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

optimal tracking control of nonlinear dynamical systems this paper presents a simple methodology for obtaining the entire set of continuous controllers that cause a nonlinear dynamical system to exactly track a given trajectory the trajectory is provid

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

certainty equivalence in nonlinear output regulation with unmeasured error in this article we consider a nonlinear output regulation problem in which the controlled output and the measured output are not the same it is assumed that the controlled plant has a single control input and that it can be transformed into gauthier kupka s observability canonical form then it is shown that a design based on certainty equivalence is effective for determining a controller that solves the given problem

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

brief mixed internal model based and feedforward control for robust tracking in nonlinear systems the purpose of this paper is to compare different features of two approaches to the problem of tracking prescribed trajectories in a nonlinear system and to propose a possible merger of these approaches in what is called here the problem of asymptotically robust perfect tracking the latter is the problem of designing a feedforward error feedback control law achieving perfect tracking in case the initial conditions of the system exosystem are known and compatible with perfect tracking and asymptotic tracking in all other cases

robust synchronization of chaotic horizontal platform systems with phase difference this paper studies a robust synchronization of non autonomous chaotic systems with parameter mismatch in the synchronization scheme a linear state error feedback control is used to couple the master and slave horizontal platform systems excited by harmonic external forces between which there exists a phase mismatch a new definition of global synchronization with error bound is introduced using lyapunov s stability theory the sufficient synchronization criteria for the scheme are proven and the corresponding synchronization error bound is estimated the synchronization criteria are further optimized by optimally designing a quadratic lyapunov function to more precisely estimate the synchronization error bound the illustrative simulations verify the effectiveness of these criteria the estimated synchronization error bound is compared with numerical one in the examples

chaos and chaos synchronization of a symmetric gyro with linear plus cubic damping the dynamic behavior of a symmetric gyro with linear plus cubic damping which is subjected to a harmonic excitation is studied in this paper the liapunov direct method has been used to obtain the sufficient conditions of the stability of the equilibrium points of the system by applying numerical results time history phase diagrams poincare maps liapunov exponents and liapunov dimensions are presented to observe periodic and chaotic motions besides several control methods the delayed feedback control the addition of constant motor torque the addition of period force and adaptive control algorithm aca have been used to control chaos effectively finally attention is shifted to the synchronization of chaos in the two identical chaotic motions of symmetric gyros the results show that one can make two identical chaotic systems to synchronize through applying four different kinds of one way coupling furthermore the synchronization time is also examined

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

chaos synchronization of nonlinear gyros in presence of stochastic excitation via sliding mode control abstract in this paper the problem of synchronization between two chaotic gyros with stochastic base excitation based on the mater slave scheme is studied the stochastic excitation is modeled by applying a gaussian white noise to the deterministic model of gyro the white noise is derived from the wiener process so the resulted system is a stochastic differential equation and is modeled by an ito differential form using a modified sliding mode control a markov synchronizing control law is designed and the convergence of error states to the sliding surface in the mean square norm is analytically proved simulation results show the high performance of the proposed controller in stochastic chaos synchronization of gyro systems

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

chaos synchronization and parameter estimation of single degree of freedom oscillators via adaptive control this paper addresses the problem of synchronizing a class of single degree of freedom oscillators with uncertain parameters a modified adaptive control scheme is proposed to achieve globally asymptotic stable synchronization between the master and slave oscillators with arbitrary different initial conditions based on the barbalat s lemma one of the advantages of the method is that it requires only a scalar driving signal which may be easily designed in practical applications on the other hand the method can ensure that the unknown parameters in the slave oscillator would be completely estimated with an adaptive updating law numerical simulations are performed on two examples to verify the analytical results

on the organisation of transient chaos application to irregular scattering it is shown how the local structure of chaotic repellers being responsible for transient chaotic behaviour is deduced from the properties of hyperbolic periodic orbits relations between static and dynamical multifractal spectra with respect to the natural invariant measure on the repeller are derived for invertible maps of the plane the results obtained for maps with unit jacobian apply to hamiltonian systems with two degrees of freedom which exhibit the phenomenon of irregular scattering and are characterised by an exponential decay of trapping probability

non resonance conditions for uniform observability in the problem of nonlinear output regulation abstract this paper deals with the design of an internal model based semiglobal output feedback regulator for possibly non minimum phase nonlinear systems taking advantage of the design tool proposed in isidori ieee trans automat control 45 10 2000 we show how the problem of output regulation can be reformulated into an output feedback stabilization problem of a suitably defined extended auxiliary system the output feedback stabilization of the extended auxiliary system is addressed in the second part of the paper where an observer based stabilizer is proposed the existence of the latter is characterized in terms of necessary and sufficient conditions which can be interpreted as nonlinear non resonance conditions between the modes of the exosystem and the zero dynamics of the controlled plant

