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

coupled map lattices with complex order parameter abstract we introduce and study coupled map lattices with complex state variable the dynamical regimes of the finite length systems are classified naturally in terms of a topological invariant the overall phase shift accumulated along the whole length at fixed time a stability analysis of the spatially uniform states is presented and the results of numerical simulations of the spatio temporal dynamics are discussed we demonstrate that fast amplitude evolution including regular and chaotic spatio temporal behavior takes place on the background of a slower phase evolution for large values of the topological invariant the phase dynamics may give rise to an instability which in some cases results in a jump of the system to another value of the invariant we also consider the formation of long lived bubbles i e local domains of complicated dynamics in the spatial regions of locally reduced phase gradient our coupled map lattice model and its generalizations may be useful for understanding the dynamics in a larger range of parameters for such nonlinear dissipative media which allow small amplitude description in terms of the complex ginzburg landau equation as well as for time delay feedback systems with nonzero central frequency of the generated signal

a center manifold for second order semilinear differential equations on the real line and applications to the existence of wave trains for the gurtin mccamy equation

an upper bound on the zero error list coding capacity presents an upper bound on the zero error list coding capacity of discrete memoryless channels using this bound we show that the list 3 capacity of the 4 3 channel is at most 0 3512 bits improving the best previous bound the relation of the bound to earlier similar bounds in particular to korner s 1986 graph entropy bound is discussed

phase transitions in coupled map lattices we clarify some aspects related to critical phenomena in 1d coupled map lattices in particular we explain why a model studied by chate and manneville did not seem to be in the same universality class as directed percolation contrary to first expectations we claim that this model is actually in this universality class but that scaling is extremely late we present a slightly modified model which seems to be in this universality class with respect to some properties but not all in contrast to directed percolation and to the model studied by chate and manneville our model shows a very complex sequence of singularities vaguely reminiscent of the richness of bifurcations in 1d maps

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

bifurcation scenarios and quasiperiodicity in coupled maps abstract the appearance of coherent structures in a model of two coupled logistic maps is studied analytical results for the existence of multiple attractors and transitions from periodic to quasiperiodic motion are presented the theoretical prediction for the hopf radius agrees well with computer experiment throughout the quasiperiodic region

wavelike patterns in one dimensional coupled map lattices we investigate the existence of wavelike solution for the logistic coupled map lattices for which the spatiotemporal periodic patterns can be predicted by a simple two dimensional mapping the existence of such wavelike solutions is proved by the implicit function theorem with constraints we also examine the stabilities of these wave solutions under perturbations of uniform small deformation type we show that in some specific cases these perturbations are completely general the technique used in this paper is also applicable to investigate other space time regular patterns

the emergence of coherent structures in coupled map lattices we show how increasing spatial interaction leads to the merging of coherent structures from chaos in some systems of coupled map lattices this phenomenon reflects the arising of new ground states in the corresponding model of statistical mechanics if we further increase the coupling then new ground states appear showing the coexistence of a large scale coherent structure with a small scale chaotic motion this allows us to propose a generalization of the notion of spatial intermittency

spatiotemporal analysis of complex signals theory and applications we present a space time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal spatial modes that we call topos this permits the introduction of several characteristics of the signal three characteristic energies and entropies one temporal one spatial and one global and a characteristic dimension although the technique is general we concentrate on its applications to hydrodynamic problems specifically the transition to turbulence we consider two cases of application a coupled map lattice as a dynamical system model for spatiotemporal complexity and the open flow instability on a rotating disk in the latter we show a direct relation between the global entropy and the different instabilities that the flow undergoes as reynolds number increases

stability of wavelengths and spatiotemporal intermittency in coupled map lattices abstract in relation to spatiotemporal intermittency as it can be observed in coupled map lattices we study the stability of different wavelengths in competition introducing a two dimensional map we compare its dynamics with the one of the whole lattice we conclude that a good agreement between the two exists the reduced model also allows to introduce an order parameter which combines the diffusion parameter and the spatial wavelength under consideration

ising type and other transitions in one dimensional coupled map lattices with sign symmetry we consider a one dimensional lattice of expanding antisymmetric maps 1 1 1 1 with nearest neighbor diffusive coupling for such systems it is known that if the coupling parameter e is small there is unique stationary in time state which is chaotic in space time a disputed question is whether such systems can exhibit ising type phase transitions as e grows beyond some critical value ec we present results from computer experiments which give definite indication that such a transition takes place the mean square magnetization appears to diverge as e approaches some critical value with a critical exponent around 0 9 we also study other properties of the coupled map system

