asymptotic stability of densities in coupled map lattices abstract sufficient conditions for the asymptotic stability strong convergence of density evolution in finite dimensional piecewise monotone map lattices with both constant and state dependent coupling are given these conditions are quite useful in numerical work since they allow one to precisely define where one expects to see numerical signatures of asymptotic stability asymptotic stability is illustrated with several examples it is also shown that in constantly coupled lattices the density formed by collapsing the higher dimensional density into one dimension can be approximated by the evolution of densities under the action of an appropriately perturbed one dimensional map

quantum function algebra at roots of 1 abstract we introduce a form of the quantum function algebra on a drinfeld jimbo quantum group over the ring z q q 1 specializing q to a root of 1 we show that over the cyclotomic field this algebra is a projective module over its central sub algebra which is the usual coordinate algebra of the group we study the induced poisson lie structure of the group a bundle of algebras on a complex simply connected lie group with hamiltonian flows in the bundle is constructed some representations of the quantum function algebra in a root of 1 are constructed as an application an estimate of the dimension of an arbitrary representation is given

nonlinear dynamics in coupled fuzzy control systems i coherence and chaos frustration in triangle configuration abstract nonlinear dynamics and chaos are studied in a system for which a complete set of equations of motion such as equations of newton navier stokes and van der pol is not available as a very general system as such we consider coupled classical spins pendulums each of which is under control by a fuzzy system that is designed to align the spin to an unstable fixed point the fuzzy system provides a deterministic procedure to control an object without use of a differential equation the positions and velocities of the spins are monitored periodically and each fuzzy control gives a momentum to its associated spin in the reverse directions if the monitoring is made with an interval short enough the spin spin interactions are overwhelmed by the fuzzy control and the system converges to a state as designed however a long interval monitoring induces dynamics of too late response and thereby results in chaos a great variety of dynamics are generated under very delicate balance between the fuzzy control and the spin spin interaction in which two independent mechanisms of creating negative and positive liapunov exponents interact with each other

maximum entropy approach to nonlinear modeling abstract we present a technique for building deterministic models of the nonlinear dynamics underlying observed time series it is formulated from maximum entropy principle within the framework of information theory two numerical examples of chaotic time series illustrate the method furthermore the theory on which the method is based provides an entropy like quantity that characterizes the suitability of the model it is defined over the space of parameters of the model we illustrate with two applications how this entropy can be a useful tool for exploring the phase space and establishing a criterion for choosing a convenient parametrized functional form

memory flow structures in lorenz chaos memory flow structures of a coupled three element model here a lorenz chaos have been investigated although in the models of coupled two element systems a bidirectional connectivity of information transference is held and the memory flows of one channel exhibit a nearly out of phase relation it is found that in this lorenz chaos one additional unidirectional connectivity can also occur and the nearly out of phase relation in the coupled two element models will be replaced by an antiphaselike relation in lorenz chaos

pixel clustering by adaptive pixel moving and chaotic synchronization in this paper a network of coupled chaotic maps for pixel clustering is proposed time evolutions of chaotic maps in the network corresponding to a pixel cluster are synchronized with each other those synchronized trajectories are desynchronized with respect to the time evolutions of chaotic maps corresponding to other pixel clusters in the same image a pixel motion mechanism is also introduced which makes each group of pixels more compact and consequently makes the model robust enough to classify ambiguous pixels another feature of the proposed model is that the number of pixel clusters does not need to be previously known

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

information and entropy in strange attractors a technique for analyzing time series data from experiments is presented that provides estimates of four basic characteristics of a system 1 the measure theoretic entropy 2 the accuracy of the measurements 3 the number of measurements necessary to specify a system state and 4 the best delay time t to use in order to construct phase space portraits by the method of delays these characteristics are obtained by separating the entropy of measurements into a part due to noise and parts due to deterministic effects for the technique to work the noise associated with each measurement must be independent of the noise associated with all other measurements an algorithm for implementing the analysis is presented with three examples

spatio temporal intermittency in coupled map lattices abstract the transition to turbulence in a one dimensional array of maps coupled by diffusion is shown to display critical properties resembling those of directed percolation the analogy is supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties numerical results suggest however that spatio temporal intermittency does not belong to the same universality class as directed percolation

complexity measures from interaction structures we evaluate information theoretic quantities that quantify complexity in terms of k text th order statistical dependences that cannot be reduced to interactions among k ensuremath 1 random variables using symbolic dynamics of coupled maps and cellular automata as model systems we demonstrate that these measures are able to identify complex dynamical regimes

