dynamical renormalisation through classical equations of motion classical approximations for critical dynamics are taken as the basis of a new dynamical renormalisation group strategy in real space the approach is phenomenological and avoids proliferation of interactions as well as memory effects for the square and cubic glauber model the best determinations of static critical properties come up with values for the dynamic exponent which appear compatible with the most recent estimates by monte carlo or series expansion methods

individual based model with global competition interaction fluctuation effects in pattern formation we present some numerical results obtained from a simple individual based model that describes clustering of organisms caused by competition our aim is to show that even when a deterministic description developed for continuum models predicts no pattern formation an individual based model displays well defined patterns as a consequence of fluctuation effects caused by the discrete nature of the interacting agents

upper bounds for survival probability of the contact process a precise description of the nontrivial upper invariant measure for c is still an open problem for the basic contact process which is a self dual attractive but nonreversible markov process of an interacting particle system by its self duality to identify the invariant measure is equivalent to determining the initial state dependence of the survival probability of the process a procedure to give rigorous upper bounds for the survival probability is presented based on a lemma given by harris two new bounds are given improving the simple branching process bound in the one dimensional case the present procedure can be viewed as a trial to make approximate measures by generalized markov extensions

the importance of being discrete life always wins on the surface many systems in chemistry biology finance and social sciences present emerging features that are not easy to guess from the elementary interactions of their microscopic individual components in the past the macroscopic behavior of such systems was modeled by assuming that the collective dynamics of microscopic components can be effectively described collectively by equations acting on spatially continuous density distributions it turns out that to the contrary taking into account the actual individual discrete character of the microscopic components of these systems is crucial for explaining their macroscopic behavior in fact we find that in conditions in which the continuum approach would predict the extinction of all of the population respectively the vanishing of the invested capital or the concentration of a chemical substance etc the microscopic granularity insures the emergence of macroscopic localized subpopulations with collective adaptive properties that allow their survival and development in particular it is found that in two dimensions life the localized proliferating phase always prevails

sharp regularity of linearization for c 1 1 hyperbolic diffeomorphisms c 1 linearization is of special significance because it preserves smooth dynamical behaviors and distinguishes qualitative properties in characteristic directions however c 1 smoothness is not enough to guarantee c 1 linearization for c 1 1 hyperbolic diffeomorphisms on banach spaces c 1 linearization was proved under a gap condition together with a band condition of the spectrum in this paper the result of c 1 linearization in banach spaces is strengthened to c 1 beta linearization with a constant beta 0 under a weaker band condition by a decomposition with invariant foliations the weaker band condition allows the spectrum to be a union of more than two but finitely many bands but restricts those bands to be bounded by a number depending on the supremum of contractive spectrum and the infimum of expansive spectrum furthermore we give an estimate for the exponent beta and prove that the estimate is sharp in the planar case

species clustering in competitive lotka volterra models we study the properties of general lotka volterra models with competitive interactions the intensity of the competition depends on the position of species in an abstract niche space through an interaction kernel we show analytically and numerically that the properties of these models change dramatically when the fourier transform of this kernel is not positive definite due to a pattern forming instability we estimate properties of the species distributions such as the steady number of species and their spacings for different types of interactions including stretched exponential and constant kernels

nonlinear diffusion effects on biological population spatial patterns motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations we investigate its implications in a paradigmatic model for the evolution of a single species density u x t the standard model includes growth and competition in a logistic expression and spreading is modeled through normal diffusion moreover the competition term is nonlocal which has been shown to give rise to spatial patterns we generalize the diffusion term through the nonlinear form tu x t d xxu x t with d 0 encompassing the cases where the state dependent diffusion coefficient either increases 1 or decreases 1 with the density yielding subdiffusion or superdiffusion respectively by means of numerical simulations and analytical considerations we display how that nonlinearity alters the phase diagram the type of diffusion imposes critical values of the model parameters for the onset of patterns and strongly influences their shape inducing fragmentation in the subdiffusive case the detection of the main persistent mode allows analytical prediction of the critical thresholds

nonequilibrium lattice models series analysis of steady states a perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state the expansion is expressed directly in terms of the kinetic parameter creation rate rather than in powers of the interaction an algorithm for generating series expansions for local properties is described order parameter series 16 terms and precise estimates of critical properties are presented for the one dimensional contact process and several related models

