dynamical behavior of lotka volterra competition systems non autonomous bistable case and the effect of telegraph noise this article is concerned with the study of trajectory behavior of lotka volterra competition bistable systems and systems with telegraph noises we proved that for bistable systems there exists a unique solution bounded above and below by positive constants the oscillatory situation of systems with telegraph noises is pointed out

analysis of a hybrid switching svir epidemic model with vaccination and levy noise abstract this paper is concerned with the dynamical behavior of a hybrid switching svir epidemic model with vaccination and levy noise besides a standard geometric brownian motion another two driving processes are considered a stationary poisson point process and a continuous time finite state markov chain to begin with we obtain sufficient conditions for persistence in the mean of the disease then we establish sufficient conditions for extinction of the disease furthermore in the case of persistence we also obtain sufficient conditions for the existence of positive recurrence of the solutions by constructing a suitable stochastic lyapunov function with regime switching

analysis of a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation abstract in this paper we consider a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation we show there is a unique positive solution to the system with positive initial value and mainly investigate the long time behavior of the system condition for the system to be extinct is given and persistent condition is established at last numerical simulations are carried out to support our results

dynamics of the deterministic and stochastic siqs epidemic model with non linear incidence the deterministic and stochastic siqs models with non linear incidence are introduced for deterministic model the basic reproductive rate r 0 is derived moreover if r 0 1 there exists a unique endemic equilibrium which is globally asymptotically stable for stochastic model sufficient condition for extinction of the disease that is regardless of the value of r 0 is presented in addition if the intensities of the white noises are sufficiently small and r 0 1 then there exists a unique stationary distribution to stochastic model numerical simulations are also carried out to confirm the analytical results

stationary distribution of stochastic population systems in this paper we consider the stochastic differential equation sde population model dx t diag x1 t xn t b ax t dt db t for n interacting species the main aim is to study the stationary distribution of the solution it is known see e g bahar and mao 2004 2 and mao 2005 6 if the noise intensity is sufficiently large then the population may become extinct with probability one our main aim here is to find out what happens if the noise is relatively small in this paper we will show the existence of a unique stationary distribution we will then develop a useful method to compute the mean and variance of the stationary distribution computer simulations will be used to illustrate our theory

asymptotic behavior of a food limited lotka volterra mutualism model with markovian switching and levy jumps abstract in this paper we investigate a food limited lotka volterra mutualism model with markovian switching and levy jumps we present the analysis and the criteria of the asymptotic behavior for this perturbed model via lyapunov functions our results show that both colored noise and levy noise have important effects on the survival and extinction of the species

new construction of solvable lattice models including an ising model in a field in this letter we report a new construction to obtain restricted solid on solid rsos models out of loop models the method is a generalization of ideas developed by owczarek and baxter and by pasquier in particular we consider a solvable o n model and point out that some of the rsos models thus obtained admit an off critical extension among these models we find a spin 1 ising model which is solvable not only at the critical point but also in a fieldlike deviation away from it we calculate the critical exponent ensuremath delta 15 directly from the relation between the free energy and the field this is the first determination of this exponent without the use of scaling relations

effects of random motility on microbial growth and competition in a flow reactor the authors investigate the effects of random motility on the ability of a microbial population to survive in pure culture and to be a good competitor for scarce nutrient in mixed culture in a flow reactor model consisting of a nonlinear parabolic system of partial differential equations for pure culture a single population a sharp condition is derived which distinguishes between the two outcomes 1 washout of the population from the reactor or 2 persistence of the population and the existence of a unique single population steady state the simulations suggest that this steady state is globally attracting for the case of two populations competing for scarce nutrient they obtain sufficient conditions for the uniform persistence of the two populations for the existence of a coexistence steady state and for the ability of one population to competitively exclude a rival extensive simulations are reported which suggest that 1 all solutions approach some steady state solution 2 all possible outcomes exhibited by the classical competitive lotka volterra ode model can occur in the model and 3 the outcome of competition between two bacterial strains can depend rather subtly on their respective random motility coefficients

integrable xyz spin chain with boundaries we consider a general class of boundary terms of the open xyz spin 1 2 chain compatible with integrability we have obtained the general elliptic solution of a k matrix obeying the boundary yang baxter equation using the r matrix of the eight vertex model and derived the associated integrable spin chain hamiltonian