the lorenz fermi pasta ulam experiment we consider a chain of lorenz 63 systems connected through a local nearest neighbour coupling we refer to the resulting system as the lorenz fermi pasta ulamlattice because of its similarity to the celebrated experiment conducted by fermi pasta and ulam at large coupling strengths the systems synchronize to a global chaotic orbit of the lorenz attractor for smaller coupling the synchronized state loses stability instead steady spatially structured equilibrium states are observed these steady states are related to the heteroclinic orbits of the system describing stationary solutions to the partial differential equation that emerges on taking the continuum limit of the lattice notably these orbits connect saddle foci suggesting the existence of a multitude of such equilibria in relatively wide systems on lowering the coupling strength yet further the steady states lose stability in what appear to be always subcritical hopf bifurcations this can lead to a variety of time dependent states with fixed time averaged spatial structure such solutions can be limit cycles tori or possibly chaotic attractors cluster states can also occur though with less regularity consisting of lattices in which the elements are partitioned into families of synchronized subsystems ultimately for very weak coupling the lattice loses its time averaged spatial structure at this stage the properties of the lattice are probably chaotic and approximately scale with the lattice size suggesting that the system is essentially an ensemble of elements that evolve largely independent of one another the weak interaction however is sufficient to induce widespread coherent phases these are ephemeral states in which the dynamics of one or more subsystems takes a more regular form we present measures of the complexity of these incoherent lattices and discuss the concept of a dynamical horizon that is the distance along the lattice that one subsystem can effectively influence another and error propagation how the introduction of a disturbance in one subsystem becomes spread throughout the lattice 2000 elsevier science b v all rights reserved

externally controlled attractor selection in a high dimensional system a high dimensional dynamical system with global couplings that can serve as a prototype for systems with very large numbers of attractors like memory is investigated and shown to be controllable by external inputs by changing the duration that noise is added final attractors are selected as the number of degrees of freedom of the nonsynchronized elements decreases one by one over time furthermore it is found that this selection of attractors is also possible by controlling the sweeping speed of a parameter the mechanism for this controlled selection is explained and shown to be rather general applications to attractor switching are given

anomalous lyapunov spectrum in globally coupled oscillators abstract numerical experiments of a globally coupled oscillator system show that one type of collective chaos of high dimension has discrete and continuous parts in its lyapunov spectrum this occurs in a scattered state i e a state in which no two oscillators behave identically it is argued from a consideration of the phase space structure that the discrete exponents are related to in a sense the macroscopic dynamics while the continuous part reflects the microscopic dynamics this type of high dimensional chaos is compared to a second type possessing an apparently continuous part only preceding the appearance of the first type we found a sequence of bifurcations of collective low dimensional behavior in scattered states and their investigation reveals the route to the first type of the high dimensional chaos

ultradiffusion the relaxation of hierarchical systems the authors show that the dynamics of relaxation in hierarchical structures leads to an anomalous decay process which they term ultradiffusion using renormalisation group techniques they explicitly calculate the behaviour of the autocorrelation function in a one dimensional hierarchical system and show its universal power law decay as a function of temperature the authors also demonstrate analytically the emergence of a hierarchy of time scales this phenomenon is relevant to systems ranging from macromolecules to computing structures

nontrivial collective behavior in coupled maps on fractal lattices abstract the collective behavior of locally coupled map lattices is investigated when the connections are defined on fractal geometries such as generalized sierpinski gaskets embedded in d dimensional euclidean spaces the collective states are described through the mean fields of the networks periodic global attractors are observed as functions of the parameters of the systems with no indications of collective quasiperiodicities which are common in high dimensional regular lattices the influence of the connectivity on the emergence of nontrivial collective behavior in coupled chaotic systems is discussed

fq mn fq gln and fq sln as quantized hyperalgebras abstract within the quantum function algebra f q gl n we study the subset f q gl n introduced in f gavarini quantization of poisson groups pacific j math 186 1998 217 266 of all elements of f q gl n which are z q q 1 valued when paired with u q gl n the unrestricted z q q 1 integral form of u q gl n introduced by de concini kac and procesi in particular we obtain a presentation of it by generators and relations and a pbw like theorem moreover we give a direct proof that f q gl n is a hopf subalgebra of f q gl n and that f q gl n q 1 u z gl n we describe explicitly its specializations at roots of 1 say e and the associated quantum frobenius epi morphism from f e gl n to f 1 gl n u z gl n also introduced in f gavarini quantization of poisson groups pacific j math 186 1998 217 266 the same analysis is done for f q sl n and as key step for f q m n

