synchronization of chaotic liouvillian systems an application to chua s oscillator in this paper we deal with the synchronization of chaotic oscillators with liouvillian properties chaotic liouvillian system based on nonlinear observer design the strategy consists of proposing a polynomial observer slave system which tends to follow exponentially the chaotic oscillator master system the proposed technique is applied in the synchronization of chua s circuit using matlab simulink r and matlab r lmi programs simulation results are used to visualize and illustrate the effectiveness of chua s oscillator in synchronization

regulatory assessment of drug dissolution profiles comparability via maximum deviation in drug development comparability of dissolution profiles of 2 different formulations is usually assessed using the similarity factor f2 in practice the drug dissolution profiles are deemed similar if the f2 exceeds 50 which occurs when a 10 maximum difference in the mean percentage of the dissolved drug at each time point between test and reference formulation is obtained according to the guideline on the investigation of bioequivalence cpmp ewp qwp 1401 98 rev 1 corr use of the f2 is however restricted by a set of validity conditions if some of these conditions are not satisfied the f2 is not considered suitable and alternative statistical methods are needed in this article we propose an inferential framework based on the maximum deviation between curves to test the comparability of drug dissolution profiles the new methodology is applicable regardless whether the validity criteria of the f2 are met or not contrary to the f2 this approach also integrates the variability of the measurements over time and not only their average to benchmark our method we performed simulations informed by 3 real case studies provided by the european medicines agency and extracted from dossiers submitted to the centralised procedure for marketing authorisation application in the scenarios of the simulation study the new method controlled its type i error rate when the maximum deviation was greater than the similarity acceptance limit of 10 the power exceeded 80 for small values of the maximum deviation while the test was more conservative for intermediate ones our results were also very robust to sampling variations based on these positive findings we encourage applicants to consider the new maximum deviation based method as a valid alternative to the f2 especially when the validity criteria of the latter are not met

chaos synchronization of different chaotic systems subjected to input nonlinearity abstract in this paper a unified mathematical expression describing a class of synchronization systems is presented for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied based on lyapunov stability theory a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the lyapunov sense in spite of the input nonlinearity this technique is applied to achieve chaos synchronization of three pairs of different chaotic systems lorenz chen chen liu and liu lorenz in drive response structure the numerical simulation results demonstrate the validity and feasibility of the proposed controller

generalized q s lag anticipated and complete synchronization in modified chua s circuit and hindmarsh rose systems abstract based on symbolic computation system maple and lyapunov stability theory a systematic powerful and concrete scheme is extended to study the generalized q s lag anticipated and complete synchronization between two identical modified chua s circuit with different initial values and between two different chaotic systems hindmarsh rose system and modified chua s circuit numerical simulations are used to verify the effectiveness of the obtained controller

control and synchronize a novel hyperchaotic system the control and hybrid projective synchronization hps strategies for a novel hyperchaotic system are investigated firstly the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables secondly based on lyapunov s direct method hps between two novel hyperchaotic systems is studied a new nonlinear feedback vector controller is designed to guarantee hps which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems finally numerical simulations are given to verify the effectiveness of these strategies the proposed methods have certain significances for reducing the cost and complexity for controller implementation

on maximal weight solutions of two matricial moment problems in the nondegenerate case abstract we first revisit the question of existence and uniqueness of maximal weight solutions of the truncated trigonometric matrix moment problem problem ttm in the nondegenerate case the starting point of the consideration is a specialized representation of the matrix weight assigned at each point on the unit circle for the solutions of nondegenerate problem ttm our approach is essentially self contained and different from the existing methods moreover based on this approach we also derive some important weight features of the so called n extremal solutions within the whole solution set of nondegenerate problem ttm and the discrete structure of them in the second part these observations inspire us to look for the corresponding weight features of the solutions of a nondegenerate moment problem for rational matrix valued functions problem r where only the theory of orthogonal matrix polynomials on the unit circle is involved