exact results for the critical behaviour of a nienhuis o n model on the square lattice exact results are obtained for a square lattice fifteen vertex model and related o n model recently proposed by nienhuis 1990 the partition function per site and finite size corrections are obtained along with the critical exponents via the temperley lieb equivalent six vertex model the exact exponents nu 4 7 and gamma 6 7 follow in the limit n 0 for even system sizes odd system sizes are also discussed the fifteen vertex model is also the vertex formulation of the anisotropic or q deformed spin 1 biquadratic model

a generalized goodwin business cycle model in random environment abstract this work develops a generalization of the goodwin lotka volterra models the traditional model describes the evolution of the employment rate and the labor share motivated by recent developments on business cycles and goodwin type models we consider a generalized goodwin business cycle model with noise we aim at investigating the impact of telegraph noise and white noise on the evolution of trajectories and the energy on trajectories of the model it is proved that with the presence of the noises all trajectories exit any compact subset of the open unit square d 0 1 0 1 and the energy along trajectories can be arbitrarily large moreover under certain additional conditions the boundary of d is the stable limit cycle of the perturbed model by white noise noise impact on the period of business cycles is also discussed numerical examples are provided to demonstrate our findings

the reconstruction of local quantum operators for the boundary xxz spin heisenberg chain the method of the reconstruction of local quantum operators in terms of the elements of the quantum monodromy matrix is applied to the xxz spin heisenberg chain with integrable boundary conditions

properties of eigenstates of the six vertex model with twisted and open boundary conditions we use the method proposed by izergin and korepin to discuss the bethe ansatz equations of the six vertex model with twisted and open boundary conditions let two parameters of the bethe wave functions be equal then an additional bethe ansatz equation arises for the open boundary condition case we also have discussed the dual pseudovacuum state and have written out the simplest scalar products of the bethe wave function

surface free energies interfacial tensions and correlation lengths of the abf models the surface free energies interfacial tensions and correlation lengths of the andrews baxter forrester models in regimes iii and iv are calculated with fixed boundary conditions the interfacial tensions are calculated between arbitrary phases and are shown to be additive the associated critical exponents are given by with in regime iii and with in regime iv our results are obtained using general commuting transfer matrix and inversion relation methods that may be applied to other solvable lattice models

on competitive lotka volterra model in random environments focusing on competitive lotka volterra model in random environments this paper uses regime switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem subject to the random changes of the external environment it is demonstrated that the growth rates of the population sizes of the species are bounded above moreover certain long run average limits of the solution are examined from several angles a partial stochastic principle of competitive exclusion is also derived finally simple examples are used to demonstrate our findings

the general uq sl 2 invariant xxz integrable quantum spin chain the boundary conditions are constructed for the general xxz quantum integrable spin chain such that the resulting system is invariant under the quantum algebra uq sl 2 action the result generalizes that due to pasquier and saleur 1990 obtained for spin 1 2 and spin 1

ergodic property of a lotka volterra predator prey model with white noise higher order perturbation under regime switching abstract in this paper we investigate a classical lotka volterra predator prey model with telephone noise and a higher order perturbation of white noise the existence of a unique positive solution is discussed and sufficient conditions for the existence of an ergodic stationary distribution is established some simulation figures are presented to illustrate the analytical findings

difference equations for correlation functions of belavin s ℤn symmetric model with boundary reflection belavin s n symmetric elliptic model with boundary reflection is considered on the basis of the boundary ctm bootstrap we find non diagonal k matrices for n 2 that satisfy the reflection equation boundary yang baxter equation and also find non diagonal boltzmann weights for the a 1 n 1 face model even for n 2 we derive difference equations of the quantum knizhnik zamolodchikov type for correlation functions of the boundary model the boundary spontaneous polarization is obtained by solving the simplest difference equations in the case of the free boundary condition the resulting quantity is the square of the spontaneous polarization for the bulk n symmetric model up to a phase factor

stochastic mutualism model under regime switching with levy jumps abstract this paper is concerned with a stochastic mutualism model under regime switching with levy jumps to begin with the existence and uniqueness of the global positive solution is proved with any given positive initial value then the sufficient conditions for stochastic permanence are established the critical value between extinction and persistence in mean is also obtained in addition under some suitable conditions we proved that there is a unique stationary distribution for the system without levy jumps our method relies on the lyapunov function analysis and the fredholm alternative the results demonstrate that regime switching may contribute to the permanence but jump noise may suppress the permanence

