synchronized chaotic intermittent and spiking behavior in coupled map chains we study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type i intermittent behavior two types of parameter distribution linear and random are considered the typical phenomena are the onset and existence of global all to all and cluster partial synchronization with increase of coupling increase of coupling strength can also lead to desynchronization phenomena i e global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states then a regime of a fully incoherent nonsynchronous state spatiotemporal intermittency appears synchronization desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one a chain of coupled maps replicating the spiking behavior of neurobiological networks

partial synchronization from symmetry towards stability abstract in this paper we study the existence and stability of linear invariant manifolds in a network of coupled identical dynamical systems symmetry under permutation of different units of the network is helpful to construct explicit formulae for linear invariant manifolds of the network in order to classify them and to examine their stability through lyapunov s direct method

predictable nonwandering localization of covariant lyapunov vectors and cluster synchronization in scale free networks of chaotic maps covariant lyapunov vectors for scale free networks of henon maps are highly localized we revealed two mechanisms of the localization related to full and phase cluster synchronization of network nodes in both cases the localization nodes remain unaltered in the course of the dynamics i e the localization is nonwandering moreover this is predictable the localization nodes are found to have specific dynamical and topological properties and they can be found without computing of the covariant vectors this is an example of explicit relations between the system topology its phase space dynamics and the associated tangent space dynamics of covariant lyapunov vectors

random matrix theory and the zeros of ζ s we study the density of the roots of the derivative of the characteristic polynomial z u z of an n n random unitary matrix with distribution given by haar measure on the unitary group based on previous random matrix theory models of the riemann zeta function s this is expected to be an accurate description for the horizontal distribution of the zeros of s to the right of the critical line we show that as n the fraction of the roots of z u z that lie in the region 1 x n 1 z 1 tends to a limit function we derive asymptotic expressions for this function in the limits x and x 0 and compare them with numerical experiments

synchronized clusters in coupled map networks ii stability analysis we study self organized and driven synchronization in some simple coupled map networks namely globally coupled networks and complete bipartite networks using both linear stability analysis and lyapunov function approach and determine stability conditions for synchronization the phase diagrams for the networks studied here have features very similar to the different kinds of structurally similar networks studied in part i lyapunov function approach shows that when any two nodes are in driven synchronization all the coupling terms in the difference between the variables of these two nodes cancel out whereas when they are in self organized synchronization the direct coupling term between the two nodes adds an extra term while the other couplings cancel out we also discuss the conditions for the occurrence of a floating node and suggest that the fluctuations of the conditional lyapunov exponent about zero can be a criterion for its occurrence

impact of heterogeneous delays on cluster synchronization we investigate cluster synchronization in coupled map networks in the presence of heterogeneous delays we find that while the parity of heterogeneous delays plays a crucial role in determining the mechanism of cluster formation the cluster synchronizability of the network gets affected by the amount of heterogeneity in addition heterogeneity in delays induces a rich cluster pattern as compared to homogeneous delays the complete bipartite network stands as an extreme example of this richness where robust ideal driven clusters observed for the undelayed and homogeneously delayed cases dismantle yielding versatile cluster patterns as heterogeneity in the delay is introduced we provide arguments behind this behavior using a lyapunov function analysis furthermore the interplay between the number of connections in the network and the amount of heterogeneity plays an important role in deciding the cluster formation

the controlled convergence theorems for the strong henstock integrals of fuzzy number valued functions in this paper we discuss the properties of the strong henstock integrals of the fuzzy number valued functions using the notion of generalized derivatives and prove the controlled convergence theorem for such integrals also we present the concept of equi integrability of a sequence for fuzzy number valued functions under this concept we prove another controlled convergence theorem and establish the relationships between the above two controlled convergence theorems

cluster splitting bifurcation in a system of coupled maps abstract we consider cluster splitting bifurcations in a system of globally coupled maps as coupling parameter decreases at these transitions the number of clusters i e groups of elements with identical dynamics increases we demonstrate that different cascades of cluster splitting can occur depending on statistics of redistribution of the oscillators between new born clusters

