the induction coefficient of induced representation theory its algebra and an analytic expression the induction coefficient is defined as the element of a matrix reducing the induced representation into irreducible constituents the authors give the algebra of these coefficients and a closed analytic expression in terms of matrix elements of coset representatives the consequences of this choice are derived and the importance of some of these results for the racah wigner coupling algebra of the symmetric and unitary groups noted

the complex lorenz equations we have undertaken a study of the complex lorenz equations x x y y r z x ay z bz 12 x y xy where x and y are complex and z is real the complex parameters r and a are defined by r r1 ir2 a 1 ie and and b are real behaviour remarkably different from the real lorenz model occurs only the origin is a fixed point except for the special case e r2 0 we have been able to determine analytically two critical values of r1 namely r1c and r1c the origin is a stable fixed point for 0 r1c a hopf bifurcation to a limit cycle occurs we have an exact analytic solution for this limit cycle which is always stable if 1 then this limit is only stable in the region r1c rlc a transition to a finite amplitude oscillation about the limit cycle occurs the nature of this bifurcation is studied in detail by using a multiple time scale analysis to derive the stuart landau amplitude equation from the original equations in a frame rotating with the limit cycle frequency this latter bifurcation is either a sub or super critical hopf like bifurcation to a doubly periodic motion the direction of bifurcation depending on the parameter values the nature of the bifurcation is complicated by the existence of a zero eigenvalue

the racah wigner approach to harmonic oscillations of the cluster of nodes of a cube the racah wigner approach is applied to demonstrate various group theoretic labelling schemes for modes of oscillations and elasticity parameters of the cluster of nodes of a cube it is shown that there exists a fundamental basis in the configuration space closed under the action of the group oh the geometric symmetry group of the equilibrium it provides a transparent interpretation of all basic invariants the fibre bundle and tensor product structure of invariant bilinear forms over the configuration space yields three classification schemes for elasticity parameters in a way that resembles racah recoupling of several angular momenta

painleve property and constants of the motion of the complex lorenz model the results of the painleve analysis and of a search for constants of the motion of the complex lorenz model are presented

one way hash function construction based on 2d coupled map lattices an algorithm for constructing one way hash function based on spatiotemporal chaos is proposed a two dimensional coupled map lattices 2d cml with parameters leading to the largest lyapunov exponent is employed the state of the 2d cml is dynamically determined by its previous state and the message bit at the corresponding positions the hash value is obtained by a linear transform on the final state of the 2d cml theoretical analysis and computer simulation indicate that our algorithm has good statistical properties strong collision resistance and high flexibility it is practical and reliable with high potential to be adopted as a strong hash function for providing data integrity

tensor fields on crystals a new method is presented to determine the irreducible representations of the space group of a crystal contained in the representation whose basis functions are the components of a tensor field defined on the atoms of a crystal this reducible representation is the direct product of a tensor representation dependent only on the tensor and a permutation representation dependent only on how the atoms permute under elements of the space group the permutation representation is first separately reduced prior to the reduction of the direct product the permutation representation is shown to be an induced representation and its reduction is facilitated using the theory of induced representations examples and tables of results of applying this method are given in the case of a polar vector tensor field applicable to lattice vibrational problems and crystals as the diamond structure of space group symmetry 07h

symmetry properties of direct sum systems an interpretation of double coset decompositions of groups is given in terms of the construction of systems from similar disjoint subsystems a natural labelling scheme is developed for the direct product states of systems of this type providing an extension of the concept of unique labelling an application of the decoupling transformation to finite direct sum systems is investigated

coupled map lattice based hash function with collision resistance in single iteration computation a new hash function based on a coupled chaotic map lattice is proposed by combining floating point chaotic computations with algebraic operations as well as local and global couplings the system reaches high bit confusion and diffusion rates and thus desirable collision resistance with even one iteration computation the algorithm can be used to calculate hash values of 128 160 192 256 384 and 512bits with little difference in performance for the different hash values the algorithm has both strong collision resistance and high efficiency and can serve as a new type of candidate hash function in software

