dynamics of kolmogorov systems of competitive type under the telegraph noise abstract this paper studies the dynamics of kolmogorov systems of competitive type under the telegraph noise the telegraph noise switches at random two kolmogorov competition type deterministic models the aim of this work is to describe the omega limit set of the system and investigates properties of stationary density

extinction and stationary distribution of a stochastic sirs epidemic model with standard incidence rate and partial immunity abstract in this paper a stochastic sirs model with standard incidence rate and partial temporary immunity is proposed the sufficient conditions of the extinction and the existence of a stationary probability measure for the disease are established our results reveal that random perturbations in the environment can restrain the spread of disease that is the deterministic model neglecting random perturbations overestimates the ability of the disease to spread the numerical simulations are carried out to demonstrate the analytical results

quantification of topological changes of vorticity contours in two dimensional navier stokes flow a characterization of reconnection of vorticity contours is made by direct numerical simulations of the two dimensional navier stokes flow at a relatively low reynolds number we identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its hessian matrix on the basis of critical point theory the numbers of hyperbolic saddles and elliptic minima and maxima points are confirmed to satisfy euler s index theorem numerically time evolution of these indices is studied for a simple initial condition generally speaking we have found that the indices are found to decrease in number with time this result is discussed in connection with related works on streamline topology in particular the relationship between stagnation points and the dissipation associated elementary procedures in physical space the merging of vortices are studied in detail for a number of snapshots a similar analysis is also done using the stream function

threshold dynamics and ergodicity of an sirs epidemic model with markovian switching abstract this work studies the threshold dynamics and ergodicity of a stochastic sirs epidemic model with the disease transmission rate driven by a semi markov process the semi markov process used in this paper for describing a randomly changing environment is a very large extension of the most common markov regime switching process we define a basic reproduction number for the semi markov regime switching environment and show that its position with respect to 1 determines the extinction or persistence of the disease in the case of disease persistence we give mild sufficient conditions for ensuring the existence and absolute continuity of the invariant probability measure under the same conditions we also prove the global attractivity of the limit set of the system and the convergence in total variation norm of the transition probability to the invariant measure compared with the existing results in the markov regime switching environment the results generalized require almost no additional conditions

dynamics of a multigroup sis epidemic model with standard incidence rates and markovian switching abstract in this paper we investigate a multigroup sis epidemic model with standard incidence rates and markovian switching first of all we establish sufficient conditions for extinction of the diseases then we obtain sufficient conditions for persistence in the mean of the diseases in addition in the case of persistence we obtain sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic lyapunov function with regime switching

on the validity of the weiss criterion in two dimensional turbulence abstract the weiss criterion for two dimensional incompressible turbulent flows separates flow regions where the motion is hyperbolic in character from regions where it is elliptic this criterion is based on the hypothesis that the velocity gradient varies slowly with respect to the vorticity gradient we inspected this hypothesis and derived a criterion linking its validity to the curvature of the pressure field it turns out from numerical experiments that the hypothesis on which relies the weiss criterion is nearly only valid in vortex cores that is in strongly elliptic regions and near stagnation points high pressures

existence of stationary distributions for kolmogorov systems of competitive type under telegraph noise abstract this work focuses on population dynamics of two species described by kolmogorov systems of competitive type under telegraph noise that is formulated as a continuous time markov chain with two states our main effort is on establishing the existence of an invariant or a stationary probability measure in addition the convergence in total variation of the instantaneous measure to the stationary measure is demonstrated under suitable conditions moreover the limit set of a model in which each species is dominant in a state of the telegraph noise is examined in detail

permanence and extinction for the stochastic sir epidemic model abstract the aim of this paper is to study the stochastic sir equation with general incidence functional responses and in which both natural death rates and the incidence rate are perturbed by white noises we derive a sufficient and almost necessary condition for the extinction and permanence for sir epidemic system with multi noises d s t a 1 b 1 s t i t f s t i t d t 1 s t d b 1 t i t g s t i t d b 3 t d i t b 2 i t i t f s t i t d t 2 i t d b 2 t i t g s t i t d b 3 t moreover the rate of all convergences of the solution are also established a number of numerical examples are given to illustrate our results