controlled convergence theorems for infinite dimension henstock integrals of fuzzy valued functions based on weak equi integrability abstract in this paper we give the concept of weak henstock equi integrability for a sequence of fuzzy number valued functions under this notion we investigate a new version of the henstock s lemma of fuzzy number valued functions thus it is possible to discuss the controlled convergence theorems of fuzzy henstock integral in sense of vitali covering moreover we prove that a uniform version of sklyarenko s and lusin s integrability condition of fuzzy henstock integrals together with pointwise convergence of a sequence of integrable functions is sufficient for a convergence theorem of fuzzy henstock integrals as the applications of the controlled convergence theorem we discuss the existence theorems of generalized solution for a class of discontinuous fuzzy differential equations

regular and chaotic phase synchronization of coupled circle maps we study the effects of regular and chaotic phase synchronization in ensembles of coupled nonidentical circle maps cms and find phase locking regions for both types of synchronization we show that synchronization of chaotic cms is crucially influenced by the three quantities i rotation number difference ii variance of the phase evolution and iii relative duration of intervals of phase increase respect decrease in the case of regular cms only variance and rotation number difference are important it is demonstrated that with increase of noncoherence of phase evolutionsin the regular and chaotic regime the regions of the main 1 1 synchronization are usually decreased we present a chaotic synchronization in the systems of coupled nonidentical circle maps where phase entrainment occurs and it is not accompanied by bifurcations of the chaotic set for ensembles chains of coupled cms with linear and random distributions of the individual frequencies soft and hard transitions to global synchronization are found

predicting the synchronization time in coupled map networks an analytical expression for the synchronization time in coupled map networks is given by means of the expression the synchronization time for any given network can be predicted accurately furthermore for networks in which the distributions of nontrivial eigenvalues of coupling matrices have some unique characteristics analytical results for the minimal synchronization time are given

random coupling of chaotic maps leads to spatiotemporal synchronization we investigate the spatiotemporal dynamics of a network of coupled chaotic maps with varying degrees of randomness in coupling connections while strictly nearest neighbor coupling never allows spatiotemporal synchronization in our system randomly rewiring some of those connections stabilizes entire networks at x where x is the strongly unstable fixed point solution of the local chaotic map in fact the smallest degree of randomness in spatial connections opens up a window of stability for the synchronized fixed point in coupling parameter space further the coupling b i f r at which the onset of spatiotemporal synchronization occurs scales with the fraction of rewired sites p as a power law for 0 1 p 1 is we also show that the regularizing effect of random connections can be understood from stability analysis of the probabilistic evolution equation for the system and approximate analytical expressions for the range and b i f r are obtained

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

on the zeros of zeta s near the critical line let rho prime beta prime i gamma prime denote the zeros of zeta prime s s sigma it it is shown that there is a positive proportion of the zeros of zeta prime s in 0 t t satisfying beta prime 1 2 ll log t 1 further results relying on the riemann hypothesis and conjectures on the gaps between the zeros of zeta s are also obtained

