critical exponents from power spectra we have simulated the two and three dimensional ising models at their respective critical points with a conventional monte carlo algorithm from the power spectrum of the magnetization autocorrelations we have determined the dynamic critical exponents and obtained the valuesz 2 16 2 19 andz 2 05 in agreement with the results quoted in the literature we have also studied the power spectrum for the kardar parisi zhang and sun guo grant equations describing interface dynamics arguments similar to what was recently used to conclude thatz 4 for model b in critical dynamics were applied to the sun guo grant growth model and the known exact values for the roughening and dynamic exponents were obtained from an analysis of the corresponding power spectrum in self organized critical sand models one obtains a recently proposed hyperscaling relation

spectral method determination of dynamic exponents for ising models abstract we have carried out extensive monte carlo simulations of the ferromagnetic ising model on square and cubic lattices by analysing the power spectrum of the magnetization autocorrelation function we have values of the dynamic exponents for the two models our results are z 2 13 0 02 in two dimensions and z 2 04 0 03 in three dimensions

time dependent critical properties of ising models by damage spreading abstract we use the method of damage spreading to study the time t taken for a spin at a distance r to be damaged for the first time in ising models with heat bath dynamics we report time dependent scaling exponents d t 2 0 1d 2 52 2d 2 26 3d and 2 0 4d if we assume that t r dt we also analyze our data assuming various forms of logarithmic corrections and we find that d t 2 25 or less 2d and 2 0 3d we argue that it is extremely plausible that d t is equal to z the dynamic critical exponent and thus our estimate of z in two dimensions is higher than the consensus value of 2 14 but we find good agreement in one three and four dimensions with the exact and expected values

connection probabilities and rsw type bounds for the two dimensional fk ising model we prove russo seymour welsh type uniform bounds on crossing probabilities for the fk ising fk percolation with cluster weight q 2 model at criticality independent of the boundary conditions our proof relies mainly on smirnov s fermionic observable for the fk ising model 24 which allows us to get precise estimates on boundary connection probabilities we stay in a discrete setting in particular we do not make use of any continuum limit and our result can be used to derive directly several noteworthy properties including some new ones among which are the fact that there is no infinite cluster at criticality tightness properties for the interfaces and the existence of several critical exponents in particular the half plane one arm exponent such crossing bounds are also instrumental for important applications such as constructing the scaling limit of the ising spin field 6 and deriving polynomial bounds for the mixing time of the glauber dynamics at criticality 17

an almost periodic competitive system subject to impulsive perturbations in this paper an almost periodic system of impulsive differential equations used in modeling two species in competition is considered by the comparison between the solutions of impulsive system and the corresponding non impulsive system and constructing lyapunov function sufficient conditions ensuring the uniformly asymptotic stability of a unique positive almost periodic solution of the system are derived finally an example and its corresponding numerical simulations are presented to explain our theoretical results

global stability of a delay differential equations model of plankton allelopathy abstract in this paper we consider a delay differential equations model of plankton allelopathy using an iterative method the global stability of the interior equilibrium point of the system is investigated which shows that toxic substances are harmless for the stability of the interior equilibrium point the results we obtained improve and complement those of chattopadhyay j chattopadhyay effect of toxic substances on a two species competitive system ecol model 84 1996 287 289 samanta g p samanta a two species competitive system under the influence of toxic substances appl math comput 216 2010 291 299 and mukhopadhyay et al a mukhopadhyay j chattopadhyay p k tapaswi a delay differential equations model of plankton allelopathy math biosci 149 1998 167 189 we also present some examples to verify our main result

initiation of damage in the kauffman model an alternate method is presented for initiating damage to the kauffman model a numerical study suggests that this modification increases the efficiency of generating damage clusters without changing their fractal properties

cutoff for the ising model on the lattice introduced in 1963 glauber dynamics is one of the most practiced and extensively studied methods for sampling the ising model on lattices it is well known that at high temperatures the time it takes this chain to mix in l 1 on a system of size n is o logn whether in this regime there is cutoff i e a sharp transition in the l 1 convergence to equilibrium is a fundamental open problem if so as conjectured by peres it would imply that mixing occurs abruptly at c o 1 logn for some fixed c 0 thus providing a rigorous stopping rule for this mcmc sampler however obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple markov chains already for the one dimensional ising model showing cutoff is a longstanding open problem