a construction of solutions to reflection equations for interaction round a face models we present a procedure in which known solutions to reflection equations for interaction round a face lattice models are used to construct new solutions the procedure is particularly well suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency 1 among such models are the andrews baxter forrester models for which we construct reflection equation solutions for fixed and free boundary conditions

surface critical behaviour of an o n loop model related to two manhattan lattice walk problems we find and discuss the scaling dimensions of the branch 0 manifold of the nienhuis o n loop model on the square lattice concentrating on the surface dimensions the results are extracted from a bethe ansatz calculation of the finite size corrections to the eigenspectrum of the six vertex model with free boundary conditions these results are especially interesting for polymer physics at two values of the crossing parameter lambda interacting self avoiding walks on the manhattan lattice at the collapse temperature lambda pi 3 and hamiltonian walks on the manhattan lattice lambda pi 2 are discussed in detail our calculations illustrate the importance of examining both odd and even strip widths when performing finite size correction calculations to obtain scaling dimensions

the inversion relation method for some two dimensional exactly solved models in lattice statistics the partition functions per site of several two dimensional models notably the eight vertex self dual potts and hard hexagon models can be easily obtained by using an inversion relation for local transfer matrices together with symmetry and analyticity properties this technique is discussed the analyticity properties compared and some equivalences and nonequivalences pointed out in particular the critical hard hexagon model is found to have the same as the self dualq state potts model withq 3 5 2 2 618 the temperley lieb equivalence between the potts and six vertex models is found to fail in certain nonphysical antiferromagnetic cases

dynamics of a stochastic heroin epidemic model abstract in this paper we investigate a stochastic heroin epidemic model by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the extinction of the drug users moreover we also establish sufficient conditions for the existence of ergodic stationary distribution to the model which reveals that the drug users will persist the sensitivity analysis indicates that prevention would be more important than cure

sensitivity of spin glass order to temperature changes by a loop expansion around parisi s mean field theory for an ising spin glass it is shown that the overlap of the magnetization patterns belonging to two different temperatures t and t vanishes to any order si t si t 0 while the correlation overlap sisj t sisj t calculated to first loop order and for technical reasons for dimensions d 8 only is found to decay exponentially with a characteristic length approximately t t 1

weight vectors of the basic a1 1 module and the littlewood richardson rule the basic representation of a1 1 is studied the weight vectors are represented in terms of schur functions a suitable base of any weight space is given the littlewood richardson rule appears in the linear relations among weight vectors

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

manhattan lattice theta point exponents from kinetic growth walks and exact results from the nienhuis o n model kinetic growth walks kgw on the manhattan lattice have previously been shown to be equivalent to the static problem of interacting self avoiding walks on that lattice at the theta temperature here we illustrate how a complete set of exponents for the static problem including the crossover exponent phi and surface exponents at the ordinary and special transition points may be obtained from simulations of kinetic walks in the process we find that phi m 0 430 or 0 006 which encompasses the conjectured value 3 7 approximately 0 42857 for the theta point on an isotropic lattice our numerics confirm a predicted set of exponents for both the bulk and surface transitions in addition to results such as the exact internal energy at the bulk transition furthermore we point out that a recently examined variant of the nienhuis o n model can be mapped onto theta point walks on the manhattan lattice which allows identification of the scaling dimensions for that problem and thereby provides a method for proving all the numerical conjectures

surface critical behaviour of the honeycomb o n loop model with mixed ordinary and special boundary conditions the o n loop model on the honeycomb lattice with mixed ordinary and special boundary conditions is solved exactly by means of the bethe ansatz the calculation of the dominant finite size corrections to the eigenspectrum yields the mixed boundary scaling index and the geometric scaling dimensions describing the universal surface critical behaviour exact results follow in the limit n 0 for the polymer adsorption transition with a mixed adsorbing and free boundary these include the new configurational exponent gamma l 85 64

surface operator content of the al face models abstract a set of fixed boundary weights for both the critical dense and dilute a l face models is constructed from the known boundary weights of the related loop model the surface operator content and the conformal partition functions then follow from the results obtained via the bethe equations