synchronization of oscillators with random nonlocal connectivity in this paper we study the existing observation in literature about synchronization of a large number of coupled maps with random nonlocal connectivity chate and manneville chaos 2 307 1992 these connectivities which lack any spatial significance can be realized in neural nets and electrical circuits it is quite interesting and of practical importance to note that a huge number of maps can be synchronized with this connectivity we show that this synchronization stems from the fact that the connectivity matrix has a finite gap in the eigenvalue spectrum in the macroscopic limit we give a quantitative explanation for the gap we compare the analytic results with the ones quoted in the above reference we also study the departures from this highly collective behavior in the low connectivity limit and show that the behavior is almost statistical for very low connectivity of late there has been considerable attention paid to the study of coupled map lattices cml in various contexts they have been used as a computationally simple and analytically tractable model for spatiotemporal systems 1 the studies on cml s have been either in one and two dimensional lattices or with global coupling in which case there is no notion of lattice geometry 2 the higher dimensional connectivities 3 or hierarchial connectivities 4 5 are studied very little one more system that has been studied is the cml with random nonlocal couplings 6 the motivation is twofold first this is an effectively high dimensional system the phenomenology in cml in higher dimensions has not been studied much and needs further investigation second there are systems like neural nets in which the local connections do not have any spatial significance there also exist systems like electrical circuits 7 in which connectivity is at one s will and such a coupling can be easily realized thus the studies of different connectivities and their effects will be useful in designing well controlled systems in this system of random nonlocal connectivity chate and manneville have presented preliminary results 6 which show that synchronization of a large number of oscillators is easily achieved with this connectivity synchronization of oscillators in spatially extended systems such as coupled oscillators is important from various points of view by achieving synchronization one can try to build huge but more controllable and better behaved systems which are effectively low dimensional 7 sometimes synchronization may serve other purposes such as sending codes that are difficult to break 8 in various contexts this problem has been subjected to several studies in the past few years 9 we would like to show that the phenomenon of synchronization can be generally understood by investigating the eigenvalue spectrum of the connectivity matrix and can help us to understand the existing observations in this paper we will explicitly illustrate how one can separate the mode leading to spatial homogeneity from the rest we will show that there exists a finite gap between the growth rates the spatially homogeneous mode and the rest in the model studied in ref 6 we will also study the departures from this behavior for lower connectivities for the linear stability analysis of the synchronized state we will study the eigenvalue spectrum of the connectivity matrix with random nonlocal connectivity we will also study the eigenspectrum of the product of such matrices we would note that a similar model of random connectivity matrix of size n3n with k nonzero elements in each row has been investigated by cook and derrida in ref 10 in connection with the random energy model the generalized random energy model and directed polymers in random media they have obtained exact analytic results for products of such matrices in the case where the matrices are sparse and the distribution function of nonzero elements is not a d function however in the model studied by chate and manneville 6 all connections have the same weight i e the distribution function of nonzero elements is a d function

phase ordering on small world networks with nearest neighbor edges we investigate global phase coherence in a system of coupled oscillators on small world networks constructed from a ring with nearest neighbor edges the effects of both thermal noise and quenched randomness on phase ordering are examined and compared with the global coherence in the corresponding xy model without quenched randomness it is found that in the appropriate regime phase ordering emerges at finite temperatures even for a tiny fraction of shortcuts the nature of the phase transition is also discussed

empirical mode decomposition and synchrogram approach to cardiorespiratory synchronization we use the empirical mode decomposition method to decompose experimental respiratory signals into a set of intrinsic mode functions imfs and consider one of these imfs as a respiratory rhythm we then use the hilbert spectral analysis to calculate the instantaneous phase of the imf heartbeat data are finally incorporated to construct the cardiorespiratory synchrogram which is a visual tool for inspecting synchronization we perform analysis on 20 data sets collected by the harvard medical school from ten young 21 34 years old and ten elderly 68 81 years old rigorously screened healthy subjects our results support the existence of cardiorespiratory synchronization we also investigate the origin of the cardiorespiratory synchronization by addressing the problem of correlations between regularities of respiratory and cardiac signals our analysis shows that regularity of respiratory signals plays a dominant role in the cardiorespiratory synchronization

desynchronization of chaos in coupled logistic maps when identical chaotic oscillators interact a state of complete or partial synchronization may be attained in which the motion is restricted to an invariant manifold of lower dimension than the full phase space riddling of the basin of attraction arises when particular orbits embedded in the synchronized chaotic state become transversely unstable while the state remains attracting on the average considering a system of two coupled logistic maps we show that the transition to riddling will be soft or hard depending on whether the first orbit to lose its transverse stability undergoes a supercritical or subcritical bifurcation a subcritical bifurcation can lead directly to global riddling of the basin of attraction for the synchronized chaotic state a supercritical bifurcation on the other hand is associated with the formation of a so called mixed absorbing area that stretches along the synchronized chaotic state and from which trajectories cannot escape this gives rise to locally riddled basins of attraction we present three different scenarios for the onset of riddling and for the subsequent transformations of the basins of attraction each scenario is described by following the type and location of the relevant asynchronous cycles and determining their stable and unstable invariant manifolds one scenario involves a contact bifurcation between the boundary of the basin of attraction and the absorbing area another scenario involves a long and interesting series of bifurcations starting with the stabilization of the asynchronous cycle produced in the riddling bifurcation and ending in a boundary crisis where the stability of an asynchronous chaotic state is destroyed finally a phase diagram is presented to illustrate the parameter values at which the various transitions occur s1063 651x 99 04509 2