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

a new swing up law for the furuta pendulum in this paper the swing up problem for the furuta pendulum is solved applying fradkov s speed gradient sg method to a dimension 4 model of the system the new law is compared with the conventional astrom furuta strategy based on a dimension 2 model a comparative analysis including simulations and experiments whereby the advantages and effectiveness of the new law for swinging the pendulum up are shown is included

master slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control global chaos synchronization of two identical non autonomous horizontal platform systems coupled by linear state error feedback controller is investigated the sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time varied systems and lyapunov s direct method of which the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices in the examples the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified it is analytically and numerically examined that the synchronization criteria based on lyapunov s direct method are sharper than the criteria based on the stability theory of linear time varied systems

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

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

anticontrol of chaos of the fractional order modified van der pol systems anticontrol of chaos of fractional order modified van der pol systems is studied addition of a constant term and addition of k x sinx term where x is a state of the system are used to anticontrol the system effectively by applying numerical results phase portrait poincare maps and bifurcation diagrams a variety of the phenomena of the chaotic motion can be presented finally it can be find that chaos under these procedures exists in the fractional order systems of a modified van der pol system

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

the direct lyapunov method for the stabilisation of the furuta pendulum a nonlinear controller for the stabilisation of the furuta pendulum is presented the control strategy is based on a partial feedback linearisation in a first stage only the actuated coordinate of the furuta pendulum is linearised then the stabilising feedback controller is obtained by applying the lyapunov direct method that is using this method we prove local asymptotic stability and demonstrate that the closed loop system has a large region of attraction the stability analysis is carried out by means of lasalle s invariance principle to assess the controller effectiveness the results of the corresponding numerical simulations are presented

adaptation and its impact on the dynamics of a system of three competing populations abstract we investigate how the adaptation of the competition coefficients of the competing populations for the same limited resource influences the system dynamics in the regions of the parameter space where chaotic motion of shilnikov kind exists we present results for two characteristic values of the competition coefficient adaptation factor the first value 0 05 belongs to the small interval of possible negative values of for this a transition to chaos by period doubling bifurcations occurs and a window of periodic motion exists between the two regions of chaotic motion with increasing the system becomes more dissipative and the number of the windows of periodic motion increases when 1 0 a region of transient chaos is observed after the last window of periodic motion we verify the picture of the system dynamics by power spectra histograms and autocorrelations and calculate the lyapunov exponents and kaplan yorke dimension finally we discuss the eligibility of the investigated system for a topological analysis

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

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

reduction principles and the stabilization of closed sets for passive systems in this technical note we explore the stabilization of closed invariant sets for passive systems and present conditions under which a passivity based feedback asymptotically stabilizes the goal set our results rely on novel reduction principles allowing one to extrapolate the properties of stability attractivity and asymptotic stability of a dynamical system from analogous properties of the system on an invariant subset of the state space

stabilization of the furuta pendulum around its homoclinic orbit we present an energy based control approach to control the furuta pendulum a controller is proposed for swinging the pendulum and raise it to its uppermost unstable equilibrium position the passivity properties of the system are used as a guideline in the control strategy the stability analysis is carried out by using a lyapunov technique

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

a dissipativity based approach to output regulation of non minimum phase systems abstract the present paper presents a new contribution to the design of output regulators for a class of nonlinear systems characterized by a possibly unstable zero dynamics it is shown that the problem in question can be reduced to a stabilization problem with a supplementary gain constraint for a suitably defined reduced auxiliary plant

chaos chaos control and synchronization of a gyrostat system abstract the dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper by applying numerical results phase diagrams power spectrum period t maps and lyapunov exponents are presented to observe periodic and choatic 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 several methods the delayed feedback control the addition of constant torque the addition of periodic force the addition of periodic impulse torque injection of dither signal control adaptive control algorithm aca control and bang bang control are used to control chaos effectively finally synchronization of chaos in the gyrostat system is studied

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

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

the regular and chaotic motions of a symmetric heavy gyroscope with harmonic excitation abstract the non linear motion of a symmetric gyro mounted on a vibrating base is investigated with particular emphasis on its long term dynamic behavior for a wide range of parameters a single modal equation is used to analyze the qualitative behaviour of the system external disturbance appears as vertical harmonic motion of the support point and linear damping is assumed the complete equation of motion is a non linear non autonomous one the stability of the system has been studied by damped mathieu equation theory and the liapunov direct method as the system is subjected to external disturbance the melnikov method is used to show the existence of chaotic motion finally the bifurcation of the parameter dependent system is studied numerically the time evolutions of the non linear dynamical system responses are described in phase portraits via the poincare map technique the occurrence and the nature of chaotic attractors are verified by evaluating liapunov exponents and average power spectra the effect of the gyroscope s spinning speed is also studied and it is shown that the gyroscope s spin velocity zhas a significant effect on the dynamic behaviour of the motion

