq and fourier expansion based differential quadrature fdq are applied to convert the existing differential equations to algebraic equations after discretization of existing differential equations the eigenvalue equation system for the functional value in the whole domain is established and solved a series of numerical tests are carried out to validate the present approach that highly accurate results are obtained only few grid points finally the parametric studies are performed to illustrate the effects of different boundary conditions fiber angle and number of layers and also various aspect ratio of the shell including thickness to radius ratio length to radius on the frequency parameter

multidimensional matrices uniquely recovered by their lines abstract we provide a method to determine if a q ary multidimensional matrix is lonesum or not by using properties of line sums of lonesum multidimensional matrices in particular we establish a graphic method that uses edge colored graphs to determine if a binary multidimensional matrix is lonesum or not we also provide two methods to determine if a q ary multidimensional matrix is lonestructure or not the first one uses properties of line structures of lonestructure multidimensional matrices and the second one uses edge colored directed multigraphs

infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations abstract the transverse vibrations of simply supported axially moving euler bernoulli beams are investigated the beam has a time varying axial velocity with viscous damping traveling beam eigenfunctions with infinite number of modes are considered approximate analytical solutions are sought using the method of multiple scales a perturbation technique a detailed analysis of the resonances in which upto four modes of vibration involved are performed stability analysis is treated for each type of resonance approximate stability borders are given for the resonances involving only two modes for higher number of modes involved in a resonance sample numerical examples are presented for stabilities

nonlinear dynamics of axially moving plates abstract the nonlinear dynamics for forced motions of an axially moving plate is numerically investigated using von karman plate theory and retaining in plane displacements and inertia the equations of motion are obtained via an energy method based on lagrange equations this yields a set of second order nonlinear ordinary differential equations with coupled terms the equations are transformed into a set of first order nonlinear ordinary differential equations and are solved via the pseudo arclength continuation technique the near resonance nonlinear dynamics is examined via plotting the frequency response curves of the system results are shown through frequency response curves time histories and phase plane diagrams the effect of system parameters such as the axial speed and the pretension on the resonant responses is also highlighted

is one dimensional poincare map sufficient to describe the chaotic dynamics of a three dimensional system study of continuous dynamical system through poincare map is one of the most popular topics in nonlinear analysis this is done by taking intersections of the orbit of flow by a hyper plane parallel to one of the coordinate hyper planes of co dimension one naturally for a 3d attractor the poincare map gives rise to 2d points which can describe the dynamics of the attractor properly in a very special case sometimes these 2d points are considered as their 1d projections to obtain a 1d map however this is an artificial way of reducing the 2d map by dropping one of the variables sometimes it is found that the two coordinates of the points on the poincare section are functionally related this also reduces the 2d poincare map to a 1d map this reduction is natural and not artificial as mentioned above in the present study this issue is being highlighted in fact we find out some examples which show that even this natural reduction of the 2d poincare map is not always justified because the resultant 1d map may fail to generate the original dynamics properly this proves that to describe the dynamics of the 3d chaotic attractor the minimum dimension of the poincare map must be two in general

a general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear time dependent internal boundary conditions abstract the subject of this paper is the development of a general solution procedure for the vibrations primary resonance and nonlinear natural frequency of systems with cubic nonlinearities subjected to nonlinear and time dependent internal boundary conditions this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements the equations of motion form a set of nonlinear partial differential equations with nonlinear time dependent and coupled internal boundary conditions the method of multiple timescales an approximate analytical method is applied directly to each partial differential equation of motion as well as coupled boundary conditions i e on each sub domain and the corresponding internal boundary conditions for a continuous system with intermediate elements which ultimately leads to approximate analytical expressions for the frequency response relation and nonlinear natural frequencies of the system these closed form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system moreover the suggested solution procedure is applied to a sample problem which is discussed in detail

approximate discrete dynamics of emg signal approximation of a continuous dynamics by discrete dynamics in the form of poincare map is one of the fascinating mathematical tool which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension than the embedding dimension the present article considers a very rare biomedical signal like electromyography emg signal it determines suitable time delay and reconstruct the attractor with embedding dimension three by measuring its lyapunov exponent the attractor so reconstructed is found to be chaotic naturally the poincare map obtained by corresponding poincare section has to be chaotic too this may be verified by calculation of lyapunov exponent of the map the main objective of this article is to show that poincare map exists in this case as a 2d map for a suitable poincare section only in fact the article considers two poincare sections of the attractor for construction of the poincare map it is seen that one such map is chaotic but the other one is not so both are verified by calculation of lyapunov exponent of the map