on the nature of the torus in the complex lorenz equations the complex lorenz equations are a nonlinear fifth order set of physically derived differential equations which exhibit an exact analytic limit cycle which subsequently bifurcates to a torus in this paper we build upon previously derived results to examine a connection between this torus at high and low r1 bifurcation parameter and between zero and nonzero r2 complexity parameter in so doing we are able to gain insight on the effect of the rotational invariance of the system and on how extra weak dispersion r2 0 affects the chaotic behavior of the real lorenz system which describes a weakly dissipative dispersive instability

on a complex beam beam interaction model with random forcing abstract in recent years many studies have been devoted to complex differential equations cde which appear in very important applications in physics and engineering this paper aims to investigate one such cde containing a random forcing term z o 2 z e 2 g z e 2 f z z p o t n t where z t x t iy t a complex function i 1 n t is a broad band process with zero mean and e2 and small real parameters in particular we use eq to model the interaction between two colliding beams in particle accelerators setting g z z f z z z z 2 and p o t cos o t and extend the work we had started in an earlier publication mahmoud physica a 216 1995 445 we apply the stochastic averaging method to derive a fokker planck kolmogorov equation for this equation and obtain analytically the exact stationary probability density function and the first and second moments in the amplitude of the solutions numerical simulations are carried out to compare with the theoretical ones and excellent agreement is found

estimating the ultimate bound and positively invariant set for the lorenz system and a unified chaotic system to estimate the ultimate bound and positively invariant set for a dynamic system is an important but quite challenging task in general in this paper we attempt to investigate the ultimate bound and positively invariant set for two specific systems the lorenz system and a unified chaotic system we derive an ellipsoidal estimate of the ultimate bound and positively invariant set for the lorenz system for all the positive values of its parameters a b and c and obtain the minimum value of volume for the ellipsoid comparing with the best results in the current literature d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 our new results fill up the gap of the estimate for the cases of 0 a 1 and 0 b 2 x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 furthermore the estimation derived here contains the results given in d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 and x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419 as special cases along the same line we also provide estimates of cylindrical and ellipsoidal bounds for a unified chaotic system for its parameter range 0 129 and obtain the minimum value of volume for the ellipsoid the estimate is more accurate than and also extends the result of d li j lu x wu g chen estimating the bounds for the lorenz family of chaotic systems chaos solitons fractals 23 2005 529 534 and x liao on the global basin of attraction and positively invariant set for the lorenz chaotic system and its application in chaos control and synchronization sci china ser e 34 2004 1404 1419

a note on hopf bifurcation analysis and ultimate bound estimation of a new 4 d quadratic autonomous hyper chaotic system in appl math comput 291 2016 323 339 by amin zarei and saeed tavakoli abstract in the recent paper entitled hopf bifurcation analysis and ultimate bound estimation of a new 4 d quadratic autonomous hyper chaotic system in appl math comput 291 2016 323 339 by amin zarei and saeed tavakoli they proposed the following new four dimensional 4 d quadratic autonomous hyper chaotic system x 1 a x 2 x 1 x 2 b x 1 x 2 e x 4 x 1 x 3 x 3 c x 3 x 1 x 2 x 1 2 x 4 d x 2 which generates double wing chaotic and hyper chaotic attractors with only one equilibrium point combining theoretical analysis and numerical simulations they investigated some dynamical properties of that system like lyapunov exponent spectrum bifurcation diagram phase portrait hopf bifurcation etc in particular they formulated a conclusion that the system has the ellipsoidal ultimate bound by employing the method presented in the paper entitled ultimate bound estimation of a class of high dimensional quadratic autonomous dynamical systems int j bifurc chaos 21 09 2011 2679 2694 by p wang et al however by means of detailed theoretical analysis we show that both the conclusion itself and the derivation of its proof in appl math comput 291 2016 323 339 are erroneous furthermore we point out that the method adopted for studying the ultimate bound of that system is not applicable at all therefore the ultimate bound estimation of that system needs further studying in future work