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

rigorous statistical procedures for data from dynamical systems various questions about the invariant measures of a dynamical system can be answered by computations of regular functionals or by ranking methods based on a set of observations this includes symmetry tests and the determination of dimension coefficients the paper contains the theoretical results and several simulations explain the methods

turbulence in multistep methods for initial value problems solving a scalar initial value problem with a numerical k step scheme amounts to iterating a k dimensional discrete dynamical system in this paper we investigate regular and chaotic behaviour of some dynamical systems associated with adams bashforth formulas applied to a simple nonlinear test equation

some applications of hausdorff dimension inequalities for ordinary differential equations upper bounds are obtained for the hausdorff dimension of compact invariant sets of ordinary differential equations which are periodic in the independent variable from these are derived sufficient conditions for dissipative analytic n dimensional periodic differential equations to have only a finite number of periodic solutions for autonomous equations the same conditions ensure that each bounded semi orbit converges to a critical point these results yield some information about the lorenz equation and the forced duffing equation

stabilization of the inverted pendulum around its homoclinic orbit the inverted pendulum has been used as a benchmark for motivating the study of nonlinear control techniques we propose a simple controller for balancing the inverted pendulum and raise it to its upper equilibrium position while the cart displacement is brought to zero the control strategy is based on an energy approach of the cart and pendulum system

adaptive sinusoidal disturbance cancellation for unknown lti systems despite input delay solutions exist for the problems of canceling sinusoidal disturbances and compensating input delays in this paper two problems are considered simultaneously and an adaptive controller is designed to cancel unknown sinusoidal disturbances forcing an unknown linear time invariant system in controllable canonical form despite input delay the design is based on three steps 1 parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters 2 representation of the delay as a transport pde 3 design of the adaptive controller by using the backstepping boundary control technique for pdes it is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t with perfect disturbance estimation the effectiveness of the controller is illustrated with a simulation example of a second order system

stability and lyapunov stability of dynamical systems a differential approach and a numerical method abstract a set of differential equations for the eigenvalues and eigenvectors of the stability matrix of a dynamical system as well as for the lyapunov exponents and the corresponding eigenvectors is derived the rate of convergence of the lyapunov eigenvectors is shown to be exponential the eigenvectors of the stability matrix can be grouped into sets each spanning a subspace which converges at an exponential rate it is demonstrated that generically the real parts of the eigenvalues of the stability matrix equal the corresponding lyapunov exponents this statement has been tested numerically the values of the lyapunov exponents i are shown to be related to the corresponding finite time values of the lyapunov exponents e g those deduced from a finite time numerical simulation i t by i t i b i i t t the b i s are constants and i t are noise terms of zero mean this observation leads to a method of extrapolation which has been used to predict lyapunov exponents from a finite amount of data it is shown that the use of the standard numerical methods to compute lyapunov exponents introduces an error a i t in the value of i t where the a i s are constants thus the standard method has a rate of convergence which is the same as that of the exact i t s finally we have shown how one can compute the eigenvectors associated with each of the eigenvalues of the stability matrix as well as the lyapunov eigenvectors

brief paper geometric characterization on the solvability of regulator equations the solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method the feedback part of the regulator equation that is the feasible controllers for the regulator equation is studied thoroughly the concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility useful results such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds are also obtained

generalized synchronization of chaotic systems by pure error dynamics and elaborate lyapunov function abstract the generalized synchronization is studied by applying pure error dynamics and elaborate lyapunov function in this paper generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation instead of current mixed error dynamics in which master state variables and slave state variables are presented the elaborate lyapunov function is applied rather than the current plain square sum lyapunov function deeply weakening the power of lyapunov direct method the scheme is successfully applied to both autonomous and nonautonomous double mathieu systems with numerical simulations

integral control for synchronization of complex dynamical networks with unknown non identical nodes this paper proposes a high gain integral controller for synchronization of complex dynamical networks with unknown non identical nodes the integral controller converts the complex dynamical system into a singular perturbation form then a sufficient condition for global synchronization is derived finally the numerical simulation is presented to illustrate the effectiveness of the proposed method

a note on the problem of semiglobal practical stabilization of uncertain nonlinear systems via dynamic output feedback it is known that if a system can be robustly globally asymptotically stabilized by means of a feedback that is driven by functions that are uniformly completely observable uco then this system can be practically semiglobally stabilized by means of possibly dynamic output feedback this papers discusses a significant structural hypothesis under which the existence of a dynamic feedback driven by uco functions is guaranteed the class of systems which satisfy this hypothesis includes any stabilizable and detectable linear system and any relative degree one nonlinear system which is stabilizable by dynamic output feedback in particular the hypothesis does not require the system to be minimum phase

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

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

chaos synchronization of double duffing systems with parameters excited by a chaotic signal chaos synchronization by driving parameter for two uncoupled identical chaotic double duffing systems is presented replacing two corresponding parameters of the identical systems by the same function of chaotic state variables of a third chaotic system the synchronization or anti synchronization of two uncoupled systems can be obtained numerical simulations are illustrated for either synchronization or anti synchronization of which the occurrence depends significantly on initial conditions and on driving strength alternative complete synchronization and anti synchronization is also discovered