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

partition complexity in a network of chaotic elements a network of chaotic elements is investigated with the use of globally coupled maps elements can split into clusters with synchronized oscillation in a partially ordered phase the clustering has an inhomogeneous tree structure like replica symmetry breaking in spin glass the clustering has large variety by attractors and strongly depends on initial conditions the variety of clusterings is characterized by the distribution of partitions originated in spin glass theory the qualitative similarity and quantitative disagreement of the given attractors with a spin glass are clarified

quasidiagonal approach to the estimation of lyapunov spectra for spatiotemporal systems from multivariate time series we describe methods of estimating the entire lyapunov spectrum of a spatially extended system from multivariate time series observations provided that the coupling in the system is short range the jacobian has a banded structure and can be estimated using spatially localized reconstructions in low embedding dimensions this circumvents the curse of dimensionality that prevents the accurate reconstruction of high dimensional dynamics from observed time series the technique is illustrated using coupled map lattices as prototype models for spatiotemporal chaos and is found to work even when the coupling is not strictly local but only exponentially decaying

predicting the future advantages of semilocal units in investigating gaussian radial basis function rbf networks for their ability to model nonlinear time series we have found that while rbf networks are much faster than standard sigmoid unit backpropagation for low dimensional problems their advantages diminish in high dimensional input spaces this is particularly troublesome if the input space contains irrelevant variables we suggest that this limitation is due to the localized nature of rbfs to gain the advantages of the highly nonlocal sigmoids and the speed advantages of rbfs we propose a particular class of semilocal activation functions that is a natural interpolation between these two families we present evidence that networks using these gaussian bar units avoid the slow learning problem of sigmoid unit networks and very importantly are more accurate than rbf networks in the presence of irrelevant inputs on the mackey glass and coupled lattice map problems the speedup over sigmoid networks is so dramatic that the difference in training time between rbf and gaussian bar networks is minor gaussian bar architectures that superpose composed gaussians gaussians of gaussians to approximate the unknown function have the best performance we postulate that an interesing behavior displayed by gaussian bar functions under gradient descent dynamics which we call automatic connection pruning is an important factor in the success of this representation

zero error capacity under list decoding shannon s zero error channel capacities c sub of c sub o with and without noiseless feedback are generalized to list decoding the receiver lists l messages erring if the correct one is not listed the corresponding capacities c sub of l c sub o l are nondecreasing in l for an i letter input alphabet c sub of l attains its maximum at l i 1 a lower bound to c sub o l approaches that maximum as l increases

mixed approximation of a population diffusion equation abstract a numerical method is proposed to approximate the solution of a nonlinear and nonlocal system of integro differential equations describing age dependent population dynamics with spatial diffusion a finite difference method along the characteristic age time direction combined with mixed finite elements in the spatial variable is used for the approximation optimal order error estimates are derived for the relevant variables using nonnegativity of the discrete solution a stability of the method is also proved

global behavior for an age dependent population model with logistic term and periodic vital rates we investigate the large time behavior of a nonlinear age dependent population model with logistic term and t periodic vital rates we prove that there exists at most two t periodic and nonnegative solutions of the given model one of them being the trivial one we show that for any initial distribution of population the solution tends to zero or to the nontrivial nonnegative t periodic solution if such solution exists a numerical algorithm to approximate the solution corresponding to a given initial datum as well as the nontrivial nonnegative t periodic solution of the given model is constructed results of the numerical tests are given

optimal harvesting for periodic age dependent population dynamics with logistic term we prove an asymptotic behavior result for an age dependent population dynamics with logistic term and periodic vital rates we investigate next an optimal harvesting problem related to a periodic age structured model with logistic term existence of an optimal control and necessary optimality conditions are established a conceptual algorithm to approximate the optimal pair is derived and some numerical experiments are presented

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

ising type transitions in coupled map lattices we study by means of computer simulations some models of coupled map lattices cml with symmetry subject to diffusive nearest neighbor coupling with the purpose of providing a better understanding of the occurrence of isingtype transitions of the type found by miller and huse we argue on the basis of numerical evidence that such transitions are connected to the appearance of a minimum in the lyapunov dimension of the system as a function of the coupling parameter two dimensional cmls similar to the one in miller and huse but with no minimum in the lyapunov dimension plot have no ising transition the condition seems to be necessary though by no means sufficient we also argue relying on the analysis of bunimovich and sinai that coupled map lattices should behave differently with respect to dimension than ising models

some unexpected consequences of the interaction between convective adjustment and horizontal diffusion abstract we consider the dynamics of a set of diffusively coupled grid points the dependent variable defined at each grid point is the salinity which is forced by a spatially uniform distribution of evaporation minus precipitation the nonlinearity in the system is a convective adjustment rule that sets the salinity back to zero if it ever exceeds one the aim of this study is to understand the spatial and temporal variability that results from the interaction between convective adjustment rules and horizontal diffusivity analytic results show that the model has a large number of different solutions which are periodic in space and time some of these solutions have a supprising structure in which convective adjustment is entirely suppressed at some grid points and occurs with a higher frequency at neighboring points numerical solutions indicate that these solutions have finite basins of attraction in the space of initial conditions thus small changes in the initial conditions can produce solutions with grossly different average properties numerical errors due to the finite size of the time step or roundoff can also have a decisive role in selecting the ultimate state which emerges from a particular condition for instance numerical errors can stabilize an unstable solution