clustering determines who survives for competing brownian and levy walkers the competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied the latter is assumed to be described either by brownian motion or levy flights competition is taken into account by assuming that individuals reproduce in a density dependent fashion it is observed that no influence of the type of motion occurs when the two species are in a well mixed unstructured state however as soon as the species develop spatial clustering the one forming more concentrated clusters gets a competitive advantage and eliminates the other a similar competitive advantage would occur between walkers of the same type but with different diffusivities if this leads also to different clustering the coexistence of both species is also possible under certain conditions

invariant manifolds for flows in banach spaces on presente une theorie des varietes invariantes lisses basee sur la methode classique de lyapunov penon pour des semi flots continus dans des espaces de banach

application of the mean field renormalization group to nonequilibrium critical phenomena abstract we present results of an extension of mfrg ideas to some nonequilibrium systems exhibiting a continuous transition to an absorbing state critical parameters are determined for the contact process in one and higher dimensions and for some related models the effects of hopping between neighbours and other changes in the dynamic rules are considered

fluctuations impact on a pattern forming model of population dynamics with non local interactions a model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters the model represents biological individuals that die or reproduce at rates depending on the number of neighbors within a given distance we evaluate the importance of the discrete and fluctuating character of this particle model on the pattern forming process to this end a deterministic mean field description including a linear stability and a weakly nonlinear analysis is given and compared with the particle model the deterministic approach is shown to reproduce some of the features of the discrete description in particular the existence of a finite wavelength instability stochasticity in the particle dynamics however has strong effects in other important aspects such as the parameter values at which pattern formation occurs or the nature of the homogeneous phase

application of time power series to nonequilibrium critical phenomena abstract we treat the kinetics of a one dimensional lattice gas adsorption model with a critical point we use a matrix method to construct an exact time power series to describe the dynamics inverting the series gives the time as a function of the density in terms of a well behaved density series from which one can derive a set of finite polynomials that give successively improving estimates of the critical parameter from the ratios of successive coefficients in the density series one can estimate the critical exponent for the time dependence of the critical process

nonequilibrium spin models with ising universal behaviour the properties of a family of nonequilibrium spin models with up down symmetry on a square lattice are determined by a mean field pair approximation and by monte carlo simulation the phase diagram in the parameter space displays a critical line that terminates at a first order critical point it is found that the critical exponents are the same as those of the equilibrium ising model

nonlocal competition and logistic growth patterns defects and fronts logistic growth of diffusing reactants on spatial domains with long range competition is studied the bifurcations cascade involved in the transition from the homogeneous state to a spatially modulated stable solution is presented and a distinction is made between a modulated phase dominated by single or few wave numbers and the spiky phase where localized colonies are separated by depleted region the characteristic defects in the periodic structure are presented for each phase together with the invasion dynamics in the case of local initiation it is shown that the basic length scale that controls the bifurcation is the width of the fisher front and that the total population grows as this width decreases a mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition

competitive brownian and levy walkers population dynamics of individuals undergoing birth and death and diffusing by short or long range two dimensional spatial excursions gaussian jumps or l evy flights is studied competitive interactions are considered in a global case in which birth and death rates are influenced by all individuals in the system and in a nonlocal but finite range case in which interaction affects individuals in a neighborhood we also address the noninteracting case in the global case one single or few cluster configurations are achieved with the spatial distribution of the bugs tied to the type of diffusion in the l evy case long tails appear for some properties characterizing the shape and dynamics of clusters under nonlocal finite range interactions periodic patterns appear with periodicity set by the interaction range this length acts as a cutoff limiting the influence of the long l evy jumps so that spatial configurations under the two types of diffusion become more similar by dividing initially everyone into different families and following their descent it is possible to show that mixing of families and their competition is greatly influenced by the spatial dynamics

non hermitian localization and population biology the time evolution of spatial fluctuations in inhomogeneous d dimensional biological systems is analyzed a single species continuous growth model in which the population disperses via diffusion and convection is considered time independent environmental heterogeneities such as a random distribution of nutrients or sunlight are modeled by quenched disorder in the growth rate linearization of this model of population dynamics shows that the fastest growing localized state dominates in a time proportional to a power of the logarithm of the system size using an analogy with a schr odinger equation subject to a constant imaginary vector potential we propose a delocalization transition for the steady state of the nonlinear problem at a critical convection threshold separating localized and extended states in the limit of high convection velocity the linearized growth problem in d dimensions exhibits singular scaling behavior described by a d ensuremath 1 dimensional generalization of the noisy burgers equation with universal singularities in the density of states associated with disorder averaged eigenvalues near the band edge in the complex plane the burgers mapping leads to unusual transverse spreading of convecting delocalized populations