coupled maps on trees we study coupled maps on a cayley tree with local nearest neighbor interactions and with a variety of boundary conditions the homogeneous state where every lattice site has the same value and the node synchronized state where sites of a given generation have the same value are both shown to occur for particular values of the parameters and coupling constants we study the stability of these states and their domains of attraction since the number of sites that become synchronized is much higher compared to that on a regular lattice control is easier to achieve a general procedure is given to deduce the eigenvalue spectrum for these states perturbations of the synchronized state lead to different spatiotemporal structures we find that a mean field like treatment is valid on this effectively infinite dimensional lattice

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

influence of noise on the synchronization of the stochastic kuramoto model we consider the kuramoto model of globally coupled phase oscillators subject to ornstein uhlenbeck and non gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process we use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise and find that the threshold of synchronization strongly depends on the nature of the noise it is found to be lower for both the ornstein uhlenbeck and non gaussian processes compared to the case of white noise a finite correlation time also favors the achievement of the full synchronization of the system in contract to the white noise process which does not allow that finally we discuss possible applications of the stochastic kuramoto model to oscillations taking place in biochemical systems

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

on the problem of characterizing derivatives for the fuzzy valued functions ii almost everywhere differentiability and strong henstock integral in this paper the concept of strong fuzzy henstock integrability for the fuzzy valued functions is presented a necessary and sufficient condition of almost everywhere differentiability for the fuzzy valued functions is given by means of this concept

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

gaps between zeros of ζ s and the distribution of zeros of ζ s abstract we assume the riemann hypothesis in this paper we settle a conjecture of farmer and ki in a stronger form roughly speaking we show that there is a positive proportion of small gaps between consecutive zeros of the zeta function s if and only if there is a positive proportion of zeros of s lying very closely to the half line our work has applications to the siegel zero problem we provide a criterion for the non existence of the siegel zero solely in terms of the distribution of the zeros of s finally on the riemann hypothesis and the pair correlation conjecture we obtain near optimal bounds for the number of zeros of s lying very closely to the half line such bounds are relevant to a deeper understanding of levinson s method allowing us to place one third of the zeros of the riemann zeta function on the half line

controlling synchronous patterns in complex networks although the set of permutation symmetries of a complex network could be very large few of them give rise to stable synchronous patterns here we present a general framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators specifically according to the network permutation symmetry we design a small size and weighted network namely the control network and use it to control the large size complex network by means of pinning coupling we argue mathematically that for any of the network symmetries there always exists a critical pinning strength beyond which the unstable synchronous pattern associated to this symmetry can be stabilized the feasibility of the control method is verified by numerical simulations of both artificial and real world networks and demonstrated experimentally in systems of coupled chaotic circuits our studies show the controllability of synchronous patterns in complex networks of coupled chaotic oscillators

stochastic dynamical model for stock stock correlations we propose a model of coupled random walks for stock stock correlations the walks in the model are coupled via a mechanism that the displacement price change of each walk stock is activated by the price gradients over some underlying network we assume that the network has two underlying structures describing the correlations among the stocks of the whole market and among those within individual groups respectively each with a coupling parameter controlling the degree of correlation the model provides the interpretation of the features displayed in the distribution of the eigenvalues for the correlation matrix of real market on the level of time sequences we verify that such modeling indeed gives good fitting for the market data of us stocks