a new approach for secure communication using constrained hyperchaotic systems a new constrained hyperchaotic system is presented a secure communication scheme using the generated chaotic signals is proposed the crls estimator for nonlinear systems is used for chaos synchronization the crls estimator and the convergence of its nonlinear update phase are analyzed simulation results demonstrate the proposed secure scheme effectiveness in this paper a new technique is developed for a typical secure communication scheme in this approach we introduce the concept of constrained hyperchaotic systems to encrypt the carrier of the data signal to be transmitted at the transmitter end two different chaotic oscillators are coupled constrained and used as a new hyperchaotic system one of the outputs of the constrained hyperchaotic system is used as a carrier for the encrypted data then the outputs of the system including the modulated carrier are encrypted using a set of pre defined encryption rules at the receiving end and after decrypting the received outputs the discrete time constrained regularized least square crls estimator is used to reconstruct the constrained hyperchaotic signals and hence retrieve the transmitted data simulation results are presented to illustrate the capability of the crls estimator in reconstructing the states of the constrained hyperchaotic system moreover the proposed secure communication scheme is applied to transmit discrete images for which the quality of the transmission process is measured by the bit error rate ber

adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters in this paper the problems of control and synchronization of a novel hyperchaotic system with uncertain parameters are studied based on the lyapunov stability theory and the adaptive control theory this uncertain hyperchaotic system is suppressed to its unstable equilibrium furthermore synchronization between two identical uncertain hyperchaotic systems is achieved by proposing an adaptive control law and a parameter estimation update law numerical simulations are presented to demonstrate the analytical results

hyperchaotic states in the parameter space abstract in this paper we propose a numerical method to characterize hyperchaotic points in the parameter space of continuous time dynamical systems the method considers the second largest lyapunov exponent value as a measure of hyperchaotic motion to construct two dimensional parameter space color plots different levels of hyperchaos in these plots are represented by a continuously changing yellow red scale as an example a particular system modeled by a set of four nonlinear autonomous first order ordinary differential equations is considered practical applications of these plots include by instance walking in the parameter space of hyperchaotic systems along desirable paths

chaos synchronization of a new hyperchaotic system abstract in this paper two kinds of synchronization schemes for a new hyperchaotic system are presented firstly on the basis of stability criterion of linear system synchronization is achieved with the help of the active control theory secondly a nonlinear controller is designed according to lyapunov stability theory to assure that synchronization can be achieved furthermore an adaptive control approach for synchronization of uncertain hyperchaotic systems is proposed finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods

more on loewner matrices abstract the study of loewner matrices is continued in a direction close to the recent work by fiedler ptak and vav in all results are stated for the general case of multiple interpolation nodes i e for generalized loewner matrices both the loewner bezoutian connection of antoulas and anderson and the loewner hankel connection of vav in in the general case which are re proved in a simple way provide a good opportunity for finding various properties of loewner matrices some of them being generalizations of results published by other authors for simple nodes only there are also results which are new especially the barnett like formulas and an intertwining relation characteristic for loewner matrices as well as the loewner matrix hankel vector connection in order to handle loewner matrices further on the authors introduce and deal with a class of so called r matrices it turns out that some known results concerning bezoutians hankel matrices and their products can in a natural way be lifted to the level of r matrices and of the products of loewner and r matrices

on hermite interpolation by cauchy vandermonde systems the lagrange formula the adjoint and the inverse of a cauchy vandermonde matrix for a given cauchy vandermonde system and for given multiple nodes a lagrange type formula for the interpolant is derived interpolating a given function in the sense of hermite we give explicit analytic representations of the basic functions in terms of the nodes and prescribed poles they are used to derive formulas for the entries of the adjoint of the confluent cauchy vandermonde matrix corresponding to the interpolation problem thus providing an explicit representation of its inverse

the general rational interpolation problem and its connection with the nevanlinna pick interpolation and power moment problem abstract the hankel vector approach in a recent work of the author with zhao and zhang on the general rational interpolation problem grip allows the problem to be reduced to what amounts to a limiting case i e a high order rational interpolation at only a single node infinity in particular it gives rise to a new method to find the coefficient matrix of the linear fractional parametrization of interpolants to the grip this approach is extended in the present paper to the nevanlinna pick np interpolation problem with multiple nodes in the class of nevanlinna functions which can be in essence considered as a grip with certain symmetries the hankel vector suitably adapted to the present situation is in fact a finite nonnegative sequence relative to an axis if the problem is solvable in particular a finite positive sequence in the indeterminate case this development leads to an intrinsic connection between the np problem and problems of the truncated power moment and reconstructing generators of the hankel vector in question and therefore opens up certain ways for the discussion and solution of the np problem and its relatives on the basis of the theories of the rational interpolation and algebraic moment problems

