why do block length and delay behave differently if feedback is present for output symmetric discrete memoryless channels dmcs at even moderately high rates fixed block length communication systems show no improvements in their error exponents with feedback this paper studies systems with fixed end to end delay and shows that feedback generally provides dramatic gains in the error exponents a new upper bound the uncertainty focusing bound is given on the probability of symbol error in a fixed delay communication system with feedback this bound turns out to have a form similar to viterbi s bound used for the block error probability of convolutional codes as a function of the fixed constraint length the uncertainty focusing bound is shown to be asymptotically achievable with noiseless feedback for erasure channels as well as for any output symmetric dmc that has strictly positive zero error capacity furthermore it can be achieved in a delay universal anytime fashion even if the feedback itself is delayed by a small amount finally it is shown that for end to end delay it is generally possible at high rates to beat the sphere packing bound for general dmcs thereby providing a counterexample to a conjecture of pinsker

brief paper on observability of nonlinear steady state generators an output regulation problem can be converted into a stabilization problem in a systematic framework thanks to an appropriately designed internal model however the successful construction of an internal model im relies on the observability condition of a steady state generator ssg in the literature the observability condition is restricted to linear or linearized ssgs this paper introduces a novel observability condition for nonlinear ssgs nonlinear observability leads to an effective combination of the internal model principle and the certainty equivalence principle for a more general class of systems

high order variational calculation for the frequency of time periodic solutions we develop a convergent variational perturbation theory for the frequency of time periodic solutions of nonlinear dynamical systems the power of the theory is illustrated by applying it to the duffing oscillator

piecewise homotopy methods for nonlinear ordinary differential equations abstract piecewise homotopy perturbation methods are developed for the solution of nonlinear ordinary differential equations these methods are based on the introduction of an artificial or book keeping parameter and the expansion of the solution in a power series of this parameter and provide analytical solutions in open intervals which are smooth everywhere three piecewise adaptive homotopy perturbation methods based on the use of either a fixed number of approximants and a variable step size a variable number of approximants and a fixed step size or a variable number of approximants and a variable step size are presented and applied to eight nonlinear ordinary differential equations it is shown that piecewise adaptive homotopy perturbation methods predict essentially the same solutions as matlab s variable step variable order solvers and variable order transition matrix techniques provided that five term approximations of the decomposition method are applied to both the displacement and the velocity it is also shown that piecewise homotopy perturbation techniques that use three term approximations to both the displacement and the velocity provide essentially the same results as those obtained with a second order accurate time linearization technique when the same step is employed in both schemes

solution of the damped cubic quintic duffing oscillator by using jacobi elliptic functions in this paper we derive an analytical solution of the damped cubic quintic duffing oscillator which is based on a rational elliptic form used to obtain exact and approximate solutions of undamped oscillators we examine different set of system parameter values to assess the accuracy of our derived solution it is shown that theoretical predictions compares well with the numerical integration solutions obtained by a fourth order runge kutta method this demonstrates the applicability of rational elliptic forms to solve damped oscillators with higher nonlinear terms

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

systematic ldpc convolutional codes asymptotic and finite length anytime properties here we propose an ensemble of non terminated systematic ldpc convolutional codes with increasing memory and show that over the binary erasure channel bec these codes achieve anytime reliability asymptotically when decoded with an expanding window message passing decoder the corresponding anytime exponents are determined through protograph based extrinsic information transfer charts fundamental complications arising when transmitting with finite block lengths are identified and a combinatorial performance analysis when transmitting over a static bec with a fixed number of erasures per codeword block is developed based on the performance analysis we explore the use of feedback for achieving anytime behavior with constraints on block length to meet complexity constraints with or without feedback the code memory can be limited at the cost of an error floor emerging with a delay proportional to the memory constraint although the analysis is developed for a static bec we show numerically that we can design efficient low complexity finite length codes with anytime properties even for the conventional bec