combinatorics of h primes in quantum matrices abstract for q c transcendental over q we give an algorithmic construction of an order isomorphism between the set of h primes of o q m n c and the sub poset s of the reverse bruhat order of the symmetric group s 2 n consisting of those permutations that move any integer by no more than n positions further we describe the permutations that correspond via this bijection to rank t h primes more precisely we establish the following result imagine that there is a barrier between positions n and n 1 then a 2n permutation s corresponds to a rank t h invariant prime ideal of o q m n c if and only if the number of integers that are moved by from the right to the left of this barrier is exactly n t the existence of such an order isomorphism was conjectured by goodearl and lenagan

transverse vibration of an axially accelerating string abstract the transverse vibration of an axially accelerating string is investigated the equation of motion is developed using hamilton s principle the resulting partial differential equations are discretized using galerkin s method assuming the axial velocity to be periodic a stability analysis is performed using floquet theory one two three four six and eight term series approximations are considered in the galerkin s method the one term approximation leads to a mathieu equation the solution of which is well known the numerical results for one term are compared with the analytical solution for the mathieu equation and they are in full agreement the two term approximation leads to gyroscopically coupled equations and the solutions differ significantly from that of the one term approximation whereas the three term approximation solutions look similar to the one term approximation solutions the analysis is carried out for higher order even approximations and the solutions are in qualitative agreement the two and four term approximation solutions are compared with the analytical results from hsu s method and are in reasonable agreement the results show that instabilities occur at much higher amplitudes and frequencies of the periodic axial velocity than that of typical devices such as tape machines and band saws

matrices uniquely determined by their lonesums abstract a matrix is lonesum if it can be uniquely reconstructed from its row and column sums brewbaker computed the number of m n binary lonesum matrices kaneko defined the poly bernoulli numbers of an integer index and showed that the number of m n binary lonesum matrices is equal to the mth poly bernoulli number of index n in this paper we are interested in q ary lonesum matrices there are two types of lonesumness for q ary matrices namely strongly and weakly lonesum we first study strongly lonesum matrices we compute the number of m n q ary strongly lonesum matrices and provide a generalization of kaneko s formulas by deriving the generating function for the number of m n q ary strongly lonesum matrices next we study weakly lonesum matrices we show that the number of forbidden patterns for q ary weakly lonesum matrices is infinite if q 5 and construct some forbidden patterns for q 3 4 we also suggest an open problem related to ternary and quaternary weakly lonesum matrices

transition behaviour from string to beam for an axially accelerating material an approximate analytical expression for the natural frequency is given for the problem for velocity profiles harmonically varying about a mean velocity stability borders are determined analytically for fluctuation frequency versus amplitudes beam effects cause the stability boundaries to shift to higher frequency values

principal parametric resonances of a general continuous system with cubic nonlinearities abstract a generalized vibrational model of cubic nonlinear continuous system with arbitrary parametric excitation is considered the method of multiple scales a perturbation method is used to find an approximate analytical solution the primary parametric resonance of the parametric excitation is considered the amplitude and phase modulation equations are derived steady state solutions and their stability are discussed the solution algorithm is applied to the problem of nonlinear vibrations of viscoelastic pipes conveying fluids natural frequencies of viscoelastic pipes are found frequency response curves and bifurcation points are drawn stable and unstable regions of trivial and nontrivial solutions are obtained

a practical method for calculating largest lyapunov exponents from small data sets detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest lyapunov exponent lyapunov exponents quantify the exponential divergence of initially close state space trajectories and estimate the amount of chaos in a system we present a new method for calculating the largest lyapunov exponent from an experimental time series the method follows directly from the definition of the largest lyapunov exponent and is accurate because it takes advantage of all the available data we show that the algorithm is fast easy to implement and robust to changes in the following quantities embedding dimension size of data set reconstruction delay and noise level furthermore one may use the algorithm to calculate simultaneously the correlation dimension thus one sequence of computations will yield an estimate of both the level of chaos and the system complexity

on the numerical computation of poincare maps abstract this note describes a method for finding simply and accurately the intersections of a numerically integrated trajectory with a surface of section

finding the embedding dimension and variable dependencies in time series we present a general method the test which establishes functional dependencies given a sequence of measurements the approach is based on calculating conditional probabilities from vector component distances imposing the requirement of continuity of the underlying function the obtained values of the conditional probabilities carry information on the embedding dimension and variable dependencies the power of the method is illustrated on synthetic time series with different time lag dependencies and noise levels and on the sunspot data the virtue of the method for preprocessing data in the context of feedforward neural networks is demonstrated also its applicability for tracking residual errors in output units is stressed

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

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