boundedness solutions of the complex lorenz chaotic system this paper is concerned with the boundedness of solutions of the complex lorenz system we have obtained the global exponential attractive set j l m and the ultimate bound w l m for this system furthermore we confirm that the rate of the trajectories of the system going from the exterior of the set j l m to the interior of the set j l m is an exponential rate the rate of the trajectories is also obtained numerical simulations are presented to show the effectiveness of the proposed scheme

spatiotemporal chaos in mixed linear nonlinear two dimensional coupled logistic map lattice abstract we investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2dcml here the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices and the former 2dcml system is only a special case in the proposed system in this paper the criteria such kolmogorov sinai entropy density and universality bifurcation diagrams space amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system furthermore we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2dcml system and the mlncml system theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors which is more suitable for cryptography

keyed hash function based on a chaotic map secure hash functions play a fundamental role in cryptographic and web applications they are mainly used within digital signature schemes to verify the integrity and authenticity of information in this paper we propose a simple and efficient keyed hash function based on a single chaotic map theoretical and simulation results demonstrate that the suggested scheme satisfies all cryptographic requirements of secure keyed hash functions such as strong confusion and diffusion capability good collision resistance high sensitivity to message and secret key etc furthermore it is fast and can be easily implemented through software or hardware moreover the length of the hash value is flexible without any impact on the algorithm this function is shown to have better statistical performance than many existing hash functions thus the suggested hash function seems to be a good candidate as a secure keyed hash function for use in cryptographic applications

cluster synchronization in directed networks of partial state coupled linear systems under pinning control this paper investigates the cluster synchronization for network of linear systems via a generalized pinning control strategy which allows the network of each cluster to take relaxed topological structure for the case with fixed topology it is shown that a feasible feedback controller can be designed to achieve the given cluster synchronization pattern if the induced network topology of each cluster has a directed spanning tree and further compared to the couplings among different clusters the couplings within the each cluster are sufficiently strong an extra balanced condition is imposed on the network topology of each cluster to allow for the cluster synchronization under arbitrary switching network topologies such a balanced condition can be removed via the use of dwell time technique for all the cases the lower bounds for such strengths of couplings within each cluster that secure the synchronization as well as cluster synchronization rate are explicitly specified finally some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings

on the boundedness of solutions of the chen system by constructing a suitable lyapunov function we show that for the system parameters in some specified regions the solutions of the chen system are globally bounded

hashing via finite field in order to produce full length probe sequences the table size m for many existing open addressing hash functions for example the widely used double hashing must be prime i e m p where p is prime in this paper we propose a new and efficient open addressing technique called hashing via finite field to construct a new class of hash functions with table size m p n where p is prime and n 1 it is clear that it includes prime m as a special case when n 1 we show that the new class of hash functions constructed via finite field produces full length probe sequences on all table elements also some theoretic analysis is provided along with concrete examples

unique labelling schemes for local modes in lattices two procedures are described which together specify a unique point group labelling scheme for the irreducible components of local distortions in crystals in the first procedure the group operators are factorised into a permutation part and a local atomic point group operation the second depends on dividing the complete shells of atoms into subshells which are invariant under subgroups of the site permutation group

new exact solutions of the complex lorenz equations the author presents two classes of particular exact solutions to the complex lorenz equations these solutions possess the painleve property the parameter range for which the above solutions hold includes as special cases two of the three parameter ranges for which the general solution of the complex lorenz equations has the painleve property