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

synchronization of a large number of continuous one dimensional stochastic elements with time delayed mean field coupling abstract we study synchronization as a means of control of collective behavior of an ensemble of coupled stochastic units in which oscillations are induced merely by external noise for a large number of one dimensional continuous stochastic elements coupled non homogeneously through the mean field with delay we developed an approach to find a boundary of synchronization domain and the frequency of the mean field oscillations on it namely the exact location of the synchronization threshold is shown to be a solution of the boundary value problem bvp which was derived from the linearized fokker planck equation here the synchronization threshold is found by solving this bvp numerically approximate analytics is obtained by expanding the solution of the linearized fokker planck equation into a series of eigenfunctions of the stationary fokker planck operator bistable systems with a polynomial and piece wise linear potential are considered as examples multistability and hysteresis in the mean field behavior are observed in the stochastic network at finite noise intensities in the limit of small noise intensities the critical coupling strength is shown to remain finite provided that the delay in the coupling function is not infinitely small delay in the coupling term can be used as a control parameter that manipulates the location of the synchronization threshold

synchronization of lurie system based on contraction analysis in this paper a new synchronization criterion for chaotic lurie systems with sector and slope restricted nonlinearities is proposed without analyzing the stability of the error system synchronization condition for general lurie systems is firstly given based on the contraction analysis furthermore the result is extended to the chua s system whose state equation is not differentiable finally three representative examples are presented to support the theoretical results

a special full state hybrid projective synchronization in symmetrical chaotic systems a special full state hybrid projective synchronization type is proposed in this paper the anti synchronization and complete synchronization can be achieved simultaneously in this new synchronization phenomenon we point out how to realize this synchronization in chaotic systems anti synchronization in symmetrical coordinate subspace and complete synchronization in its normal coordinate subspace two illustrative examples multi scroll chaotic system by the partial lyapunov stability theory and a four dimensional chaotic system by the invariance principle of differential equation are presented to exhibit this new synchronization

on an interpolation problem for j potapov functions abstract the main goal of this paper is the study of an analogue of the matricial schur problem for the potapov class p j d of j contractive meromorphic functions in the open unit disk d using an approach which is based on an analysis of j central j potapov functions we will solve this problem in the most general case moreover in the nondegenerate case we will give a description of the corresponding weyl matrix balls furthermore we will investigate the limit behaviour of the weyl matrix balls associated with the functions belonging to some particular subclass of p j d

the nevanlinna pick interpolation problems and power moment problems for matrix valued functions abstract this paper is concerned with the study of several types of matrix interpolation problems including the matrix nevanlinna pick interpolation problem in the nevanlinna class n p the matrix nevanlinna pick interpolation problem in the stieltjes class l p the truncated matrix power moment problem on the real axis the stieltjes matrix power moment problem we use the so called block hankel vector approach for the treatment of these problems and make explicit the correspondence between solutions to the nevanlinna pick interpolation problem and solutions to an associated power moment problem with the block hankel vector under consideration this enables one not only to find existence criteria for the solutions of the nevanlinna pick interpolation problem but also to describe the solutions based on the results of power moment problem and vice versa

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

design of pd controller for master slave synchronization of lur e systems with time delay in this paper design of pd controller for master slave synchronization of lur e systems with time delay has been considered a new delay dependent synchronization criterion is derived based on the integral inequality method and free weighting matrices the criteria are given in terms of lmis which can be easily solved by lmi toolbox in matlab a numerical example is given to illustrate the effectiveness of the method

the function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems the function cascade synchronization scheme for the hyperchaotic systems is proposed to make the states of two identical the hyperchaotic systems both with and without uncertain parameters asymptotically synchronized based on lyapunov stability theory and the proposed scheme the lu system and chen hyperchaotic system with and without uncertain parameters are chosen to achieve the function cascade synchronization simultaneously numerical simulations are used to verify the effectiveness and feasibility of the presented control scheme