universality along the critical line of the ising cellular automata the author checks the hypothesis of universality along the critical line of the ising cellular automata ica by measuring critical exponents of damage propagation at the transition temperature tk in zero field and at higher temperatures in nonzero field and at the kauffman limit t infinity numerical results support the claim of universality

time optimal simultaneous control of two level quantum systems in this paper we solve the problem of simultaneously driving in minimum time to arbitrary final conditions n two level quantum systems subject to independent controls the solution of this problem is obtained via an explicit description of the reachable set of the associated control system on s u 2 the treatment generalizes previous results on the time optimal control of two level quantum systems and suggests that similar techniques could be used to solve the minimum time control problem for a larger class of right invariant systems on lie groups

approach to equilibrium of glauber dynamics in the one phase region i the attractive case various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed in particular somefinite size conditions are discussed together with their implications for the gibbs measures and for the approach to equilibrium of glauber dynamics inarbitrarily large volumes it is shown that dobrushin shlosman s theory ofcomplete analyticity and its dynamical counterpart due to stroock and zegarlinski cannot be applied in general to the whole one phase region since it requires mixing properties for regions ofarbitrary shape an alternative approach based on previous ideas of oliveri and picco is developed which allows to establish results on rapid approach to equilibrium deeply inside the one phase region in particular in the ferromagnetic case we considerably improve some previous results by holley and aizenman and holley our results are optimal in the sene that for example they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed dimensional ising model with or without an external field in part ii we extensively consider the general case not necessarily attractive and we develop a new method based on renormalizations group ideas and on an assumption of strong mixing in a finite cube to prove hypercontractivity of the markov semigroup of the glauber dynamics

emergent properties in random complex automata abstract studies of large randomly assembled binary boolean node automata have demonstrated that such systems can spontaneously exhibit enormously ordered dynamical behavior an important approach to characterizing these behaviors has consisted of studying ensembles of automata ensemble specifications have been based on 1 choice of boolean function regulating each node in the automaton 2 random or biased mappings of the 2 n automata states into themselves 3 the numbers of inputs k per node this article briefly reviews these approaches reports new results on the expected behavior of threshold automata and automata with a particular class of biased mappings in addition it discusses emergent highly ordered dynamical behavior in random automata rich in a specific class of canalizing boolean functions due to the crystallization of powerful subautomata called forcing structures the ordered behaviors may be of importance in biological evolution in physics and in the design of adaptive automata

critical slowing down in ising model for creutz algorithm abstract dynamical critical exponents for the two dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation and auto correlation functions for the order parameter and the internal energy at the critical temperatures and from the nonlinear relaxation time for the order parameter near the critical temperature the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives z m z e 2 20 and z a m 1 91 and z a e 0 19 for the linear dynamical exponents corresponding respectively to the relaxations of the correlation and the autocorrelation functions for the order parameter and the internal energy and nl m 2 07 for the nonlinear dynamical exponent for the order parameter these values verify the scaling relations between the dynamical exponents

on the dynamic exponent of the two dimensional ising model the authors use the method of damage spreading to measure the time taken for the equilibrium damage the magnetization to disappear in finite systems 10 or 2 27

on weak mixing in lattice models for lattice models on d weak mixing is the property that the influence of the boundary condition on a finite decays exponentially with distance from that region for a wide class of models on 2 including all finite range models we show that weak mixing is a consequence of gibbs uniqueness exponential decay of an appropriate form of connectivity and a natural coupling property in particular on 2 the fortuin kasteleyn random cluster model is weak mixing whenever uniqueness holds and the connectivity decays exponentially and the q state potts model above the critical temperature is weak mixing whenever correlations decay exponentially a hypothesis satisfied if q is sufficiently large ratio weak mixing is the property that uniformly over events a and b occurring on subsets and respectively of the lattice p a b p a p b 1 decreases exponentially in the distance between and we show that under mild hypotheses for example finite range weak mixing implies ratio weak mixing

high temperature series for scalar field lattice models generation and analysis an implementation of the free embedding scheme for high temperature series generation on the body centered cubic family of lattices in arbitrary dimensiond is described series to order 21 in inverse temperature are tabulated for several scalar field models both for the magnetic susceptibility and for the second moment of the spin correlation function the critical behavior of a family of 3 dimensional double gaussian models which interpolate continuously between the spin 1 2 ising model and the gaussian model is analyzed in detail away from the gaussian model limit using confluent inhomogeneous secondorder differential approximants with our best estimate of the correction to scaling exponent 0 52 0 03 the leading exponents for the susceptibility and correlation length for this family are consistent with universality and are given by 1 237 0 002 and 0 630 0 0015 respectively and 2 0 0359 0 0007