cluster synchronization of complex networks via event triggered strategy under stochastic sampling abstract this paper is concerned with the issue of mean square cluster synchronization of non identical nodes connected by a directed network suppose that the nodes possess nonlinear dynamics and split into several clusters then an event triggered control scheme is proposed for synchronization based on the information from stochastic sampling meanwhile an equilibrium is considered to be the synchronization state or the virtual leader for each cluster which can apply pinning control to the following nodes assume that a spanning tree exists in the subgraph consisting of the nodes belonging to the same cluster and the corresponding virtual leader and the instants for updating controllers are determined by the given event triggered strategy then some sufficient conditions for cluster synchronization are presented according to the lyapunov stability theory and linear matrix inequality technique finally a specific numerical example is shown to demonstrate the effectiveness of the theoretical results

exponential synchronization of complex valued complex networks with time varying delays and stochastic perturbations via time delayed impulsive control considering the fact that time delays are unavoidable in the control of practical systems this paper considers globally exponential synchronization of complex valued complex dynamical networks with multiple time varying delays and stochastic perturbations by designing a time delayed impulsive control scheme by taking the advantage of lyapunov method in complex field and utilizing an impulsive inequality with delays several synchronization criteria are obtained through strict mathematical proofs our results are general which extend some existing ones concerning impulsive synchronization a numerical example is given to illustrate the effectiveness of theoretical results

combinatorial enumeration and group representations it is shown that in addition to the number of distinct equivalence classes the representation characters of a labelling can also be derived using standard combinatorial methods these characters provide additional information on the structure of the equivalence classes which is relevant in physical applications

hopf bifurcation analysis and ultimate bound estimation of a new 4 d quadratic autonomous hyper chaotic system based on lorenz system a new four dimensional quadratic autonomous hyper chaotic attractor is presented in this paper it can generate double wing chaotic and hyper chaotic attractors with only one equilibrium point several properties of the new system are investigated using lyapunov exponents spectrum bifurcation diagram and phase portraits using the center manifold and normal form theories the local dynamics the stability and hopf bifurcation at the equilibrium point are analyzed to obtain the ellipsoidal ultimate bound the ultimate bound of the proposed system is theoretically estimated using lagrange multiplier method lagrangian function and local maximizer point by properly choosing p and q matrices an estimation of the ultimate bound region as a function of the lagrange coefficient is obtained using local maximizer point and reduced hessian matrix to demonstrate the evolution of the bifurcation and to show the ultimate bound region numerical simulations are provided

cluster synchronization in directed networks of non identical systems with noises via random pinning control abstract this paper is concerned with the issue of mean square cluster synchronization in directed networks which consist of non identical nodes infected by communication noises the pinning control method is employed in designing controllers for guaranteeing cluster synchronization meanwhile all the controllers are supposed to occur with different probabilities by introducing the bernoulli stochastic variables based on the lyapunov stability theory and the stochastic theory the sufficient synchronization conditions are derived and proved theoretically which are mainly for the controllers to be designed and the noise intensities finally some numerical examples are presented to demonstrate the effectiveness of the results

randomness criteria in binary visibility graph and complex network perspective we introduce the binary visibility graph bvg for mapping random binary sequences into complex networks several topological aspects of the constructed graphs such as degree distribution clustering coefficient and mean visibility length have been thoroughly investigated our simulations on the probability distributions for four sample random binary sequences rbs confirm the reliability of the bvg for rbs analysis moreover we propose the topological properties of the graph as a randomness criteria in this way we have presented some possible randomness tests using bvg a comparison has been made between these tests and national institute of standards and technology nist tests on four samples and the results are promising these tests can distinguish between weak and strong rbss

branching processes in the annni model the mean field equations of the simple cubic annni model are studied on finite lattices the results are consistent with the sequence of distinct commensurate phases 2k 13 k 1 2 3 springing from the multiphase point found using low temperature series expansions moreover evidence for new structure combination branching processes is presented which generate phases of type 2l3 m 2l 13 n or 23l m 23l 1 n where l m and n are integers