encoding via conjugate symmetries of slow oscillations for globally coupled oscillators we study properties of the dynamics underlying slow cluster oscillations in two systems of five globally coupled oscillators these slow oscillations are due to the appearance of structurally stable heteroclinic connections between cluster states in the noise free dynamics in the presence of low levels of noise they give rise to long periods of residence near cluster states interspersed with sudden transitions between them moreover these transitions may occur between cluster states of the same symmetry or between cluster states with conjugate symmetries given by some rearrangement of the oscillators we consider the system of coupled phase oscillators studied by hansel et al phys rev e 48 3470 1993 in which one can observe slow noise driven oscillations that occur between two families of two cluster periodic states in the noise free case there is a robust attracting heteroclinic cycle connecting these families the two families consist of symmetric images of two inequivalent periodic orbits that have the same symmetry for n 5 oscillators one of the periodic orbits has one unstable direction and the other has two unstable directions examining the behavior on the unstable manifold for the two unstable directions we observe that the dimensionality of the manifold can give rise to switching between conjugate symmetry orbits by applying small perturbations to the system we can easily steer it between a number of different marginally stable attractors finally we show that similar behavior occurs in a system of phase energy oscillators that are a natural extension of the phase model to two dimensional oscillators we suggest that switching between conjugate symmetries is a very efficient method of encoding information into a globally coupled system of oscillators and may therefore be a good and simple model for the neural encoding of information

conversion of local transient chaos into global laminar states in coupled map lattices with long range interactions abstract spatially extended dynamical systems may exhibit intermittent behavior in both spatial and temporal scales characterized by repeated conversions from spatially localized transient chaos into global laminar patterns a simple model yet retaining some features of more complex systems consists of a lattice of a class of tent maps with an escaping region the coupling prescription we adopt in this work considers the interaction of a site with all its neighbors the corresponding strength decaying with the lattice distance as a power law this makes possible to pass continuously from a local nearest neighbor to a global kind of coupling we investigate statistical properties of both the chaotic transient bursts and the periodic laminar states with respect to the coupling parameters

mutual information functions versus correlation functions this paper studies one application of mutual information to symbolic sequences the mutual information functionm d this function is compared with the more frequently used correlation function d an exact relation betweenm d and d is derived for binary sequences for sequences with more than two symbols no such general relation exists in particular d 0 may or may not lead tom d 0 this linear but not general independence between symbols separated by a distance is studied for ternary sequences also included is the estimation of the finite size effect on calculating mutual information finally the concept of symbolic noise is discussed

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

extended information in one dimensional maps abstract an information theoretical structure of one dimensional maps is investigated by regarding the maps as a channel rather than a source computing various mutual information numerically for one dimensional dynamical systems we can observe directly the movement of information as to initial conditions one feature of information theoretical structure emerged from this computation is such that initially localized information spreads over whole system as time passes two groups of maps which are contrasting with each other concerning this feature exhibit a striking difference in their transmission ability of information when coupled to form a linear chain

vulnerability to noise of a phase locked oscillator array abstract the effect of noise on the in phase attractor of a set of n globally coupled oscillators is studied these discrete time maps are associated with the continuous time equations of motion for a series array of josephson junction oscillators we investigate both geometrical properties of the basin of attraction in the large n limit and the implications of this geometry on the average time for the system to escape from the phase locked mode our main results are that the attractor basin maintains a box shaped core of finite radius even as n and that the in phase attractor of a large n array is much less vulnerable to noise than are the out of phase attractors

strict aperiodic property of polynomials with perturbed coefficients let a family of polynomials be p s t sub 0 s sup n t sub 1 s sup n or sup 1 t sub n where 0

on the largest polytope of polynomials with a precise number of distinct real zeros abstract this paper presents a procedure to construct the largest polytope of polynomials with every polynomial having a precise number of distinct real zeros in a specific real line segment this polytope can be specified from the zeros of a finite number of polynomials

from collective oscillations to collective chaos in a globally coupled oscillator system abstract various types of collective behaviors are discovered in globally coupled ginzburg landau oscillators when the coupling is sufficiently weak the oscillators are either in complete synchrony or their phases are scattered completely randomly for finite coupling new collective behaviors emerge such as splitting of the population into a small number of clusters or their fusion into a continuous stringlike distribution in the phase plane low dimensional chaotic dynamics arises from the coupled motion of 3 point clusters chaotic motion is also exhibited by fused clusters which is of extremely high dimension possibly proportional to the system size as is implied from its lyapunov analysis in the latter type of chaos the motion of the string is in some cases characterized by repeated stretching and foldings it is argued how this kind of coherent behavior seen on a collective level does not contradict the high dimensionality of the corresponding chaotic attractor