linearized galerkin and artificial parameter techniques for the determination of periodic solutions of nonlinear oscillators abstract linearized harmonic balance galerkin methods for the determination of the periodic solutions of nonlinear oscillators are presented and the results are compared with those of an artificial parameter method based on the introduction of a linear stiffness term and the linstedt poincare technique the linearized harmonic balance methods presented in this paper are not iterative and are based on taylor series expansions the neglect of nonlinear terms in the resulting series a fourier approximation to the solution and orthogonality conditions it is shown that the first approximation provided by the linearized harmonic balance technique is identical to that of the artificial parameter method whereas the second one depends on how the equation is linearized and written and the discrepancies have been found to be caused by the neglect of the nonlinear terms in the taylor series expansion because a fourier series expansion of these terms introduces harmonics which are not accounted for in the linearization procedure it is also shown that the first approximation of the artificial parameter method and the linearized harmonic balance procedure are asymptotically equivalent to that derived from a modified linstedt poincare method when the nonlinearities are small and that these techniques may not be applicable to some oscillators

a perturbation technique that works even when the non linearity is not small abstract we extend the lindstedt poincare small non linearity based perturbation scheme to strongly non linear systems the extended technique starts from a physically non existent neighboring linear system this system is created by adding an optimal linear spring term to the system side of each linear differential equation starting at the zeroth level and balancing that term by adding an equal one to the forcing side one level down unlike the ritz method which also works for strongly non linear systems results can be obtained beyond the first level without resorting to numerical techniques thus the extended method keeps the intuition guiding straightforwardness of the perturbation method while giving accurate beyond first level hand derivable numerical results examples are presented for free vibrations with cubic and antisymmetric quadratic non linearities and for harmonic solutions of the undamped duffing equation the forms of the solutions allow the regions of validity of the expansions to be estimated an internal method of estimating accuracy of the perturbation solutions is developed and checked with the free vibration examples the exact solutions of which are available this internal method is then used to estimate the accuracy of the new solutions to the duffing equation these new duffing equation solutions give accurate results in all regions where stable harmonic solutions are known to exist in particular they give accurate results at and near the vertical tangent to the resonance curve a region where hayashi s amplitude expansion based perturbation solution necessarily breaks down

iteration method solutions for conservative and limit cycle x1 3 force oscillators abstract an iterative technique is used to calculate a higher order approximation to the periodic solutions of a conservative oscillator for which the elastic force term is proportional to x 1 3 the related van der pol type limit cycle oscillator is also studied

computation of periodic solutions in perturbed second order odes abstract the poincare lindstedt technique is used to compute periodic solutions in perturbed ordinary differential equations in this paper we give a general algorithm for its application on a special purpose symbolic computation package

distributed output regulation of nonlinear multi agent systems via host internal model this note presents a host internal model h im approach to distributed output regulation of reaching nonlinear leader following consensus focusing on a basic nonlinear scenario of identical or homogeneous agents of a normal form it is shown that the problem is solvable as long as its interaction digraph contains a certain directed spanning tree a constructive lyapunov protocol is proposed by incorporating a single h im the result is also demonstrated by fitzhugh nagumo fhn and lorenz type nonlinear dynamic networks

scalar estimation and control with noisy binary observations we consider a simple one dimensional system whose observations are sent to a state estimator over a noisy binary communication link the interesting thing about the system is that it is unstable the problem is to design an encoding scheme and a decoder such that the estimation error is stable we explicitly construct a simple but efficient estimator for the binary symmetric channel bsc we are not aware of any such previous codes for the bsc we compare our results to the nonconstructive bounds of sahai

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

on the implementation of the poincare lindstedt technique abstract the aim of this paper is to present a new algebraic processor which implements the basic algebra of modified quasipolynomials including routines to compute the solution to a linear second order differential equation presenting undetermined coefficients the kernel of this algebraic system is a very useful tool for a generic implementation of the poincare lindstedt method to find periodic solutions in slightly perturbed systems

adaptive synchronization for generalized lorenz systems in literature it is conjectured that the states of the generalized lorenz system with an unknown parameter can not be estimated by adaptive observers in this paper we show that this unknown parameter and the states can actually be estimated simultaneously by some kind of adaptive observer the proof is obtained by constructing some exponential observer to achieve chaotic synchronization for the generalized lorenz system the result implies that more work needs to be done to apply generalized lorenz system in secure communication

determination of periodic solution for a u1 3 force by he s modified lindstedt poincare method abstract this paper applies he s modified lindstedt poincare method to determine the periodic solutions of oscillators in a u 1 3 force the result obtained and comparison with analytical solution provides confirmation for the validity of he s modified lindstedt poincare method