fingerprint images encryption via multi scroll chaotic attractors this paper proposes a chaotic fingerprint images encryption approach an image of a fingerprint is encrypted via a two dimensional 2d chaotic sequence obtained from multi scroll chaotic attractors initial values of the chaotic attractors are served as the private key which can be generated from the pixel distribution of the binary images of the captured fingerprints due to the dynamic uncertainties in the acquisition process of fingerprint images the keys generated from the pixel value distribution are virtually random with the elaborately designed 2d chaotic sequence the encrypted fingerprint images have balanced 0 1 ratio and ideal nonlinearity only with the valid private key can the images of fingerprint be recovered simulation results and 2d dft validate this chaotic encryption approach

consensus of discrete time second order multiagent systems based on infinite products of general stochastic matrices traditionally the consensus of a discrete time multiagent system mas with a switching topology is transformed into the convergence problem of the infinite products of stochastic matrices which can be resolved by using the wolfowitz theorem however such a transformation is very difficult or even impossible for certain mass such as discrete time second order mass dtso mass whose consensus can only be transformed into the convergence problem of the infinite products of general stochastic matrices ipgsm these general stochastic matrices are matrices with row sum 1 but their elements are not necessarily nonnegative since there does not exist a general theory or an effective technique for dealing with the convergence of ipgsm establishing the consensus criteria for a dtso mas with a switching topology is rather difficult this paper concentrates on the consensus problem of a class of dtso mass and develops a method to cope with the corresponding ipgsm moreover it is pointed out that the method

event based cluster synchronization of coupled genetic regulatory networks abstract in this paper the cluster synchronization of coupled genetic regulatory networks with a directed topology is studied by using the event based strategy and pinning control an event triggered condition with a threshold consisting of the neighbors discrete states at their own event time instants and a state independent exponential decay function is proposed the intra cluster states information and extra cluster states information are involved in the threshold in different ways by using the lyapunov function approach and the theories of matrices and inequalities we establish the cluster synchronization criterion it is shown that both the avoidance of continuous transmission of information and the exclusion of the zeno behavior are ensured under the presented triggering condition explicit conditions on the parameters in the threshold are obtained for synchronization the stability criterion of a single grn is also given under the reduced triggering condition numerical examples are provided to validate the theoretical results

event based h_ infty state estimation for time varying stochastic dynamical networks with state and disturbance dependent noises in this paper the event based finite horizon h infty state estimation problem is investigated for a class of discrete time varying stochastic dynamical networks with state and disturbance dependent noises also called x v dependent noises an event triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator where the signal is transmitted only when certain conditions are satisfied the purpose of the problem addressed is to design a time varying state estimator in order to estimate the network states through available output measurements by employing the completing the square technique and the stochastic analysis approach sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed h infty performance constraint over a finite horizon the desired estimator parameters can be designed via solving coupled backward recursive riccati difference equations finally a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme

adaptive pinning cluster synchronization of fractional order complex dynamical networks the problem about cluster synchronization of fractional order cdns is studied via a pinning adaptive approach in this paper based on the stability theory of fractional differential equations some sufficient criteria for local and global cluster synchronization of fractional order cdns are derived in this paper the coupling configuration matrix can be asymmetric as well as reducible and the inner coupling matrix can also be asymmetric moreover the number of pinning nodes in each cluster can be evaluated especially when the coupling strength is large enough and the coupling configuration matrix is symmetric cluster synchronization can be achieved via pinning a single node in each cluster finally some typical examples are given to illustrate the correctness and effectiveness of our results a surprising finding is that the synchronization performance will become better as the fractional order decreases in this simulation

event based robust control for uncertain nonlinear systems using adaptive dynamic programming in this paper the robust control problem for a class of continuous time nonlinear system with unmatched uncertainties is investigated using an event based control method first the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function under the event based mechanism we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition that is the designed event based controller is robust to the original uncertain system note that the event based controller is updated only when the triggering condition is satisfied which can save the communication resources between the plant and the controller then a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies the stability of the closed loop system with the event based control policy and the augmented control policy is analyzed using the lyapunov approach furthermore we prove that the minimal intersample time is bounded by a nonzero positive constant which excludes zeno behavior during the learning process finally two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme

continuous symmetry reduction and return maps for high dimensional flows we present two continuous symmetry reduction methods for reducing highdimensional dissipative flows to local return maps in the hilbert polynomial basis approach the equivariant dynamics is rewritten in terms of invariant coordinates in the method of moving frames or method of slices the state space is sliced locally in such a way that each group orbit of symmetry equivalent points is represented by a single point in either approach numerical computations can be performed in the original state space representation and the solutions are then projected onto the symmetry reduced state space the two methods are illustrated by reduction of the complex lorenz system a 5 dimensional dissipative flow with rotational symmetry while the hilbert polynomial basis approach appears unfeasible for high dimensional flows symmetry reduction by the method of moving frames offers hope

permutational symmetry of clebsch gordan coefficients for the metacyclic groups abstract a complete discussion of the permutational symmetry for the 3 gcy symbols for k metacyclic groups an example of non simple phase groups is carried out the analytic formulas for the 3 gcy symbols and for the derome sharp matrices describing the permutational properties of these symbols are given it is shown that these matrices constitute a permutation representation m which is an appropriate coarse grained version of the ordinary permutation representation of the group of all permutations of columns of the 3gcy symbols a detailed structure of the representation m has been determined

permutational properties of the generalized clebsch gordan coefficients the properties of the permutational symmetry of the 3 symbols for an arbitrary compact group have been generalized to a multiple kronecker product of irreducible representations it has been shown that these properties of the corresponding n symbols under a permutation of their columns are related to a choice of the coupling schemes for the appropriate polyads 1 n the simplest permutational symmetry i e associated with a young diagram for the symmetric group n is in general incompatible with schemes having definite intermediate representations and in the case of mixed symmetry does not preserve the absolute value of a n symbol the case of n 4 for su 2 has been studied in detail

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

the real and complex lorenz equations and their relevance to physical systems abstract we summarize some recently obtained results on real and complex lorenz equations and discuss their possible significance in relation to real fluid dynamical processes

an improved secure communication scheme based passive synchronization of hyperchaotic complex nonlinear system in this paper an improved secure communication scheme is proposed based on passive synchronization of hyperchaotic complex nonlinear system the hyperchaotic complex lu system is employed to encrypt the emitted signal comparing with the existing approaches the useful information in our work can be unbounded in the transmitter the original information signal is modulated into one parameter of hyperchaotic complex lu system and it is assumed that the parameter of the receiver system is unknown in the receiver based on the passivity theory the controllers and corresponding parameter update rule are designed to make two identical hyperchaotic complex lu systems asymptotically synchronized and identify the unknown parameter simultaneously the information signal can be recovered accurately by the estimated parameter corresponding theoretical proofs and numerical simulations demonstrate the feasibility and effectiveness of the proposed method it is also shown that the presented secure communication scheme is robust against different channel noise

chaotic and hyperchaotic attractors of a complex nonlinear system in this paper we introduce a complex nonlinear hyperchaotic system which is a five dimensional system of nonlinear autonomous differential equations this system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich based on the lyapunov exponents the parameter values at which this system has chaotic hyperchaotic attractors periodic and quasi periodic solutions and solutions that approach fixed points are calculated the stability analysis of these fixed points is carried out the fractional lyapunov dimension of both chaotic and hyperchaotic attractors is calculated some figures are presented to show our results hyperchaos synchronization is studied analytically as well as numerically and excellent agreement is found