pattern generation in space and aspect a survey is presented of theories for the generation and maintenance of spatial pattern in reaction diffusion equations and their generalizations applications are selected from the biological sciences and physical chemistry special emphasis is placed on nonlocal interaction as manifested by the inclusion of terms involving higher derivatives or integrals it is stressed that traditional ideas of spatial pattern generation can usefully be extended to the study of pattern in general descriptive aspect variables particularly in understanding ecological diversity and heterogeneity

perturbative series expansion for the gap of the evolution operator associated with the contact process the gap between the eigenvalues of the dominant and subdominant eigenvectors of the evolution operator associated with the contact process in one dimension is studied by perturbative series expansions in powers of the creation rate the series expansion for the gap was computed with 49 coefficients an analysis by pade approximants allowed the determination of the critical creation rate and the time correlation critical exponent

nonlocal competition and the speciation transition on random networks a simple model for competition induced speciation is presented and analyzed logistic growth with nonlocal interaction is studied on regular and random networks and the large scale structure of the emerging genomic frequencies is examined the neutrality assumption is violated if the network is random and the competition is nonlocal instead hubs in the sequence space are suppressed by the competition more than nodes of a lower degree thus speciation is unavoidable for large scale free networks the emerging genetic mixture depends strongly on the initial conditions the frequency of hubs is much greater in a population that evolved from a single nucleation event than in a population that recovered from a catastrophe

clustering of diffusing organisms recently a brownian bugs model has been proposed as a possible explanation for the clustering of organisms such as planktons w r young a j roberts and g stuhne nature london 412 328 2001 in this model diffusing organisms die and give birth with equal probabilities and are independent of each other the clustering phenomenon is due to the discreteness of birth and death events and cannot be explained in the framework of the continuous model of population dynamics we show by exact calculation that at dimensions smaller than or equal to 2 this simple mechanism is enough to provoke aggregations of the organisms at dimensions higher than 2 the clustering phenomenon disappears but reproductive fluctuations can still be large compared to diffusive ones

on invariant manifolds and invariant foliations without a spectral gap abstract it is known that a spectral gap condition is required for the existence and smoothness of invariant manifolds and invariant foliations near a fixed point however any planar mapping with a unipotent linear part having a center manifold on the whole phase plane does not have such a gap in this paper we give the existence and smoothness of invariant manifolds which are invariant submanifolds of the center manifold for the aforementioned planar mapping corresponding to the invariant submanifolds we further prove the existence and smoothness of invariant foliations on the center manifold

smooth conjugacy of centre manifolds in this paper we prove that for a system of ordinary differential equations of class c r 1 1 r 0 and two arbitrary c r 1 1 local centre manifolds of a given equilibrium point the equations when restricted to the centre manifolds are c r conjugate the same result is proved for similinear parabolic equations the method is based on the geometric theory of invariant foliations for centre stable and centre unstable manifolds

length scaling in mfrg the mean field renormalisation group mfrg has so far given poor estimates for critical indices it is argued that this can be traced to an unsatisfactory definition of the length scaling factor a new definition that improves the estimates in most cases is proposed

critical behaviour of nonequilibrium three state systems the phase diagram of two different nonequilibrium three state systems is here studied by means of mfrg and computer simulations critical exponents are obtained by a finite size scaling analysis of the mc data a symmetry argument used by grinstein et al to predict the critical behaviour of two state nonequilibrium systems with up down symmetry is shown to apply to these three state systems with symmetry of interchange between two of those states

time dependent perturbation theory for diffusive non equilibrium lattice models the authors recently presented a perturbation theory for the asymptotic survival probability of an interacting particle system which can become trapped in an absorbing state they extend the method to a simple diffusive model analysis of the resulting series shows that diffusion is an irrelevant perturbation i e it does not change the critical behaviour quantitative predictions of the phase boundary are confirmed by results of monte carlo simulations