mixing times of critical two dimensional potts models we study dynamical aspects of the q state potts model on an n n box at its critical c q heat bath glauber dynamics and cluster dynamics such as swendsen wang that circumvent low temperature bottlenecks are all expected to undergo critical slowdowns in the presence of periodic boundary conditions the inverse spectral gap which in the subcritical regime is o 1 should at criticality be polynomial in n for 1 4 in accordance with the predicted discontinuous phase transition this was confirmed for q 2 the ising model by the second author and sly and for sufficiently large q by borgs et al here we show that the following holds for the critical potts model on the torus for q 3 the inverse gap of glauber dynamics is no 1 for q 4 it is at most no log n and for every q 4 in the phase coexistence regime the inverse gaps of both glauber dynamics and swendsen wang dynamics are exponential in n for free or monochromatic boundary conditions and large q we show that the dynamics at criticality is faster than on the torus unlike the ising model where free periodic boundary conditions induce similar dynamical behavior at all temperatures the inverse gap of swendsen wang dynamics is exp no 1 2017 wiley periodicals inc

damage spreading in the kawasaki ising model abstract we observe no phase transition in the damage spreading probability at the curie point of the 2d ising model with nearest neighbor spin exchange dynamics furthermore we report values of the growth exponent z close to unity implying speed of light transmission of information and values of the exponents describing the scaling behavior of the damage mass with time and distance close to two finally we discuss the spreading of damage in a one dimensional system

effective analysis of damage spreading in ising models using large lattices and different methods of simulation and analysis the kinetic critical exponent z for damage spreading is shown to be consistent with z 2 in two to five dimensions without the logarithmic problems seen in some earlier work

bound on the mass gap for finite volume stochastic ising models at low temperature we consider a sequence of finite volume z d d 2 reversible stochastic ising models in the low temperature regime and having invariant measures satisfying free boundary conditions we show that associated with the models are random hitting times whose expectations regarded as a function of grow exponentially in d 1 d moreover the mass gaps for the models shrink exponentially fast in d 1 d a geometrical lemma is employed in the analysis which states that if a peierls contour is sufficiently small relative to the faces of then the fraction of the contour tangent to the faces is less than a constant smaller than one

critical dynamics of the three dimensional ising model a monte carlo study extensive monte carlo simulations have been performed to analyze the dynamical behavior of the three dimensional ising model with local dynamics we have studied the equilibrium correlation functions and the power spectral densities of odd and even observables the exponential relaxation times have been calculated in the asymptotic one exponential time region we find that the critical exponentz 2 09 0 02 characterizes the algebraic divergence with lattice size for all observables the influence of scaling corrections has been analyzed we have determined integrated relaxation times as well their dynamical exponentzint agrees withz for correlations of the magnetization and its absolute value but it is different for energy correlations we have applied a scaling method to analyze the behavior of the correlation functions this method verifies excellent scaling behavior and yields a dynamical exponentzscal which perfectly agrees withz

static and dynamic critical phenomena of the two dimensional q state potts model theq state potts model on the square lattice is studied by monte carlo simulation forq 3 4 5 6 very good agreement is obtained with exact results of kiharaet al and baxter for energy and free energy at the critical point critical exponent estimates forq 3 are 0 4 0 1 1 45 in rough agreement with high temperature series extrapolation and real space renormalization group methods the transition forq 5 6 is found to be a very weakly first order transition i e pronounced pseudocritical phenomena occur specific heat susceptibility etc nearly diverge at the first order transition temperature dynamics is associated to the model in the same way as for the kinetic ising model and the nonlinear slowing down of the order parameter and of the energy is studied the dynamic exponent is estimated to be zv 1 9 within our accuracy noq dependence is detected the relaxation is found to be consistent with dynamic scaling predictions and dynamic scaling functions associated with the nonlinear relaxation are estimated

a two species competitive system under the influence of toxic substances the effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view in this paper we have studied the dynamical behaviours of a two species competitive system affected by toxic substances boundedness local and global stabilities are addressed we have also studied the stability of this system with diffusion around the non trivial stable in the deterministic case equilibrium point in a random environment extensive numerical simulations are performed using analytical results for a hypothetical set of parameter values

geometrical properties of swendsen wang clusters abstract several geometrical properties of swendsen wang clusters are studied numerically for the 2d ising and 3 state potts models at the critical temperature the fractal dimensions of the total mass backbone elastic backbone shortest path and red bonds are determined the results agree with some theoretical predictions