mutual synchronization and clustering in randomly coupled chaotic dynamical networks we introduce and study systems of randomly coupled maps rcm where the relevant parameter is the degree of connectivity in the system global almost synchronized states are found equivalent to the synchronization observed in globally coupled maps until a certain critical threshold for the connectivity is reached we further show that not only the average connectivity but also the architecture of the couplings is responsible for the cluster structure observed we analyse the different phases of the system and use various correlation measures in order to detect ordered non synchronized states finally it is shown that the system displays a dynamical hierarchical clustering which allows the definition of emerging graphs

the statistical convergence for sequences of fuzzy number valued functions based on the concept of statistical convergence of sequences of fuzzy numbers the statistical convergence uniformly statistical convergence and equi statistical convergence of sequences of fuzzy number valued functions are defined and investigated in this paper the relationship among statistical convergence uniformly statistical convergence equi statistical convergence of sequences of fuzzy number valued functions and their representations of sequences of level cuts are discussed in addition the egorov and lebesgue theorems for the statistical convergence of sequences of fuzzy number valued functions are obtained in a finite measure set finally the statistical convergence in measure for sequences of fuzzy number valued functions is investigated and it is proved that the outer and inner statistical convergence in measure are equivalent in a finite measure set for a sequence of fuzzy number valued functions

differentiation evens out zero spacings if f is a polynomial with all of its roots on the real line then the roots of the derivative f are more evenly spaced than the roots of f the same holds for a real entire function of order 1 with all its zeros on a line in particular we show that if f is entire of order 1 and has sufficient regularity in its zero spacing then under repeated differentiation the function approaches after normalization the cosine function we also study polynomials with all their zeros on a circle and we find a close analogy between the two situations this sheds light on the spacing between zeros of the riemann zeta function and its connection to random matrix polynomials

synchronization and symmetry breaking bifurcations in constructive networks of coupled chaotic oscillators the spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest neighbor couplings is studied by using master stability equations and numerical simulations the generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row sum the symmetry breaking oscillation patterns that resulted from the hopf bifurcation from synchronous states are analyzed by the symmetry group theory

stability of synchronized network of chaotic electromechanical devices with nearest and all to all couplings abstract a shift invariant set of n mutually nearest neighbour or all to all coupled moving coil electromechanical devices is analytically and numerically investigated the study of the stability of synchronization process is undertaken using the master stability function msf approach the emanating properties of this method make it possible to have a general study of the network dynamics and to explain de synchronization phenomena appearing in the synchronization stability parametric areas a detailed attention is paid to the effects of the dissipative component of the dispersive dissipative coupling tested here

synchronized states in a ring of mutually coupled self sustained electrical oscillators we investigate in this paper different states of synchronization in a ring of mutually coupled self sustained electrical oscillators the good coupling parameters leading to complete and partial synchronization or disordered states are calculated using the properties of the variational equations of stability a stability map showing domains of synchronization to an external excitation locally injected in the ring is also obtained in both cases the numerical simulation validates and complements the results of the analytical investigation

maximum performance at minimum cost in network synchronization we consider two optimization problems on synchronization of oscillator networks maximization of synchronizability and minimization of synchronization cost we first develop an extension of the well known master stability framework to the case of non diagonalizable laplacian matrices we then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the laplacian eigenvalues among the optimal networks we identify a subclass of hierarchical networks characterized by the absence of feedback loops and the normalization of inputs we show that most optimal networks are directed and non diagonalizable necessitating the extension of the framework we also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role

the distribution of zeros of ζ s and gaps between zeros of ζ s abstract assume the riemann hypothesis we establish a local structure theorem for zeros of the riemann zeta function s and its derivative s as an application we prove a stronger form of half of a conjecture of radziwill 18 concerning the global statistics of these zeros roughly speaking we show that on the riemann hypothesis if there occurs a small gap between consecutive zeta zeros then there is exactly one zero of s lying not only very close to the critical line but also between that pair of zeta zeros this refines a result of zhang 22 some related results are also shown for example we prove a weak form of a conjecture of soundararajan and suggest a repulsion phenomena for zeros of s