invariant foliations near normally hyperbolic invariant manifolds for semiflows let m be a compact c1 manifold which is invariant and normally hyperbolic with respect to a c1 semiflow in a banach space then in an neighborhood of m there exist local c1 center stable and center unstable manifolds w cs and w cu respectively here we show that w cs and w cu may each be decomposed into the disjoint union of c1 submanifolds leaves in such a way that the semiflow takes leaves into leaves of the same collection furthermore each leaf intersects m in a single point which determines the asymptotic behavior of all points of that leaf in either forward or backward time

spatial structures and periodic travelling waves in an integro differential reaction diffusion population model an integro differential reaction diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase it is claimed that this is inherently more realistic than the usual kind of reaction diffusion model for mobile populations three kinds of bifurcation from the uniform steady state solution are considered i to steady spatially periodic structures ii to periodic standing wave solutions and iii to periodic travelling wave solutions these correspond to aggregation and motion of populations

linearization and invariant manifolds on the carrying simplex for competitive maps abstract a result due to m w hirsch states that most competitive maps admit a carrying simplex i e an invariant hypersurface of codimension one which attracts all nontrivial orbits the common approach in the study of these maps is to focus on the dynamical behavior on the carrying simplex however this manifold is normally non smooth therefore not every tool coming from differential geometry can be applied in this paper we prove that the restriction of the map to the carrying simplex in a neighborhood of an interior fixed point is topologically conjugate to the restriction of the map to its pseudo unstable manifold by an invariant foliation this implies that the linearization techniques are applicable for studying the local dynamics of the interior fixed points on the carrying simplex we further construct the stable and unstable manifolds on the carrying simplex our results give partial responses to hirsch s problem regarding the smoothness of the carrying simplex we discuss some applications in classical models of population dynamics

critical behaviour of a long range non equilibrium system the critical behaviour of a long range one dimensional non equilibrium system where the desorption rate decreases with distance as some power approximately r alpha d is studied by means of the coherent anomaly method the alpha dependence of the critical parameter lambda c and the critical exponent beta is determined

scaling in reaction diffusion systems the authors study irreversible reaction diffusion models of the form px from k1 from mx to k2 to qx sx from k3 from nx m dc 2 n m 1 n 1 which they study for d dc using the renormalisation group in conjunction with then epsilon expansion and exact techniques for m 1 and any n the transition remains continuous they present epsilon expansions for the case n 3 by contrast for m 2 and any n the system shows a fluctuation induced first order transition

diffusion reproduction processes interesting physics emerges from studying a population of reproducing individuals each can be regarded as a random walker but it can either duplicate or die novel features of the collective behavior are quite surprising if individuals reproduce or die freely the life expectation is proportional to the size of the population and if it is kept constant the center of mass moves in space as if it were a single walker i e the diffusion constant is independent of population s size biology inspired interactions are also considered

cellular automata and statistical mechanical models we elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata transient and stationary properties of probabilistic automata are linked to surface and bulk properties respectively of restricted statistical mechanical systems it is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata some exact results are derived including duality transformations exact mappings disorder and linear solutions many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties this approach is considered to be a first step toward the design of fully parallel probabilistic systems whose computational abilities rely on the cooperative behavior of their components

non equilibrium scaling in the schlogl model from the reaction diffusion master equation formulation of the schlogl model the authors develop a comprehensive description of the non equilibrium dynamics using the poisson transformation and the dynamical renormalisation group they firstly show how the equilibrium limit is recovered and secondly describe the low frequency low momenta scaling behaviour of the concentration fluctuations the approach extends simplifies or corrects previous studies and is easily generalised to treat more complicated systems

asymptotic behavior of the order parameter in a stochastic sandpile we derive the first four terms in a series for the order paramater the stationary activity density in the supercritical regime of a one dimensional stochastic sandpile in the two dimensional case the first three terms are reported this is done by reorganizing the pertubation theory derived using a path integral formalism dickman and vidigal j phys a 35 7269 2002 to obtain an expansion for stationary properties since the process has a strictly conserved particle density p the fourier mode n 1 k 0 p when n and so is not a random variable isolating this mode we obtain a new effective action leading to an expansion for in the parameter 1 1 4p this requires enumeration and numerical evaluation of more than 200 000 diagrams for which task we develop a computational algorithm predictions derived from this series are in good accord with simulation results we also discuss the nature of correlation functions and one site reduced distributions in the small high density limit