the role of droplet fluctuations in kinetic ising models the authors examine by monte carlo simulation and the damage algorithm the late time behaviour of fluctuations in the low temperature ordered phase of the two dimensional kinetic ising model it has been suggested that at late times correlations could be dominated by long lived droplet fluctuations of the other ordered phase giving rise to stretched exponential decays of the spin auto correlation function over the time regimes they have studied they see no evidence for anomalous long lived droplets and find that the probability distribution for droplet lifetimes decays by an ordinary exponential

critical dynamics of the potts model in several dimensionalities abstract we study critical dynamics of general q state potts models on d dimensional hypercubic lattices the master equation is formulated according to a theory recently presented by the author a simple bond moving technique followed by decimation is used to obtain the dynamical exponents although this approximation yields poor results for the static exponents the dynamic behaviour is closer to monte carlo simulations we compare our results with those obtained with a different formulation of dynamics a final discussion is included

domain growth kinetics and symmetry breaking in a thermally quenched system the authors simulate thermal quenches on a two dimensional hard core model with symmetry breaking phase transition by dividing large configurations into many small sub squares lack of self averaging is avoided and statistics are improved dynamic scaling is observed during more than two decades

completely analytical interactions constructive description an interactionu is called a completely analytical ca interaction if it satisfies one of 12 given conditions formulated in terms of analyticity properties of the partition functions zv u or correlation decay or truncated correlation bounds or asymptotic behavior of ln zv u v the 12 conditions are presented together with part of the proof of their equivalence the main result of the paper is that each condition is constructive in the following sense instead of checking it in all finite volumesv v it is enough to consider only a finite amount of volumes with restricted size in particular the partition functions z v u for the complex perturbationsu ofu do not vanish for all v v and all with provided this is true only forv with diam v c and but with

dynamical finite size scaling function of the four dimensional ising model for creutz algorithm abstract dynamical critical exponents for the four dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation for the order parameter and the internal energy at the critical temperatures the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives the linear dynamical critical exponents for the order parameter and the internal energy in our calculation the linear dynamical critical exponents are found z m z h i 2 04 at t c z m 1 99 z h i 2 00 at t c l the values of z m z h i 2 04 obtained for t c verify the dynamical finite size scaling for which it was adopted four dimensional ising model

critical dynamics of finite ising model the glauber kinetics of ising spins is considered as a queueing process and simulated event by event as first proposed by bortz kalos and lebowitz the advantage of this algorithm compared to the standard single flip monte carlo method is discussed for the situation of slowing down of dynamics this process is used to generate fluctuations of magnetization and energy in the critical regimet tc of two dimensional ising models the analysis of these fluctuations leads to numerical determination of the critical exponents for dynamics for the size dependence of correlation time attc and for frequency dependence of the power spectrums from the finite size scaling hypothesis scaling relations are settled which are confirmed by this numerical experiment

the logarithmic sobolev inequality for continuous spin systems on a lattice abstract in this article we give cf theorem 1 6 a sufficient condition on a local specification for the associated gibbs state to satisfy a logarithmic sobolev inequality in the final section cf theorem 3 10 we relate our condition to the type of mixing condition introduced by dobrushin and shlosman in connection with their work on complete analyticity

the dynamic critical exponent of the q 3 and 4 state potts model the dynamic monte carlo renormalisation group method introduced by jan moseley and stauffer 1983 is used to determine the dynamic critical exponent z for the q 3 and q 4 state potts model in two dimensions the authors find that z 2 43 or 0 15 and 2 36 or 0 20 for the q 3 and q 4 state potts models these results are in disagreement with the recent conjecture of domany 1984

dynamical properties of the two and three dimensional ising models by damage spreading the method of damage spreading is used to measure the dynamic exponent z for both the two and three dimensional ising models with heat bath dynamics the authors also measure a new exponent alpha describing the rate at which a damage cloud grows they report values of z 2 24 or 0 04 and alpha 0 77 or 0 11 in two dimensions and z 2 202 or 0 03 and alpha 0 92 or 0 10 in three dimensions

selective harvesting of two competing fish species in the presence of toxicity with time delay abstract in this paper we have considered a two competing fish species with the delay due to gestation each of which obeys the law of logistic growth and releases a substance toxic to the other we also consider the selective harvesting of fishes above a certain age or size by incorporating a time delay in the harvesting term the dynamical behavior of the exploited system is examined in the presence and absence of delay boundedness local and global stabilities are addressed the possibility of the existence of a dynamic equilibrium and the optimal harvesting policy is studied in the absence of delay it is shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities extensive numerical simulations are performed using analytical results for a hypothetical set of parameter values