orthogonal matrix polynomials and applications orthogonal matrix polynomials on the real line or on the unit circle have properties which are natural generalizations of properties of scalar orthogonal polynomials appropriately modified for the matrix calculus we show that orthogonal matrix polynomials both on the real line and on the unit circle appear at various places and we describe some of them the spectral theory of doubly infinite jacobi matrices can be described using orthogonal 2 x 2 matrix polynomials on the real line scalar orthogonal polynomials with a sobolev inner product containing a finite number of derivatives can be studied using matrix orthogonal polynomials on the real line orthogonal matrix polynomials on the unit circle are related to unitary block hessenberg matrices and are very useful in multivariate time series analysis and multichannel signal processing finally we show how orthogonal matrix polynomials can be used for gaussian quadrature of matrix valued functions parallel algorithms for this purpose have been implemented using pvm and some examples are worked out

multiple nevanlinna pick interpolation with both interior and boundary data and its connection with the power moment problem abstract the so called hankel vector approach is used to handle three boundary versions of the multiple nevanlinna pick interpolation problem in the nevanlinna class n involving both interior and boundary data it turns out that each of these boundary interpolation problems can be reduced to what amounts to a certain truncated standard or nonstandard hamburger moment problem associated with the hankel vector of the former with some possible constraint on distribution functions that assign no mass to any of the real nodes in particular this leads to solvability criteria for each of these interpolation problems and the description of solutions by using results from theory of moments

on the multiple nevanlinna pick matrix interpolation in the class cp and the caratheodory matrix coefficient problem abstract in the present paper an intrinsic one to one correspondence between the finite multiple nevanlinna pick matrix interpolation np problem in the caratheodory class and the caratheodory matrix coefficient cc problem or equivalently the truncated trigonometric matrix moment tm problem is established thanks to this correspondence the np problem is reduced to what amounts to solving the cc problem or the tm problem associated with the so called toeplitz block vector of the former in both the nondegenerate and degenerate cases simultaneously

on rank invariance of generalized schwarz pick potapov block matrices of matrix valued caratheodory functions abstract in view of a multiple nevanlinna pick interpolation problem we study the rank of generalized schwarz pick potapov block matrices of matrix valued caratheodory functions those matrices are determined by the values of a caratheodory function and the values of its derivatives up to a certain order we derive statements on rank invariance of such generalized schwarz pick potapov block matrices these results are applied to describe the case of exactly one solution for the finite multiple nevanlinna pick interpolation problem and to discuss matrix valued caratheodory functions with the highest degree of degeneracy

conditions for common noise induced synchronization in time delay systems we studied synchronization induced by a common external noise in scalar time delay systems we have found a set of sufficient conditions for the synchronization this set of conditions shows that the synchronization occurs in a wide class of time delay systems numerical evidence for the analytically obtained conditions is also presented

a new hyperchaotic system and its synchronization in this paper a four dimensional 4d continuous autonomous hyperchaotic system is introduced and analyzed this hyperchaotic system is constructed by adding a linear controller to the 3d autonomous chaotic system with a reverse butterfly shape attractor some of its basic dynamical properties such as lyapunov exponents poincare section bifurcation diagram and the periodic orbits evolving into chaotic hyperchaotic dynamical behavior by varying parameter d are studied furthermore the full state hybrid projective synchronization fshps of new hyperchaotic system with unknown parameters including the unknown coefficients of nonlinear terms is studied by using adaptive control numerical simulations are presented to show the effective of the proposed chaos synchronization scheme

a modified chua chaotic oscillator and its application to secure communications a new modification to the chua oscillator is proposed bifurcation diagrams poincare map and the lyapunov exponents are presented an application to secure communications is presented a synchronization scheme based on the modified oscillator is proposed system simulations are performed for analysis in this paper a new modified chua oscillator is introduced the original chua oscillator is well known for its simple implementation and mathematical modeling a modification of the oscillator is proposed in order to facilitate the synchronization and the encryption and decryption scheme the modification consists in changing the nonlinear term of the original oscillator to a smooth and bounded nonlinear function a bifurcation diagram a poincare map and the lyapunov exponents are presented as proofs of chaoticity of the newly modified oscillator an application to secure communications is proposed in which two channels are used numerical simulations are performed in order to analyze the communication system