global robust distributed output consensus of multi agent nonlinear systems an internal model approach abstract this paper studies the problem of global robust distributed output consensus of heterogeneous leader follower multi agent nonlinear systems by general directed output interactions for a class of minimum phase single input single output nonlinear agents having unity relative degree it is shown that the problem is solvable by an internal model approach under certain mild conditions a lyapunov function based output feedback control law is developed by converting the global output consensus into a global distributed stabilization problem for an augmented network

a convolution integral method for certain strongly nonlinear oscillators a modification of the convolution integral method for linear oscillators is presented for the analysis of certain strongly nonlinear oscillators the modification provides an iteration scheme two examples are given to illustrate the effectiveness of the proposed method

a modified mickens iteration procedure for nonlinear oscillators based on the mickens procedure a new iteration scheme is proposed for nonlinear oscillators different from the existing mickens procedures in the proposed procedure the algebraic equation governing the frequency of oscillation deduced at each iteration stage is always linear taking the duffing equation as an illustrative example excellent approximations can be easily obtained furthermore the proposed procedure is extended to obtain the limit cycle of the van der pol equation additionally a computational disadvantage of the mickens procedure is eliminated

improved lindstedt poincare method for the solution of nonlinear problems abstract we apply the linear delta expansion lde to the lindstedt poincare distorted time method to find improved approximate solutions to nonlinear problems we find that our method works very well for a wide range of parameters in the case of the anharmonic oscillator duffing equation of the non linear pendulum and of more general anharmonic potentials the approximate solutions found with this method converge more rapidly to the exact ones than in the simple lindstedt poincare method

a generalized iteration procedure for calculating approximations to periodic solutions of truly nonlinear oscillators abstract an extended iteration method for calculating the periodic solutions of nonlinear oscillator equations is given the procedure is illustrated by applying it to two truly nonlinear oscillator differential equations

a non iterative derivative free method for nonlinear ordinary differential equations most methods for the determination of approximate solutions of nonlinear ordinary differential equations require that the nonlinearities be sufficiently differentiable with respect to the dependent variable and its derivatives in this paper a non iterative method for obtaining approximate solutions of nonlinear ordinary differential equations which does not require the derivatives of the nonlinearities is presented and its convergence is proved the method is also generalized for the determination of the periodic solutions of autonomous nonlinear ordinary differential equations by introducing as dependent variable the unknown frequency of oscillation the method does not require the presence of small parameters and can be used in a piecewise fashion

analytic upper and lower bounds for the period of nonlinear oscillators we show that analytic expressions for the frequency of second order nonlinear oscillations can be obtained from dual variational principles at each amplitude two analytic expressions can be constructed which constitute upper and lower bounds to the exact value of the frequency the results are accurate at small and large amplitude and compare well with the perturbative approach

on the variational iteration method and other iterative techniques for nonlinear differential equations abstract a variety of iterative methods for the solution of initial and or boundary value problems in ordinary and partial differential equations is presented these iterative procedures provide the solution or an approximation to it as a sequence of iterates for initial value problems it is shown that these iterative procedures can be written in either an integral or differential form the integral form is governed by a volterra integral equation whereas the differential one can be obtained from the volterra representation by simply differentiation it is also shown that integration by parts variation of parameters adjoint operators green s functions and the method of weighted residuals provide the same volterra integral equation and that this equation in turn can be written as that of the variational iteration method it is therefore shown that the variational iteration method is nothing else by the picard lindelof theory for initial value problems in ordinary differential equations and banach s fixed point theory for initial value problems in partial differential equations and the convergence of these iterative procedures is ensured provided that the resulting mapping is lipschitz continuous and contractive it is also shown that some of the iterative methods for initial value problems presented here are special cases of the bellman kalaba quasilinearization technique provided that the nonlinearities are differentiable with respect to the dependent variable and its derivatives but such a condition is not required by the techniques presented in this paper for boundary value problems it is shown that one may use the iterative procedures developed for initial value problems but the resulting iterates may not satisfy the boundary conditions and two new iterative methods governed by fredholm integral equations are proposed it is shown that the resulting iterates satisfy the boundary conditions if the first one does so the iterative integral formulation presented here is applied to ten nonlinear oscillators with odd nonlinearities and it is shown that its results coincide with those of differential two and three level iterative techniques harmonic balance procedures and standard and modified linstedt poincare techniques the method is also applied to two boundary value problems