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

time optimal control of quantum lambda systems in the kp configuration we consider the problem of time optimal control for a three level quantum system where one level is coupled by the control field to the lowest two which are not coupled to each other a bound is assumed on the norm of the control at every time such a problem belongs to the class of kp sub riemannian problems for which we can perform a symmetry reduction and reduce to a riemannian problem on the associated quotient space we prove several properties of such a quotient space in our case including the fact that it is an example of an almost kahler manifold that is not kahler we provide the explicit form of the optimal controls for any unitary transformation on the lowest two levels and discuss the geometric and practical implications of this result

dynamic exponent for 2d ising model by power spectra method we consider power spectra for fluctuating quantities at a critical point p omega varies as omega phi where phi is determined by the dynamic exponent z and static exponents specific to the quantity considered from the magnetization spectra obtained with simulations z is found to be 2 13 or 0 03 for the two dimensional glauber kinetic ising model hence in accord with recent monte carlo relaxational studies but at odds with those obtained by series expansion and damage spreading methods excellent dynamic finite size scaling for system sizes l 10 to 128 supports our estimate

polynomial time approximation algorithms for the ising model the paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic ising system to any specified degree of accuracy the running time of the algorithm in

critical dynamics a consequence of a random stepwise growth of clusters critical dynamics of correlated particles here glauber dynamics of singly flipping ising spins is explained by a random stepwise growth and contraction of clusters as follows at equilibrium a cluster of size s is described by its length l a random walk like path connecting a sequence of neighbor spins the length scales as l s where constitutes a new static critical exponent we assume that on the average the random growth of a cluster from zero to size s and length ls requires a sequence of l2 spin flips this gives for dynamic critical exponent z 2 where and are the usual static exponents exact results at dimension d 1 and 4 and simulation results at d 2 and 3 support the theory

simulation of time exponent in 2d glauber kinetic ising model abstract simulations of the magnetization relaxation of large square lattices at the curie point give a dynamical exponent near 2 2 somewhat higher than expected

hyperscaling and universality in 3 dimensions abstract a brief discussion of the relationships between critical exponents known as hyperscaling and the universality of amplitudes at the critical point in 3 dimensions is given numerical evidence for hyperscaling based on series analysis of ising models is reviewed with special emphasis on the assumptions underlying the various methods of analysis revised critical exponent estimates based on a preliminary analysis of recently extended series on the body centered cubic lattice are presented

critical ising on the square lattice mixes in polynomial time the ising model is widely regarded as the most studied model of spin systems in statistical physics the focus of this paper is its dynamic stochastic version the glauber dynamics introduced in 1963 and by now the most popular means of sampling the ising measure intensive study throughout the last three decades has yielded a rigorous understanding of the spectral gap of the dynamics on mathbb z 2 everywhere except at criticality while the critical behavior of the ising model has long been the focus for physicists mathematicians have only recently developed an understanding of its critical geometry with the advent of sle cle and new tools to study conformally invariant systems

approach to equilibrium of glauber dynamics in the one phase region ii the general case we develop a new method based on renormalization group ideas block decimation procedure to prove under an assumption of strong mixing in a finite cube 0 a logarithmic sobolev inequality for the gibbs state of a discrete spin system as a consequence we derive the hypercontractivity of the markov semigroup of the associated glauber dynamics and the exponential convergence to equilibrium in the uniform norm in all volumes multiples of the cube 0

minimal time trajectories for two level quantum systems with two bounded controls in this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude the controls are modeled as real functions and we do not use the rotating wave approximation after projection on the bloch sphere we treat the time optimal control problem with techniques of optimal synthesis on 2d manifolds based on the pontryagin maximum principle we characterize a restricted set of candidate optimal trajectories properties on this set crucial for complete optimal synthesis are illustrated by numerical simulations furthermore when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the initial condition