critical exponents of manhattan hamiltonian walks in two dimensions from potts and o n models we consider a set of hamiltonian circuits filling a manhattan lattice i e a square lattice with alternating traffic regulation we show that the generating function with fugacityz of this set is identical to the critical partition function of aq state potts model on an unoriented square lattice withq1 2 z the set of critical exponents governing correlations of hamiltonian circuits is derived using a coulomb gas technique these exponents are also found to be those of an o n vector model in the low temperature phase withn q1 2 z the critical exponents in the limitz 0 are then those of spanning trees q 0 and of dense polymers n 0 t tc corresponding to a conformal theory with central chargec 2 this shows that the manhattan orientation and the hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of hamiltonian walks

threshold behavior in a stochastic siqr epidemic model with standard incidence and regime switching abstract this paper is concerned with the dynamical behavior of a stochastic siqr epidemic model with standard incidence which is disturbed by both white and telegraph noises firstly we obtain sufficient conditions for persistence in the mean of the disease then we establish sufficient conditions for extinction of the disease in addition in the case of persistence we get sufficient conditions for the existence of positive recurrence of the solutions by constructing a suitable stochastic lyapunov function with regime switching meanwhile the threshold between persistence in the mean and extinction of the stochastic system is also obtained finally some numerical simulations are introduced to demonstrate the analytical results

the ergodic property and positive recurrence of a multi group lotka volterra mutualistic system with regime switching abstract in this paper we consider a stochastic multi group lotka volterra mutualistic system under regime switching it is well known that the population is forced to expire when the perturbation is sufficiently large the main aim here is to investigate its ergodic property and positive recurrence by stochastic lyapunov functions under small perturbation which can be used to explain some recurring phenomena in practice and thus provide a good description of permanence the mean of the stationary distribution is estimated simulations are also carried out to confirm our analytical results

phase transitions in csos models the exact solution of the csos models by pearce and seaton is analysed this solution appears to describe a first order transition without droplet singularities the authors show that the system with free boundaries has no such transition whereas the system with fixed boundary conditions has a first order transition at an anisotropy dependent locus unlike the findings of pearce and seaton they also explain the absence of droplet singularities finally they present a simple coulomb gas calculation of some critical exponents resulting in the same expressions as given by pearce and seaton 1989

dynamics of a stochastic predator prey model with distributed delay and markovian switching abstract in this paper we study a stochastic predator prey model with distributed delay and markovian switching firstly we obtain sufficient criteria for weak persistence of the predator population then in the case of weak persistence we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic lyapunov function with regime switching finally we establish sufficient conditions for extinction of the predator population

operator content of the cyclic solid on solid models the operator content of the cyclic solid on solid models is derived under general boundary conditions by mapping the row to row transfer matrix onto the six vertex model and xxz heisenberg chain for the shift boundary conditions the dimensions and spins of the primary operators are derived analytically from finite size corrections to the scaling spectra the full operator content agrees with results for a quantum chain model having the same local symmetry

two renewal theorems for general random walks tending to infinity necessary and sufficient conditions for the existence of moments of the first passage time of a random walk s n into x for fixed x 0 and the last exit time of the walk from x are given under the condition that s n a s the methods which are quite different from those applied in the previously studied case of a positive mean for the increments of s n are further developed to obtain the order of magnitude as x of the moments of the first passage and last exit times when these are finite a number of other conditions of interest in renewal theory are also discussed and some results for the first time for which the random walk remains above the level x on k consecutive occasions which has applications in option pricing are given

factorized s matrices and generalized baxter models we prove that solutions of the factorization equations for s matrices with zn symmetry can be given in terms of theta functions we present a class of vertex models based on a symmetric s matrices a being an abelian group as natural generalizations of the baxter model the mapping of these models into spin systems is described

periodic solutions and stationary distribution for a stochastic predator prey system with impulsive perturbations abstract in this paper we consider a stochastic predator prey system with beddington deangelis functional response and impulsive perturbations first we prove that the model admits a unique global positive solution by constructing the equivalent system without impulsive perturbations second we establish a sufficient condition which allows the existence of a positive periodic solution using stochastic lyapunov functions finally for the predator prey system with beddington deangelis functional response disturbed by both white noise and telephone noise we give the sufficient conditions for the stationary distribution which is ergodic and positive recurrent of the solution the conclusion implies that the stochastic system has a positive t periodic markov process in a certain condition when the corresponding deterministic system has at least one positive t periodic solution

explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons abstract focusing on hybrid diffusion dynamics involving continuous dynamics as well as discrete events this article investigates the explicit approximations for nonlinear switching diffusion systems modulated by a markov chain different kinds of easily implementable explicit schemes have been proposed to approximate the dynamical behaviors of switching diffusion systems with locally lipschitz continuous drift and diffusion coefficients in both finite and infinite intervals without additional restriction conditions except those which guarantee the exact solutions possess their dynamical properties the numerical solutions converge strongly to the exact solutions in finite horizon moreover realize the approximation of long time dynamical properties including the moment boundedness stability and ergodicity some simulations and examples are provided to support the theoretical results and demonstrate the validity of the approach

stationary distribution of a regime switching predator prey model with anti predator behaviour and higher order perturbations abstract in this paper we study a regime switching predator prey model with anti predator behaviour and higher order perturbations we obtain the ergodic property by constructing a suitable stochastic lyapunov function with regime switching which provides us a biological perspective of cycling phenomena of a population system and can better describe the stochastic persistence of a population system in practice we find that these restrictive assumptions on the functional response are relative weak and valid for many types of response functions

boundary critical behavior of d 2 self avoiding walks on correlated and uncorrelated vacancies in this paper we present exact results for the critical exponents of interacting self avoiding walks with ends at a linear boundary effective interactions are mediated by vacancies correlated and uncorrelated on the dual lattice by choosing different boundary conditions several ordinary and special regimes can be described in terms of clusters geometry and of critical and lowtemperature properties of the mathcal o n 1 model in particular the problem of boundary exponents at the point is fully solved and implications for point universality are discussed the surface crossover exponent at the special transition of noninteracting self avoiding walks is also interpreted in terms of percolation dimensions

sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching in this paper we prove that a stochastic logistic population under regime switching controlled by a markov chain is either stochastically permanent or extinctive and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions in the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems of the population model finally we illustrate our conclusions through two examples

connection problems for quantum affine kz equations and integrable lattice models cherednik attached to an affine hecke algebra module a compatible system of difference equations called quantum affine knizhnik zamolodchikov kz equations in the case of a principal series module we construct a basis of power series solutions of the quantum affine kz equations relating the bases for different asymptotic sectors gives rise to a weyl group cocycle which we compute explicitly in terms of theta functions

exact solution and surface critical behaviour of an o n model on the honeycomb lattice the authors obtain the exact bethe ansatz solution of an o n model on the honeycomb lattice with open boundaries across a finite strip several quantities relevant to the surface critical behaviour of the o n model are derived from this solution the exact surface critical exponents are in agreement with those obtained by cardy 1987 and by duplantier and saleur 1986 based on conformal invariance arguments

logistic models with regime switching permanence and ergodicity abstract focusing on stochastic dynamics involving continuous states as well as discrete events this paper investigates stochastic logistic model with regime switching and obtains sufficient conditions for stochastic permanence which are much weaker than the existing results in the literature furthermore under the conditions of stochastic permanence the existence and uniqueness of stationary distribution is proved an interesting fact is the regime switching can suppress the non permanence a couple of examples and numerical simulations are given to illustrate our results

modelling the effect of telegraph noise in the sirs epidemic model using markovian switching abstract we discuss the effect of introducing telegraph noise which is an example of an environmental noise into the susceptible infectious recovered susceptible sirs model by examining the model using a finite state markov chain mc first we start with a two state mc and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence we then explain how the results can be generalised to a finite state mc the results for the sir susceptible infectious removed model with markovian switching ms are a special case numerical simulations are produced to confirm our theoretical results

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

stochastic replicator dynamics subject to markovian switching abstract population dynamics are often subject to random independent changes in the environment for the two strategy stochastic replicator dynamic we assume that stochastic changes in the environment replace the payoffs and variance this is modeled by a continuous time markov chain in a finite atom space we establish conditions for this dynamic to have an analogous characterization of the long run behavior to that of the deterministic dynamic to create intuition we first consider the case when the markov chain has two states a very natural extension to the general finite state space of the markov chain will be given

solvable lattice models labelled by dynkin diagrams an equivalence between generalized restricted solid on solid models associated with sets of graphs and multi colour loop models is established as an application the authors consider solvable loop models and in this way obtain new solvable families of critical rsos models these families can all be classified by the dynkin diagrams of the simply laced lie algebras for one of the rsos models labelled by the lie algebra pair al al and related to the c2 1 vertex model they give an off critical extension which breaks the z2 symmetry of the dynkin diagrams