interplay of degree correlations and cluster synchronization we study the evolution of coupled chaotic dynamics on networks and investigate the role of degree degree correlation in the networks cluster synchronizability we find that an increase in the disassortativity can lead to an increase or a decrease in the cluster synchronizability depending on the degree distribution and average connectivity of the network networks with heterogeneous degree distribution exhibit significant changes in cluster synchronizability as well as in the phenomena behind cluster synchronization as compared to those of homogeneous networks interestingly cluster synchronizability of a network may be very different from global synchronizability due to the presence of the driven phenomenon behind the cluster formation furthermore we show how degeneracy at the zero eigenvalues provides an understanding of the occurrence of the driven phenomenon behind the synchronization in disassortative networks the results demonstrate the importance of degree degree correlations in determining cluster synchronization behavior of complex networks and hence have potential applications in understanding and predicting dynamical behavior of complex systems ranging from brain to social systems

on retarded fuzzy functional differential equations and nonabsolute fuzzy integrals abstract we prove a generalized convergence theorem for fuzzy henstock integrals based on the sequence of fuzzy number valued functions which are weak generalized uniformly absolute continuous u a c g to widen the applications of this convergence theorem we provide some existence theorems for the generalized solution for retarded fuzzy functional differential equations and the dependence of the solutions on a parameter under the assumption of the strong generalized derivative of the solution our results generalize existence results in a kaleva integral setting to a fuzzy henstock integral setting

synchronized clusters in coupled map networks i numerical studies we study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks scale free networks small world networks tree networks and random networks for small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases when nodes show synchronized behavior we observe two interesting phenomena first there are some nodes of the floating type that show intermittent behavior between getting attached to some clusters and evolving independently second we identify two different ways of cluster formation namely self organized clusters which have mostly intracluster couplings and driven clusters which have mostly intercluster couplings the synchronized clusters may be of dominant self organized type dominant driven type or mixed type depending on the type of network and the parameters of the dynamics we define different states of the coupled dynamics by considering the number and type of synchronized clusters for the local dynamics governed by the logistic map we study the phase diagram in the plane of the coupling constant and the logistic map parameter ensuremath mu for large coupling strengths and nonlinear coupling we find that the scale free networks and the caley tree networks lead to better cluster formation than the other types of networks with the same average connectivity for most of our study we use the number of connections of the order of the number of nodes as the number of connections increases the number of nodes forming clusters and the size of the clusters in general increase

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

moments of the riemann zeta function assuming the riemann hypothesis we obtain an upper bound for the moments of the riemann zeta function on the critical line our bound is nearly as sharp as the conjectured asymptotic formulae for these moments the method extends to moments in other families of l functions

information transfer and nontrivial collective behavior in chaotic coupled map networks the emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method the resulting prediction error is used to measure the amount of information that a local unit possesses about the collective dynamics applications to locally and globally coupled map systems are considered the prediction error exhibits phase transitions at critical values of the coupling for the onset of ordered collective behavior in these networks this information measure may be used as an order parameter for the characterization of complex behavior in extended chaotic systems

on the strength of attractors in a high dimensional system milnor attractor network robust global attraction and noise induced selection abstract strength of attractor is studied by the return rate to itself after perturbations for a multi attractor state of a globally coupled map it is found that fragile milnor attractors have a large basin volume at the partially ordered phase such dominance of fragile attractors is understood by robustness of global attraction in the phase space change of the attractor strength and basin volume against the parameter and size are studied in the partially ordered phase the dynamics is often described as milnor attractor network which leads to a new interpretation of chaotic itinerancy noise induced selection of fragile attractors is found that has a sharp dependence on the noise amplitude relevance of the observed results to neural dynamics and cell differentiation is also discussed

paths to globally generalized synchronization in scale free networks we apply the auxiliary system approach to study paths to globally generalized synchronization in scale free networks of identical chaotic oscillators including h enon maps logistic maps and lorentz oscillators as the coupling strength ensuremath epsilon between nodes of the network is increased transitions from partially to globally generalized synchronization and intermittent behaviors near the synchronization thresholds are found the generalized synchronization starts from the hubs of the network and then spreads throughout the whole network with the increase of ensuremath epsilon our result is useful for understanding the synchronization process in complex networks