self triggered output feedback control of linear plants in the presence of unknown disturbances this note addresses the control of linear time invariant plants in the presence of unknown bounded disturbances when the output of the plant is only measured at sampling instants determined by a self triggered strategy in a self triggered scenario the controller is allowed to choose when the next sampling time should occur and does so based on available measurements and on a priori knowledge about the plant the proposed solution is a cascade interconnection of a state observer and a self triggered state feedback controller we focus our attention on state observers that are only updated at sampling times and that are input to state stable iss with respect to disturbances due to the cascade structure of the closed loop system and the fact that self triggered control strategies presented in the literature are iss with respect to observation errors and exogenous disturbances we conclude that the closed loop is rendered iss with respect to exogenous disturbances

unique labelling of many electron states in multicentre systems general methods of generating complete sets of states for l or 2n electrons in s states on n centres are described it is shown that a unique labelling of these states can always be obtained using a fictitious sn symmetry of the n centres explicit descriptions of eight seven and four electrons on eight centres are derived and the problem of determining a unique labelling for these states on rigid eight centre structures with cubic and lower symmetry is solved

the unique labelling of states via mackey s theorem a new approach to finding unique labels for many electron states in multicentre systems is described and a particular example eight electrons in s states on eight centres is worked out in detail this approach is shown to provide a labelling with a more direct physical interpretation than has previously been found

event based agreement protocols for multi agent networks abstract this paper considers an average consensus problem for multiple integrators over fixed or switching undirected and connected network topologies event based control is used on each agent to drive the state to their initial average eventually an event triggering scheme is designed based on a quadratic lyapunov function the derivative of the lyapunov function is made negative by an appropriate choice of the event condition for each agent the event condition is sampled data and distributed in the sense that the event detector uses only neighbor information and local computation at discrete sampling instants the event based protocol design is illustrated with simulations

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

experiments on node to node pinning control of chua s circuits abstract in this paper we study the global intermittent pinning controllability of networks of coupled chaotic oscillators we explore the feasibility of the recently presented node to node pinning control strategy through experiments on chua s circuits we focus on the case of two peer to peer coupled chua s circuits and we build a novel test bed platform comprised of three inductorless chua s oscillators we investigate the effect of a variety of design parameters on synchronization performance including the coupling strength between the oscillators the control gains and the switching frequency of node to node pinning control experimental results demonstrate the effectiveness of this novel pinning control strategy in rapidly taming chaotic oscillator dynamics onto desired reference trajectories while minimizing the overall control effort and the number of pinned network sites from an analytical standpoint we present sufficient conditions for global node to node pinning controllability and we estimate the maximum switching period for network controllability by adapting and integrating available results on lyapunov stability theory and partial averaging techniques

global stability properties of the complex lorenz model abstract by means of a quadratic lyapunov function it is shown that the complex lorenz model is globally stable in the sense that the trajectories asymptotically settle within a finite region around the zero fixed point thus similar to the original lorenz model the five dimensional complex model does not have runaway solutions for conditions appropriate to model single mode lasers an analytical expression is given for the upper bound on the magnitude of the time dependent electric field as a function of the model parameters pumping rate detuning and relaxation constants when compared with the time dependent solutions found by direct integration the upper bounds exceed the maximum values reached by the asymptotic solutions by factors between 3 and 6 or between 2 and 3 for conditions below and above the second threshold respectively in extreme cases of transient evolution the solutions approach within 20 of the predicted upper bounds

classification of configurations of systems of identical particles on finite sets all possible configurations of a system of n identical particles are classified for the case when the configuration space q of a single particle reduces to a finite set the classification is achieved by means of a combinatorial analogue of the duality of weyl two groups the pauli group permuting identical particles and the symmetric group on q act on the nth cartesian power of q these actions mutually commute and their orbit structure is classified by appropriate epikernels moreover each stratum of each group is invariant under the dual action which yields a coarsening of permutation representations acting on appropriate sets of orbits it is shown that such a coarsening recovers the geometric symmetry for the case when particles are indistinguishable