coupled map lattices some topological and ergodic properties abstract lattice dynamical systems ldss form the class of extended systems that is the intermediate one between partial differential equations pdes and cellular automata the most popular class of ldss is formed by coupled map lattices cmls while being introduced rather recently ldss allowed already to clarify and to define exactly some notions that form the basis of the modern phenomenological theory of spatio temporal dynamics and to obtain some new and even rigorous results on space time chaos intermittency and pattern formation we discuss the rigorous results that were obtained in this area but eventually give also some applications

note on some periodic optimal harvesting problems for age structured population dynamics we consider two optimal harvesting problems related to age structured population dynamics with logistic term and time periodic of period t control and vital rates we derive the first order necessary optimality conditions for both problems we prove that in the particular case of time independent vital rates and under a natural hypothesis on the logistic term the optimal control for the first problem is constant the second problem concerns the constant harvesting efforts which act on subintervals of 0 t the maximizing here is treated with respect to the subinterval where the control acts we find the directional derivative of the cost functional some final comments concerning the population dynamics with diffusion are given as well

chaotic traveling waves in a coupled map lattice traveling waves triggered by a phase slip are studied in a coupled map lattice a local phase slip affects globally the system which is in strong contrast with kink propagation attractors with different velocities coexist and form quantized bands determined by the number of phase slips if the system size is not far from an integer multiple of the selected wavelength attractors are tori otherwise weak chaos induces modulation of waves or a chaotic itinerancy of traveling states with a long ranged temporal correlation supertransients before the formation of traveling waves are noted in the high nonlinearity regime in the weaker nonlinearity there are fluctuations of domain sizes and brownian like motion of domains propagation of chaotic domains by phase slips is also found

an improved bound on the zero error list decoding capacity of the 4 3 channel we prove a new upper bound on the size of codes c subseteq 1 2 3 4 n with the property that every four distinct codewords in c have a coordinate where they all differ specifically we provide a self contained proof that such codes have size at most 2 6n 19 o n that is rate bounded asymptotically by 6 19 0 3158 measured in bits this improves the previous best upper bound of 0 3512 due to arikan 1994 which in turn improved the 0 375 bound that followed from general bounds for perfect hashing due to fredman and komlos 1984 and korner and marton 1988 finally using a combination of our approach with a simple idea which exploits powerful bounds on the minimum distance of codes in the hamming space we further improve the upper bound to 0 31477

existence and uniqueness for a kinetic model of population dynamics with character dependence and spatial structure this work we consider a one species population dynamics model with character dependence spatial structure and a nonlocal renewal process arising as a boundary condition the individual interaction are based on boltzmann kinetic type modeling using fixed point arguments and the div rot lemma we prove that our model admits a unique global nonnegative solution

mode locking in coupled map lattices abstract we study propagation of pulses along one way coupled map lattices which originate from the transition between two superstable states of the local map the velocity of the pulses exhibits a staircase like behaviour as the coupling parameter is varied for a piecewise linear local map we prove that the velocity of the wave has a devil s staircase dependence on the coupling parameter a wave travelling with rational velocity is found to be stable to parametric perturbations in a manner akin to rational mode locking for circle maps we provide evidence that mode locking is also present for a broader range of maps and couplings

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

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

competitively coupled maps and spatial pattern formation spatial pattern formation is a key feature of many natural systems in physics chemistry and biology the essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo spontaneous symmetry breaking leading to a stable spatial pattern this problem is most commonly studied using partial differential equations to model a reaction diffusion system of the type introduced by turing we report here on a much simpler and more robust model of spatial pattern formation which is formulated as a novel type of coupled map lattice in our model the local site dynamics are coupled through a competitive rather than diffusive interaction depending only on the strength of the interaction this competitive coupling results in spontaneous symmetry breaking of a homogeneous initial configuration and the formation of stable spatial patterns this mechanism is very robust and produces stable pattern formation for a wide variety of spatial geometries even when the local site dynamics is trivial

universality and scaling of period doubling bifurcations in a dissipative distributed medium abstract a homogeneous medium consisting of nonlinear elements demonstrating transition to chaos via period doubling bifurcations is considered the coupling between the elements is supposed to be of a dissipative type i e it tends to equalize their instantaneous states using the renormalization group approach the following scaling law for weakly inhomogeneous states near the critical point is obtained at each period doubling the spatial scale increases by 2 on the basis of this law the scaling hypotheses for the transition to chaos in the semi infinite and finite systems are proposed the scaling properties are verified by the numerical calculations with a simple model