the nevanlinna pick interpolation problems and power moment problems for matrix valued functions iii the infinitely many data case abstract the objective of this paper is to establish an intrinsic and simple correspondence between a multiple nevanlinna pick matrix interpolation np problem in the nevanlinna class n p with a denumerable set of nodes and a certain full hamburger matrix moment problem with the help of the indicated correspondence the solution of an infinite np problem in n p can be reduced to what amounts to the study of the associated full hamburger matrix moment problem with the so called block hankel vector of the former and vice versa these investigations can be regarded as a natural extension of our previous work on both the np problems with a finite set of interpolation data and the truncated power matrix moment problems

adaptive control and synchronization of a modified chua s circuit system this study addresses the adaptive control and synchronization of the modified chua s circuit system with unknown system parameters adaptive control law is applied to suppress chaos to one of the three steady states adaptive control law is applied to achieve synchronization of two identical modified chua s circuit systems routh hurwitz criteria and lyapunov direct method are used to study the asymptotic stability of the steady states numerical simulations are included to show the effectiveness of the proposed control method

singular reduced order observer based synchronization for uncertain chaotic systems subject to channel disturbance and chaos based secure communication this paper deals with the issues of chaotic synchronization and chaos based secure communication for chaotic systems subject to uncertain parameters and channel disturbance first an augmented singular system is constructed by introducing an augmented vector which consists of both the state and channel disturbance vectors of original drive system and a singular reduced order observer which can not only synchronize the drive system but also reconstruct channel disturbance is developed for the augmented singular system second a second order sliding mode observer is considered to get the exact estimates of output derivatives in a finite time based on the estimates of states and output derivatives a kind of algebraic unknown information recovery method which can recover information signal injected into the drive system and estimate parameter disturbance is proposed finally a numerical simulation example is given to illustrate the effectiveness of the proposed methods

chaos control and hybrid projective synchronization of several new chaotic systems abstract the problems on purposefully creating and controlling chaos are investigated first several new 4d chaotic systems are presented based on a 3d chaotic system and three dynamical characteristics are verified second it is demonstrated that they can be stabilized to their equilibrium points by a same single scalar adaptive feedback control law third two of the chaotic systems with constant parameters are in hybrid projective synchronization hps by presented adaptive feedback control strategies which can be simplified into a scalar form for identical drive response systems to achieve complete synchronization furthermore hps between two of the chaotic systems with response system parameters unknown is also considered and adaptive parameter update laws are developed numerical simulations show their characteristics and verify the effectiveness of the strategies

quadratic optimal synchronization of uncertain chaotic systems abstract this paper investigates the quadratic optimal synchronization of uncertain chaotic systems with parameter mismatch parametric perturbations and external disturbances on both master and slave systems a robust control scheme based on lyapunov stability theory and quadratic optimal control approach is derived to realize chaotic synchronization the sufficient criterion for stability condition is formulated in a linear matrix inequality lmi form the effect of uncertain parameters and external disturbance is suppressed to an h norm constraint an adaptive algorithm is proposed to adjust the uncertain bound in the robust controller avoiding the chattering phenomena the simulation results for synchronization of the chua s circuit system and the lorenz system demonstrate the effectiveness of the proposed scheme

solution of a multiple nevanlinna pick problem via orthogonal rational functions abstract we consider a nevanlinna pick type interpolation problem for caratheodory functions where the values of the function and its derivatives up to certain orders are given at finitely many points of the unit disk the set of all solutions of this problem is described by means of the orthogonal rational functions which play here a similar role as the orthogonal polynomials on the unit circle in the classical case of the trigonometric moment problem in particular we use a connection between szego and schur parameters which in the classical situation was discovered by ja l geronimus

on boundary nevanlinna pick interpolation for caratheodory matrix functions abstract a matrix version of the boundary nevanlinna pick interpolation problem in the class of caratheodory matrix functions is considered this matrix interpolation problem is reduced to a certain matrix trigonometric moment problem with specified constraints that the nonnegative matrix valued measure has no mass distributions at a finite number of boundary points basing on the use of recent results due to bolotnikov and dym and this reduction we obtain solvability criteria for both the boundary nevanlinna pick interpolation problem and the moment problem a parameterized description of all the solutions of each of these two problems under consideration in the nondegenerate case is given as well