a symmetric image encryption algorithm based on mixed linear nonlinear coupled map lattice abstract we propose a new image encryption algorithm based on the spatiotemporal chaos of the mixed linear nonlinear coupled map lattices this spatiotemporal chaotic system has more outstanding cryptography features in dynamics than the logistic map or the system of coupled map lattices does in the proposed image encryption we employ the strategy of bit level pixel permutation which enables the lower bit planes and higher bit planes of pixels permute mutually without any extra storage space simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed algorithm

classification and determination of irreducible bases for induced representations for chains of subgroups of finite groups the problem of classification and determination of standard irreducible bases for induced representations of an arbitrary finite group is discussed a general prescription for classification and determination of these bases for an arbitrary induced representation is proposed and an extra independent prescription for the special case of primitive representations is given relations between appropriate transformation coefficients are investigated and in particular a matrix similar to the racah recoupling matrix from theory of multiple coupling of angular momentum is introduced

structure and representations of the symmetry group of the four dimensional cube in this paper we give explicitly the description of the structure the characters and the complete system of irreducible representations of the hyperoctahedral group in four dimensions which we call w4 from the german wurfel in a second step we do the same for the subgroup sw4 which is formed by all pure rotations contained in w4

secure group key agreement protocol based on chaotic hash recently xiao et al proposed an improved key agreement protocol based on chaotic maps in which only a predetermined long term key is utilized to ensure its security this paper demonstrates that none of these schemes can satisfy the contributory nature of key agreement to fill the gaps we present a secure key agreement protocol based on chaotic hash the proposed scheme utilizes the chaotic hash function to achieve the contributory nature and enhance its security cryptanalysis demonstrates that our chaotic hash based scheme can overcome all the current deficiencies

symmetry coordinates for oh atomic shells the group factorisation and correlation theorem methods used previously to provide a unique labelling of atomic shell symmetry coordinates are shown to give also a simple means for deriving explicit expressions for these coordinates results are given for the 12 atom shell and the two types of 24 atom shells in oh symmetry

unique labelling of symmetry coordinates and cyclic regions in crystals earlier work on unique labelling schemes in oh symmetry is extended to include 48 atom shells and the symmetry coordinates of shells subject to periodicity conditions a new approach to labelling is introduced based on the concept of cyclic regions in a crystal these are described by finite factor groups of the crystallographic space group which contain the isogonal group as a subgroup some examples are worked out in detail

true random number generator based on mouse movement and chaotic hash function a true random number generator trng makes use of a non deterministic source to produce randomness it is considered as more secure than a pseudorandom number generator as the degree of randomness is higher in this letter we propose a novel trng which generates random bits by moving the mouse casually it is convenient universal and low cost for the personal computer pc platform to eliminate the regular patterns of mouse movements caused by the habit of the same user we propose three trngs based on chaotic hash functions experiments are conducted to evaluate the speed diffusion and randomness performance of these trngs the results show that two of them possess satisfactory performance and can be implemented on common pc platform

security analysis of the public key algorithm based on chebyshev polynomials over the integer ring zn recently kocarev and tasev 20 proposed to use chebyshev polynomials over real numbers to design a public key algorithm by employing the semigroup property bergamo et al 4 pointed out that the public key algorithm based on chebyshev polynomials working on real numbers is not secure and devised an attack which permits to recover the corresponding plaintext from a given ciphertext later kocarev et al 19 generalized the chebyshev polynomials from real number fields to finite fields and finite rings to make the public key algorithm more secure and practical however we analyzed the period distribution of the sequences generated by the chebyshev polynomials over finite fields 21 when the modulus n is prime we found this algorithm was also not secure and proposed an attack on this algorithm over finite fields we then proposed some schemes to improve the security in this paper we further analyze in detail the period distribution of the sequences generated by chebyshev polynomials over the integer ring z n when n is composite it turns out that the period distribution is poor if n is not chosen properly and there are many small periods which are not secure in the sense of cryptology based on these findings we devise an attack on the public key algorithm based on chebyshev polynomials over the integer ring z n we also propose some suggestions to avoid this attack