sde sis epidemic model with demographic stochasticity and varying population size an sde sis epidemic model with demographic stochasticity is developed existence of a unique non negative solution is shown an upper bound is found for the infectives in terms of the population size the infectives and susceptibles go extinct in finite time a s results are supported numerically some with real examples in this paper we look at the two dimensional stochastic differential equation sde susceptible infected susceptible sis epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size first we look at the sde model for the total population size and show that there exists a unique non negative solution then we look at the two dimensional sde sis model and show that there exists a unique non negative solution which is bounded above given the total population size furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely lastly we support our analytical results with numerical simulations using theoretical and realistic disease parameter values

permanence of hybrid competitive lotka volterra system with levy noise abstract this paper concerns stochastic permanence of a hybrid competitive lotka volterra system with levy noise sufficient conditions of stochastic permanence are obtained by combining stochastic analytical techniques with m matrix analysis

interaction round a face models with fixed boundary conditions the abf fusion hierarchy we use boundary weights and reflection equations to obtain families of commuting double row transfer matrices for interaction round a face models with fixed boundary conditions in particular we consider the fusion hierarchy of the andrews baxter forrester abf models for which we obtain diagonal elliptic solutions to the reflection equations and find that the double row transfer matrices satisfy functional equations with the same form as in the case of periodic boundary conditions

a free energy bound for the hopfield model the author gives a simple upper and lower bound on the free energy density of the hopfield model of size n with p stored patterns in the limit where n and p tend to infinity with p n to alpha 1 the two bounds coincide for alpha 0

integrable and conformal boundary conditions for widehat s ell 2 a d e lattice models and unitary minimal conformal field theories integrable boundary conditions are studied for critical a d e and general graph based lattice models of statistical mechanics in particular using techniques associated with the temperley lieb algebra and fusion a set of boundary boltzmann weights which satisfies the boundary yang baxter equation is obtained for each boundary condition when appropriately specialized these boundary weights each of which depends on three spins decompose into more natural two spin edge weights the specialized boundary conditions for the a d e cases are naturally in one to one correspondence with the conformal boundary conditions of widehat s ell 2 unitary minimal conformal field theories supported by this and further evidence we conclude that in the continuum scaling limit the integrable boundary conditions provide realizations of the complete set of conformal boundary conditions in the corresponding field theories

critical behaviour and conformal anomaly of the o n model on the square lattice finite size scaling and transfer matrix techniques are used to determine the conformal anomaly and critical exponents of o n models on the square lattice these calculations were performed on five branches of critical points parametrised by n the results for two of the branches agree with the known universal properties of the o n model as derived for the honeycomb lattice finite size convergence is poor for most of the third branch so that in this case the classification in terms of known models is uncertain the authors data show that the fourth branch can be interpreted in terms of a combination of a low temperature o n and a critical ising model finally the numerical results for the o n model on the remaining branch agree accurately with the known results for the low temperature o n 1 model they prove this equivalence by means of an exact mapping

on hybrid competitive lotka volterra ecosystems abstract this paper is concerned with competitive lotka volterra model in random environments it uses regime switching diffusion to model the dynamic of population sizes of n different species in a ecosystem subject to the random changes of the external environment we show that the positive solution of the associated stochastic differential equation does not explode in finite time with probability 1 moreover we demonstrate that the solution is stochastically bounded continuous and has finite moments furthermore we obtain certain asymptotic results regarding large time behavior and present some numerical experimental results

asymptotic properties of stochastic hybrid gilpin ayala system with jumps this paper focuses on studying the dynamics of the stochastic gilpin ayala model under regime switching with jumps the aim is to analyze what happens under the perturbations of regime switching and jumps some asymptotic properties are investigated and sufficient conditions for stochastic permanence extinction non persistence in the mean and weak persistence are provided the critical value among the extinction non persistence in the mean and weak persistence is obtained our results demonstrate that the dynamics of the model have close relations with the jumps and the stationary distribution of the markov chain

surface free energy of the critical six vertex model with free boundaries the bethe ansatz equations are derived for the six vertex model with general boundary weights on a lattice in a diagonal orientation these are solved in the thermodynamic limit finite size corrections to the free energy for a restricted class of boundary weights including those corresponding to a potts model with free boundaries are calculated in the critical region the first order term gives the surface free energy of the model the second order term is found to be pi okt tan pi nu 2 mu c 48n 2 where c 1 6 mu 2 pi 2 pi mu is the conformal anomaly this can be compared to pi kt sin pi nu mu c 6n 2 for a calculation on the lattice in the standard orientation and with periodic boundary conditions this difference can be explained geometrically using conformal invariance