landau siegel zeros and zeros of the derivative of the riemann zeta function abstract we show that if the derivative of the riemann zeta function has sufficiently many zeros close to the critical line then the zeta function has many closely spaced zeros this gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields

local estimates for entropy densities in coupled map lattices we present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations to do this we use an embedding technique that is a combination of time delay and spatial embedding this embedding allows us to identify the local character of the equations of motion based on this method we present an approximate estimate of the entropy density by the correlation integral

on the problem of characterizing derivatives for the fuzzy valued functions in this paper the concept of locally mean fuzzy henstock integrability for the fuzzy valued functions is presented several necessary and sufficient conditions of differentiability for the fuzzy valued functions are given by means of this concept

clustering coding switching hierarchical ordering and control in a network of chaotic elements abstract a network of chaotic elements is investigated with the use of globally coupled maps a simple coding of many attractors with clustering is shown through the coding the attractors are organized so that their change exhibits bifurcation like phenomena a precision dependent tree is constructed which leads to the similarity of our attractor with those of spin glasses hierarchical dynamics is constructed on the tree which leads to the dynamical change of trees and the temporal change of effective degrees of freedom by a simple input on a site we can switch among attractors and tune the strength of chaos a threshold on a cluster size is found beyond which a peculiar posi nega switch occurs possible application to biological information processing is discussed with the emphasis on the fuzzy switch chaotic search and hierarchical code categorization

stability of synchronous chaos and on off intermittency in coupled map lattices in this paper we consider the stability of synchronous chaos in lattices of coupled n dimensional maps for global coupling we derive explicit conditions for computing the parameter values at which the synchronous chaotic attractor becomes unstable and bifurcates into asynchronous chaos in particular we show that after the bifurcation one generally observes on off intermittency a process in which the entire system evolves nearly synchronously but chaotically for long periods of time which are interrupted by brief bursts away from synchrony for nearest neighbor coupled systems however we show that the stability of the synchronous chaotic state is a function of the system size in particular for large systems we will not be able to observe synchronous chaos we derive a condition relating the local map s largest lyapunov exponent to the maximal system size under which one can still observe synchronous chaos and on off intermittency other issues related to the characterization of on off intermittent signals are also discussed

partial synchronization and spontaneous spatial ordering in coupled chaotic systems a model of many symmetrically and locally coupled chaotic oscillators is studied partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated very rich patterns of the system are revealed based on partial synchronization analysis the stabilities of different partially synchronous spatiotemporal structures and some dynamical behaviors of these states are discussed both numerically and analytically

stability and transverse manifolds of periodic points for coupled maps abstract we consider the domains of stability of periodic points for linear internal and external coupled maps we obtain the approximation expressions of the transverse manifolds at periodic points which show that the transverse manifolds of periodic points are asymptotically elliptic paraboloids we point out that the action of maps on the transverse manifold has the symmetry only in two coupled maps we study in detail the hereditary properties of domains of stability of period doubling points for the internal coupling of an arbitrary one dimensional map with the help of its quadratic approximation and show that these domains follow the universal rules similar to the feigenbaum universality rules for one dimensional maps

scale free characteristics of random networks the topology of the world wide web the world wide web forms a large directed graph whose vertices are documents and edges are links pointing from one document to another here we demonstrate that despite its apparent random character the topology of this graph has a number of universal scale free characteristics we introduce a model that leads to a scale free network capturing in a minimal fashion the self organization processes governing the world wide web c 2000 elsevier science b v all rights reserved pacs 84 35 i 64 60 fr 87 23 ge

on henstock integral of fuzzy number valued functions i abstract in this paper we define and discuss the fh integral for fuzzy number valued functions using a concrete structure into which we embed the fuzzy number space e 1 several necessary and sufficient conditions of integrability for fuzzy number valued functions are given by means of abstract function theory