robust space time intermittency and 1 f noise abstract we investigate a type of intermittency that occurs in space as well as time studying a one dimensional lattice of coupled quadratic maps this system naturally forms spatial domains motion of the domain walls causes spatially localized changes from chaotic to almost periodic behavior the almost periodic phases have eigenvalues quite close to one resulting in long lived laminar bursts with a 1 f low frequency spectrum this behavior has aspects of both crutchfield and pomeau manneville intermittency unlike pomeau manneville however the behavior that we observe here is quite robust under changes of parameters

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

clustering in globally coupled inhibitory neurons abstract a model of a large population of identical excitable neurons with a global slowly decaying inhibitory coupling is studied and its patterns of synchrony are examined in addition to converging to a homogeneous fixed point and a homogeneous limit cycle the system exhibits cluster states in which it breaks spontaneously into a few macroscopically big clusters each of which is fully synchronized a method for calculating the stability of cluster states is described and used for investigating the dynamical behavior of the network versus the parameters that describe the neurons and synapses effects of stochastic noise on the network dynamics are discussed at large enough noise the system goes to a globally stationary state low levels of noise preserve the cluster like neuron trajectories in the regime where a noiseless system converges to a fully synchronized periodic state relatively low noise levels cause neurons to burst only every two or more consecutive time periods

on the bifurcation structure of the mean field fluctuation in the globally coupled tent map systems abstract a theoretical analysis on the behavior of the globally coupled tent map systems based on the kinetics of the mean field value is presented we investigated the nature of the mean field fluctuation in large system size limit and uncovered the existence of a complicated bifurcation structure that leads the appearance of collective motion with the increase of the coupling strength the way to the appearance of the collective motion sensitively depends on the gradient a of individual tent maps for a belonging to a set which is dense in 2 2 the collective motion appears when the coupling strength exceeds a certain threshold value while for a belonging to another dense set in 2 2 any non zero coupling will induce the collective motion the dependence of the amplitude of mean field fluctuation on the coupling strength is also obtained as a function of the parameter a and the coupling strength

synchronization and cluster periodic solutions in globally coupled maps abstract the purpose of this work is to investigate mechanisms by which synchronization takes place in networks of elements with global couplings we consider a family of globally coupled nonlinear maps and find for each model sufficient conditions for synchronization we also analyze bifurcations of syncrhonized dynamics to other homogeneous and cluster periodic solutions in terms of corresponding low dimensional maps

invariance of the aperiodic property for polynomials with perturbed coefficients a procedure for obtaining the maximal intervals of the coefficients for a perturbed polynomial to be still strictly aperiodic is presented lemmas theorems and proofs are given an illustrative example is presented

how fast elements can affect slow dynamics a chain of coupled chaotic elements with different time scales is studied in contrast with the adiabatic approximation we find that correlations between elements are transferred from faster to slower elements when the differences in the time scales of the elements lie within a certain range for such correlations to occur three features are essential strong correlations among the elements a bifurcation in the dynamics of the fastest element by changing its control parameter and cascade propagation of the bifurcation by studying coupled rossler equations we demonstrate that fast elements can affect the dynamics of slow elements when these conditions are satisfied the relevance of our results to biological memory is briefly discussed

macroscopic chaos in globally coupled maps abstract we study the coherent dynamics of globally coupled maps showing macroscopic chaos with this term we indicate the hydrodynamical like irregular behavior of some global observables with typical times much longer than the times related to the evolution of the single or microscopic elements of the system the usual lyapunov exponent is not able to capture the essential features of this macroscopic phenomenon using the recently introduced notion of finite size lyapunov exponent we characterize in a consistent way these macroscopic behaviors basically at small values of the perturbation we recover the usual microscopic lyapunov exponent while at larger values a sort of macroscopic lyapunov exponent emerges which can be much smaller than the former a quantitative characterization of the chaotic motion at hydrodynamical level is then possible even in the absence of the explicit equations for the time evolution of the macroscopic observables

state differentiation by transient truncation in coupled threshold dynamics dynamics with a threshold input output relation commonly exist in gene signal transduction and neural networks coupled dynamical systems of such threshold elements are investigated in an effort to find differentiation of elements induced by the interaction through global diffusive coupling novel states are found to be generated that are not the original attractor of single element threshold dynamics but are sustained through the interaction with the elements located at the original attractor this stabilization of the novel state s is not related to symmetry breaking but is explained as the truncation of transient trajectories to the original attractor due to the coupling single element dynamics with winding transient trajectories located at a low dimensional manifold and having turning points are shown to be essential to the generation of such novel state s in a coupled system the universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed

solution of the optimization problem using the neural network model as a globally coupled map abstract in solving optimization problems by the neural network models the hopfield model and the boltzmann machine etc a serious problem is that the existence of a huge number of local minimum solutions makes the search efficiency very bad in this report the hopfield model is modified in the framework of the globally coupled map gcm to overcome the problem and the traveling salesman problem tsp is solved by the gcm model it is demonstrated that the gcm model is able to search for the optimal solutions of the tsp based on the chaotic itinerancy and the chaotic search by the gcm model is more efficient than the probabilistic search of other neural network models for solution of the tsp

spatiotemporal chaos and noise low dimensional chaotic dynamical systems can exhibit many characteristic properties of stochastic systems such as broad fourier spectra they are distinguishable from stochastic processes through finite values for their dimension lyapunov exponents and kolmogorov sinai entropy we discuss how these characteristic observables are modified in spatiotemporal chaotic systems like coupled map lattices we analyze with the help of lyapunov concepts how the stochastic limit is approached and how these properties can be observed directly through local dimension measurements from reconstructed time series finally we discuss the interaction of spatiotemporal attractors with external noise and possible connections to problems of pattern selection and stability

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

order in the turbulent phase of globally coupled maps abstract the broad peaks seen in the power spectra of the mean field in a globally coupled map system indicate a subtle coherence between the elements even in the turbulent phase these peaks are investigated in detail with respect to the number of elements coupled nonlinearity and global coupling strengths we find that this roughly periodic behavior also appears in the probability distribution of the mapping which is therefore not invariant we also find that these peaks are determined by two distinct components effective renormalization of the nonlinearity parameter in the local mappings and the strength of the mean field interaction term finally we demonstrate the influence of background noise on the peaks which is quite counterintuitive as they become sharper with increase in strength of the noise up to a certain critical noise strength

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

effects of correlation among stored patterns on associative dynamics of chaotic neural network abstract we numerically investigate the effects of correlation among stored patterns on the associative dynamics in a chaotic neural network model in the model there are two kinds of parameters one is a measure of the hopfield like behavior of the retrieval process and another controls the chaotic behavior the parameter dependence of the associative dynamics is also examined the following results are found i two dimensional parameter space is divided into two kinds of associative states by a distinct boundary one is the retrieval state of the association such as the hopfield like retrieval state and another is the wandering state of the associative dynamics where the network retrieves stored patterns and their reverse patterns ii the area of the wandering state becomes larger as the degree of correlation becomes larger iii as the degree of correlation becomes larger both the recall ratio of correlated patterns and the transition frequency between correlated patterns becomes larger in the wandering state iv the whole region of the wandering state in the parameter space is not necessarily chaotic from the view point of the lyapunov dimension but most of the region of the wandering state is chaotic

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

theory of reentrant excitation in a ring of cardiac tissue a cardiac pathology reentrant tachycardia is caused by the sustained circulation of activation along a reentrant path in cardiac tissue a new theoretical model for wave propagation in discrete excitable media employing coupled maps with continuous time is used to derive analytical stability criteria for the uni directional circulation of the excitation pulse on the ring of cardiac tissue numerical simulations of the model that incorporate experimentally measurable characteristics of the cardiac tissue reproduce the experimental data quantitatively the complex oscillations in the cycle length of unstable tachycardia observed experimentally are quasiperiodic oscillations that arise via the multiple hopf bifurcation in high dimensional maps

phenomenology of nonlocal cellular automata dynamical systems with nonlocal connections have potential applications to economic and biological systems this paper studies the dynamics of nonlocal cellular automata in particular all two state three input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings although it is observed that sometimes a rule can have different dynamical behaviors with different wirings the nonlocal cellular automata rule space is studied using a mean field parametrization which is ideal for the situation of random wiring nonlocal cellular automata can be considered as computers carrying out computation at the level of each component their computational abilities are studied from the point of view of whether they contain many basic logical gates in particular i ask the question of whether a three input cellular automaton rule contains the three fundamental logical gates two input rules and and or and one input rule not a particularly interesting edge of chaos nonlocal cellular automaton the rule 184 is studied in detail it is a system of coupled selectors or multiplexers it is also part of the fredkin s gate a proposed fundamental gate for conservative computations this rule exhibits irregular fluctuations of density large coherent structures and long transient times

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