permanence and asymptotic behaviors of stochastic predator prey system with markovian switching and levy noise abstract this paper concerns the dynamics of a stochastic predator prey system with markovian switching and levy noise first the existence and uniqueness of global positive solution to the system is proved then by combining stochastic analytical techniques with m matrix analysis sufficient conditions of stochastic permanence and extinction are obtained furthermore for the stochastic permanence case by means of four constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated finally our conclusions are illustrated through an example

stochastic population dynamics under regime switching ii this is a continuation of our paper q luo x mao stochastic population dynamics under regime switching j math anal appl 334 2007 69 84 on stochastic population dynamics under regime switching in this paper we still take both white and color environmental noise into account we show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population in some special but important situations we precisely describe the limit of the average in time of the population

operator content of the fusion cyclic solid on solid model the fusion model of the l state cyclic solid on solid csos model is considered at criticality each zl charge sector of the fusion csos model is related to a sum of total spin sectors of the fusion vertex model with a seam on which the vertex weights are modified by a phase factor the latter in turn becomes the higher spin xxz quantum chain with a twisted boundary condition in the extremely anisotropic limit using the known operator content of the higher spin xxz chain the authors deduce that of the fusion csos model the modular invariant partition function of the fusion csos at fusion level k is a sum of products of the z k parafermionic and free boson sectors with the effective coupling g l2 k lambda pi for l odd and g l2 1 k lambda pi 4 for l even where lambda is the crossing parameter where l is odd and a multiple of k or when l 2 is a multiple of k for l even the modular invariant partition function becomes a simple product of the z k parafermionic and the gaussian partition function

exact solution and surface critical behaviour of open cyclic sos lattice models we consider the l state cyclic solid on solid lattice models under a class of open boundary conditions the integrable boundary face weights are obtained by solving the reflection equations functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions the eigenspectra of the unfused transfer matrix is obtained from the functional relations using the analytic bethe ansatz for a special case of crossing parameter the finite size corrections to the eigenspectra of the critical models are obtained from which the corresponding conformal dimensions follow the calculation of the surface free energy away from criticality yields two surface specific heat exponents and where coprime to l these results are in agreement with the scaling relations and

solution of the dual reflection equation for an 1 1 solid on solid model we obtain a diagonal solution of the dual reflection equation for the elliptic an 1 1 solid on solid model the isomorphism between the solutions of the reflection equation and its dual is studied

the three colouring problem as a special eight vertex model the equations giving the free energy per site and those governing the bethe ansatz wavefunctions for a solid on solid sos model equivalent to the eight vertex model are shown to be identical to those arising in the three colouring problem for the particular choice of parameters eta ik 3 v 0 using the original baxter notation

asymptotic behaviors of stochastic periodic differential equation with markovian switching some asymptotic behaviors of hybrid stochastic periodic differential equations are investigated in this paper firstly by constructing the space of the periodic functions with probability measure values we prove that the solution processes converge to a stochastic process with periodic distribution under the conditions of the existence and uniqueness tightness of the transition probability and global attractivity of the solutions for stochastic periodic differential equations with markovian switching then we give the definition of stochastic periodic solution of stochastic periodic differential equations which can be regarded as the stochastic counterpart of the periodic solution for the deterministic systems for the stochastic periodic logistic equation we firstly give the expression of the unique explicit solution and other properties such as p moment boundedness global attractivity and asymptotic stability in distribution we then prove the existence uniqueness and stability of the unique stochastic periodic solution finally we simulate the sample trajectory of stochastic periodic logistic equation the results show a certain degree of periodicity in fact it is a simulation result for the mixture of periodicity and randomness

asymptotic properties of switching diffusion epidemic model with varying population size the purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical sis epidemic model with standard incidence and varying population size the stochastic model studied here includes white vector noise and telegraph noise modeled by markovian switching we established conditions for extinction both in probability one and in pth moment we also established the persistence of disease under different conditions on the intensities of noises and the parameters of the model furthermore we showed the existence of a stationary distribution and derive expressions for its mean and variance the presented results are demonstrated by numerical simulations