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

geometry and dynamics of randomly connected fractal clusters abstract the dynamics of critical ising droplets and suitable other clusters is argued to come from growth and decay in small steps not via aggregation of large clusters the resulting critical exponent z for metropolis glauber kinetics is related to the exponent for the chain lengths of the cluster branches simulations of 60960 2 and 1409 3 ising models confirm roughly the exponent z but throw doubts on the small step approach when interpreted with the help of the becker doring equation

a cluster model of critical dynamics abstract critical relaxation exponent z is described by a reversible growth of clusters particles of a cluster are ordered into connected sequences such that a stepwise variation of their length describes relaxation we derive z z where is a scaling exponent relating cluster size to connected length at equilibrium available from simulation of ising clusters furthermore a flory like equation gives and hence z z in d 2 and 3 theoretical z an simulation aided z agree reasonably well with each other and with direct simulations of z in d 4 e z agrees with the exact rg

on the dynamic consistency of a two species competitive discrete system with toxicity local and global analysis abstract discretization of a highly nonlinear system is inevitable for good approximation of its solutions due to lack of its analytical solution however a discrete model constructed by standard discretization technique frequently produces spurious dynamics which are not observed in its constituent continuous model it is therefore important to construct a discrete model that produces the exact dynamics of its continuous counterpart here we transform a continuous time two species nonlinear competition model with the effect of toxic substances into a discrete time system to show its dynamic consistencies with the continuous system by employing nonstandard finite difference scheme linear stability property of each fixed point of the derived model has been proven to be identical with those of the continuous system and the dynamics has been shown to be independent of the step size moreover we prove the global stability of the coexisting equilibrium point of our discrete model comparative simulation results demonstrate that the standard discrete system shows complex dynamics like flip bifurcation and chaos depending on the step size but the proposed discrete model does not show any such spurious dynamics

qualitative analysis on a diffusive predator prey model with toxins abstract this paper is concerned with the diffusive predator prey model with toxins subject to dirichlet boundary conditions the uniform persistence of positive solution is given under certain conditions in addition by the liapunov schmidt method the existence and stability of the bifurcation solution from a double eigenvalues are investigated moreover by the fixed point index theory and perturbation theory of eigenvalues the uniqueness stability and multiplicity of coexistence states are analyzed when some key parameter changes finally some numerical simulations are presented to verify the theoretical conclusions and further to reflect the importance of parameters to the number of coexistence states

the dynamic critical exponent of the three dimensional ising model we measure the dynamic exponent of the three dimensional ising model using a damage spreading monte carlo approach as described by macisaac and jan we simulate systems froml 5 tol 60 at the critical temperature tc 4 5115 we report a dynamic exponent z 2 35 0 05 a value much larger than the consensus value of 2 02 whereas if we assume logarithmic corrections we find thatz 2 05 0 05

fractal dimensions in three dimensional kauffman cellular automata the kauffman random networks of automata are studied on a simple cubic lattice by computer simulations each automaton follows random rules depending on its six neighbours and fixed in time a transition between the frozen and the chaotic phase is observed and the fractal dimension of the asymptotic actual damage at the phase transition is measured

hamiltonian point of view of non euclidean geometry and elliptic functions abstract this paper offers a new way of looking at the classical geometries and the theory of elliptic functions through hamiltonian systems on lie groups in particular the paper shows that i the classical models of non euclidean geometries are canonically induced by bi invariant sub riemannian metrices on lie groups which act by left actions on the underlying space ii there is a class of canonical variational problems on lie groups g whose projections on homogeneous spaces g k generalize euler s elasticae and include all curves of constant curvature and all functions of weierstrass iii complex lie groups unify non euclidean geometries and complex elasticae offer a distinctive look at the elliptic functions

time dependent thermodynamic properties of the ising model from damage spreading the relationship between damage spreading and static thermodynamic properties in the ising model developed by coniglioet al is here extended to include time dependent thermodynamic quantities we exploit this new result to measure the time dependent spin correlation function from damage spreading in the ising model with heat bath and glauber dynamics until now only static thermodynamic quantities have been correctly determined from damage spreading and even then only with heat bath dynamics we also show that there are significant differences between the kinetics of damage spreading as found in heat bath and glauber dynamics

description of critical dynamics by static geometry of clusters abstract critical slowing down of relaxation exponent z is modelled by clusters which grow and recede at the end of connected sequences of particles consequently the relaxation time of a cluster of size s is proportional to the number of back and forth steps needed to travel its typical connected length ls this and an assumption on mutual screening of ends lead to z 2 5 0 25 where is a static geometric exponent in ls s ising exponents measured elsewhere with the help of simulation give z in addition a flory like approximation is derived here it relates to and analytically giving z in d 2 3 and 4 respectively we findz 2 14 2 05 and 2 275 1 while z 2 17 4 and 2 04 4 both sets of values are in fair agreement with the literature