cooperative global robust output regulation for nonlinear output feedback multiagent systems under directed switching networks in this paper we study the cooperative global robust output regulation problem for nonlinear multiagent systems in output feedback form with any relative degree subject to directed switching networks through the augmentation by a distributed internal model and a distributed observer of the given system we first convert the original problem into the global robust stabilization problem of the so called extended augmented system which is a multi input coupled switched system then we establish a few technical lemmas to lay the foundation for constructing a switching control law and the corresponding multiple lyapunov functions for the switched system then we present the solvability conditions of our problem via the multiple lyapunov functions and average dwell time method the main result will be applied to the leader following synchronization problem for a group of hyperchaotic lorenz multiagent systems with a directed switching network

solutions of nonlinear oscillators with fractional powers by an iteration procedure a modified iteration procedure is applied to nonlinear oscillations with fractional powers with the procedure the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained

a classical iteration procedure valid for certain strongly nonlinear oscillators a classical iteration procedure is applied to nonlinear oscillations of conservative single degree of freedom systems with odd nonlinearity with the procedure the analytical approximate frequency and the corresponding periodic solution valid for small as well as large amplitudes of oscillation can be obtained two examples are given to illustrate the accuracy and effectiveness of the method another advantage of this classical iteration approach is that it also works if the linear part of restoring force is zero

periodic orbits of the fourth order non autonomous differential equation u qu pu ef t u u u u abstract we provide sufficient conditions for the existence of periodic solutions of the fourth order differential equation u qu pu e f t u u u u where q p and e are real parameters e is small and f is a nonlinear non autonomous periodic function with respect to t moreover we provide some applications

synchronization and transient dynamics in the chains of electrically coupled fitzhugh nagumo oscillators chains of n fitzhugh nagumo oscillators with a gradient in natural frequencies and strong diffusive coupling are analyzed in this paper we study the system s dynamics in the limit of infinitely large coupling and then treat the case when the coupling is large but finite as a perturbation of the former case in the large coupling limit the 2n dimensional phase space has an unexpected structure there is an n 1 dimensional cylinder foliated by periodic orbits with an integral that is constant on each orbit when the coupling is large but finite this cylinder becomes an analog of an inertial manifold the phase trajectories approach the cylinder on the fast time scale and then slowly drift along it toward a unique limit cycle we analyze these dynamics using geometric theory for singularly perturbed dynamical systems asymptotic expansions of solutions rigorously justified and lyapunov s method

a new perturbative approach to nonlinear problems a recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the lagrangian such as 4 by 2 1 and then treating as a small parameter it is shown here that the same approach gives excellent results when applied to difficult nonlinear differential equations such as the lane emden thomas fermi blasius and duffing equations

a new perturbation technique in solution of nonlinear differential equations by using variable transformation a perturbation algorithm using a new variable transformation is introduced this transformation enables control of the independent variable of the problem the problems are solved with new transformation classical duffing equation with cubic nonlinear term and a singular perturbation problem results of multiple scales lindstedt poincare method new method and numerical solutions are contrasted

development of accurate solutions for a classical oscillator abstract we present a method to obtain arbitrarily accurate solutions for conservative classical oscillators the method that we propose here works both for small and large nonlinearities and provides simple analytical approximations a comparison with the standard lindstedt poincare method is presented from which the advantages of our method are clear

on linstedt poincare techniques for the quintic duffing equation abstract an artificial parameter method for the quintic duffing equation is presented the method is based on the introduction of a linear stiffness term and a new dependent variable both of which are proportional to the unknown frequency of oscillation the introduction of an artificial parameter and the expansion of both the solution and the unknown frequency of oscillation in series of the artificial parameter and results in linear ordinary differential equations at each order in the parameter by imposing the nonsecularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation the method does not require that a small parameter be present in the governing equation and its results are compared with those of linstedt poincare modified linstedt poincare harmonic balance and galerkin techniques it is shown that these four techniques predict the same first order approximation to the frequency of oscillation as the artificial parameter method presented in this paper and the latter introduces higher order corrections at second order whereas similar corrections are introduced by the linstedt poincare and modified linstedt poincare methods at orders equal to and higher than three