row transfer matrix spectra of cyclic solid on solid lattice models the eigenvalue spectra of cyclic solid on solid csos row transfer matrices are studied an equivalence is established between the inversion identity and the bethe ansatz functional equations and these equations are solved in the thermodynamic limit by a wiener hopf perturbation technique for the bands of leading excitations thel state csos model with crossing parameter s l possesses a 2 l s fold degenerate largest eigenvalue corresponding to the 2 l s coexisting phases the expressions for the largest eigenvalue and free energy coincide with those of the eight vertex model the string excitations for 2s l admit different classifications and are treated separately the correlation length is calculated in both regimes yielding the critical exponentv l 2s in agreement with the scaling relations

permanence and asymptotical behavior of stochastic prey predator system with markovian switching in this paper we investigate the stochastic permanence and extinction of a stochastic ratio dependent prey predator model controlled by a markov chain in the permanent case we estimate the superior limit and the inferior limit of the average in time of the sample path of the solution the boundaries are related to the stationary probability distribution of the markov chain and the parameters of the subsystems finally we illustrate our main results by two examples and some numerical experiments

small time compactness and convergence behavior of deterministically and self normalised levy processes the first author s research was partially supported by arc grant dp0664603 the second author s research was partially supported by nsf grant dms 0503908

stationary distribution and extinction of the ds i a model disease with periodic parameter function and markovian switching this paper introduces the ds i a model with periodic parameter function and markovian switching first we will prove that the solution of the system is positive and global furthermore we draw a conclusion that there exists nontrivial positive periodic solution for the stochastic system and we establish sufficient conditions for extinction of system moreover we construct stochastic lyapunov functions with regime switching to obtain the existence of ergodic stationary distribution of the solution to ds i a model perturbed by white and telephone noises and we also establish sufficient conditions for extinction of system with regime switching finally we test our theory conclusion by simulations

evolution of predator prey systems described by a lotka volterra equation under random environment abstract in this paper we consider the evolution of a system composed of two predator prey deterministic systems described by lotka volterra equations in random environment it is proved that under the influence of telegraph noise all positive trajectories of such a system always go out from any compact set of int r 2 with probability one if two rest points of the two systems do not coincide in case where they have the rest point in common the trajectory either leaves from any compact set of int r 2 or converges to the rest point the escape of the trajectories from any compact set means that the system is neither permanent nor dissipative

boundary k matrices for the xyz xxz and xxx spin chains the general solutions for the factorization equations of the reflection matrices k or theta for the eight vertex and six vertex models xyz xxz and xxx chains are found the associated integrable magnetic hamiltonians are derived explicitly finding families depending on several continuous as well as discrete parameters

population dynamical behavior of lotka volterra system under regime switching in this paper we investigate a lotka volterra system under regime switching dx t diag x 1 t x n t b r t a r t x t dt s r t db t where b t is a standard brownian motion the aim here is to find out what happens under regime switching we first obtain the sufficient conditions for the existence of global positive solutions stochastic permanence and extinction we find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the markov chain the limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients finally the main results are illustrated by several examples

stationary distribution of a stochastic within host dengue infection model with immune response and regime switching abstract in this paper we develop a mathematical model of viral infection of monocytes population by dengue virus with immune response which is perturbed by both white and telegraph noises by constructing a suitable stochastic lyapunov function with regime switching we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model the existence of a stationary distribution implies stochastic weak stability

the sis epidemic model with markovian switching abstract population systems are often subject to environmental noise motivated by takeuchi et al 7 we will discuss in this paper the effect of telegraph noise on the well known sis epidemic model we establish the explicit solution of the stochastic sis epidemic model which is useful in performing computer simulations we also establish the conditions for extinction and persistence for the stochastic sis epidemic model and compare these with the corresponding conditions for the deterministic sis epidemic model we first prove these results for a two state markov chain and then generalise them to a finite state space markov chain computer simulations based on the explicit solution and the euler maruyama scheme are performed to illustrate our theory we include a more realistic example using appropriate parameter values for the spread of s t r e p t o c o c c u s p n e u m o n i a e in children

general solution of reflection equation for eight vertex sos model by using the general solution of the reflection equation for the eight vertex model a general solution of the reflection equation for the eight vertex sos model is obtained we also discuss the solution of the reflection equation for the case of the rsos model