minimum w entropy interpolants for matricial caratheodory functions and maximum determinant completions of associated block pick matrix abstract the so called modified block toeplitz vector approach is used to connect a class of particular solutions g w for w d of a nondegenerate interpolation problem of the nevanlinna pick type with a class of particular solutions f w of a certain matricial caratheodory coefficient problem in a transparent way this will suggest a simple approach to the minimum w entropy interpolants and the maximum determinant completions of the associated block pick matrix within the framework of that nevanlinna pick type interpolation problem by using the known assertions corresponding to f w it turns out that g w w d is exactly or provides us with the unique solution to these two extremal problems in a manner

on the multiple nevanlinna pick interpolation problems in some matrix valued function classes abstract someintrinsicone to onecorrespondencesbetweenthesolutionstothemultiplenevanl inna pick interpolation problems and the solutions to the associated truncated power trigonometric moment problems are established the solvability criteria for the interpolation problems are given the method used in the paper is the so called hankel toeplitz block vector approach

synchronization control of stochastic delayed neural networks abstract in this paper synchronization control of stochastic neural networks with time varying delays has been considered a novel control method is given using the lyapunov functional method and linear matrix inequality lmi approach several sufficient conditions have been derived to ensure the global asymptotical stability in mean square for the error system and thus the drive system synchronize with the response system also the estimation gains can be obtained with these new and effective methods synchronization can be achieved simulation results are given to verify the theoretical analysis in this paper

exponential synchronization of a new lorenz like attractor with uncertain parameters via single input the new lorenz like attractor reported by li et al 2009 1 includes a product term of system parameters it can be predicted that chaotic synchronization of this new chaotic system becomes more complicated by taking account of uncertain system parameters in this paper the exponential synchronization between two nearly identical lorenz like attractors by applying single input controller associated with system parameter update laws is proposed unlike multiple control inputs and state variable feedbacks required in chaotic synchronization in the literature the proposed single input controller includes only one state variable proportional feedback two kinds of system parameter update laws are introduced and sufficient conditions are provided to guarantee exponential stability of both synchronous errors and system parameter errors in addition numerical simulations are also performed to verify the effectiveness of presented schemes

controlling hyperchaos in the new hyperchaotic chen system in this paper we investigate the new hyperchaotic chen system which was present recently by introducing a feedback controller to the chen system the linear speed nonlinear doubly periodic function and nonlinear hyperbolic function feedback controls are used to suppress hyperchaos to unstable equilibrium the routh hurwitz theorem is used to derive the conditions of stability of controlled hyperchaotic chen systems moreover numerical simulations are used to verify the effectiveness of the proposed controllers

generating hyperchaotic lu attractor via state feedback control this paper constructs a new hyperchaotic system based on lu system by using a state feedback controller the detailed dynamical behaviors of this hyperchaotic system are further investigated including lyapunov exponents spectrum bifurcation and poincare mapping moreover a novel circuit diagram is designed for verifying the hyperchaotic behaviors and some experimental observations are also given

comparison of drug dissolution profiles a proposal based on tolerance limits meaningful comparison of the dissolution profiles between the reference and test formulations of a drug is critical for assessing similarity between the two formulations and for quality control purposes such a dissolution profile comparison is required by regulatory authorities and the criteria used for this include the widely used difference factor f1 and a similarity factor f2 recommended by the food and drug administration in spite of their extensive use in practice the two factors have been heavily criticized on various grounds the criticisms include ignoring sampling variability and ignoring the correlations across time points while using the criteria in practice the goal of this article is to put f1 and f2 on a firm statistical footing by developing tolerance limits for the distributions of f1 and f2 so that both the sampling variability and the correlations over time points are taken into account because f1 and f2 are defined in terms of sample mean dissolution profiles they are not appropriate for comparing individual dissolution profiles for the latter we have considered similar criteria and have derived tolerance limits both parametric and nonparametric approaches are explored and a bootstrap calibration is used to improve accuracy of the tolerance limits simulated coverage probabilities show that the method leads to accurate tolerance limits two examples are used to illustrate the methodology copyright 2016 john wiley sons ltd

analysis of a new chaotic system abstract this paper reports a new three dimensional continuous quadratic autonomous chaotic system modified from the lorenz system in which each equation contains a single quadratic cross product term which is different from the lorenz rossler chen lu systems basic properties of the new system are analyzed by means of lyapunov exponent spectrum and bifurcation diagrams analysis results show that this system has complex dynamics with some interesting characteristics