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

nontrivial periodic solution for a stochastic brucellosis model with application to xinjiang china abstract brucellosis is a kind of zoonotic disease caused by gram negative bacteria of the genus brucella in this paper we propose a stochastic periodic brucellosis model by introducing the effect of environmental white noise on transmission dynamics of brucellosis by has minskii theory of periodic solution and constructing a novel combination of lyapunov functions we establish the existence of nontrivial positive periodic solution if the condition r 0 s 1 holds based on the reported data of newly acute human brucellosis cases for each season from 2010 to 2014 in xinjiang numerical simulations have been performed to support our result and indicate that brucellosis in xinjiang takes on the feature of long term prevalence and cyclical fluctuation

detecting barriers to transport a review of different techniques abstract we review and discuss some different techniques for describing local dispersion properties in fluids a recent lagrangian diagnostics based on the finite scale lyapunov exponent fsle is presented and compared to the finite time lyapunov exponent ftle to the okubo weiss ow and hua klein hk criteria we show that the ow and hk are the limiting case of the ftle and that the fsle is the most efficient method for detecting the presence of cross stream barriers we illustrate our findings by considering two examples of geophysical interest a kinematic model of a meandering jet and lagrangian tracers advected by stratospheric circulation

densities for piecewise deterministic markov processes with boundary abstract we study the existence of densities for distributions of piecewise deterministic markov processes we also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times in our approach we use functional analytic methods and the theory of linear operator semigroups by imposing general conditions on the characteristics of a given markov process we show the existence of a substochastic semigroup describing the evolution of densities for the process and we identify its generator our main tool is a new perturbation theorem for substochastic semigroups where we perturb both the action of the generator and of its domain allowing to treat general transport type equations with non local boundary conditions a couple of particular examples illustrate our general results

the threshold of a periodic stochastic sivs epidemic model with nonlinear incidence abstract in this paper a stochastic periodic sivs epidemic model with nonlinear incidence and vaccination is investigated the threshold conditions on the existence of stochastic positive periodic solutions and the extinction of disease with probability one are established by constructing the new stochastic lyapunov functions and using the new technique to deal with the nonlinear incidence and vaccination for the stochastic epidemic model the numerical simulations are given to illustrate the main theoretical results and present some new interesting conjectures

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

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

an exact criterion for the stirring properties of nearly two dimensional turbulence abstract an exact criterion can be found for partitioning the fluid into regions with different dynamical properties from both the points of view of particle dispersion and tracer gradient evolution this criterion differs markedly both in its magnitude and spatial scales from the okubo weiss criterion which depends upon the differential geometry of the streamfunction field and coincides with the eigenvalues of the velocity gradient tensor the new criterion corresponds to the eigenvalues of the acceleration gradient tensor whose spatial distribution depends instead upon the topology of the pressure field this result holds for all flows for which a continuous momentum equation can be prescribed we provide numerical evidence for the quantitative importance of the time change of the strain rate components in the dispersion problem in freely decaying two dimensional turbulence

risk minimizing option pricing in a semi markov modulated market we address risk minimizing option pricing in a semi markov modulated market where the floating interest rate depends on a finite state semi markov process the growth rate and the volatility of the stock also depend on the semi markov process using the follmer schweizer decomposition we find the locally risk minimizing price for european options and the corresponding hedging strategy we develop suitable numerical methods for computing option prices

stochastic stability of ito differential equations with semi markovian jump parameters in this note the problem of stochastic stability for linear systems with jump parameters being semi markovian rather than full markovian is further investigated in particular the system under consideration is described by ito type nonlinear stochastic differential equations with phase type semi markovian jump parameters stochastic stability conditions are presented

long time behaviors of a stochastic cooperative lotka volterra system with distributed delay abstract this article focuses on a stochastic cooperative lotka volterra system with distributed delay we first transfer the stochastic system with weak kernel into a degenerate stochastic system made up of four equations for the deterministic system global stability of the positive equilibrium is investigated for the stochastic system with distributed delay sharp sufficient conditions for the persistence of two species are established what is more we obtain the existence and uniqueness of the stationary distribution by constructing suitable lyapunov function and proving the global attraction of the positive solution the results show that the weaker white noises can ensure the existence of a unique stationary distribution and the stronger white noises can result in the extinction of one or two species though the positive equilibrium is globally stable without white noises

a stochastic sis epidemic model with saturating contact rate abstract in this paper we formulate and investigate the dynamics of a sis epidemic model with saturating contact rate and its corresponding stochastic differential equation version for the deterministic epidemic model we show that the disease free equilibrium is global asymptotically stable if the basic reproduction number is less than unity and if the basic reproduction number is greater than unity model 1 2 admits a unique endemic equilibrium which is locally asymptotically stable by analyzing the corresponding characteristic equations for the stochastic epidemic model the existence and uniqueness of the positive solution are proved by employing the lyapunov analysis method the basic reproduction number r 0 s is proved to be a sharp threshold which determines whether there is an endemic outbreak or not if r 0 s 1 and under mild extra conditions the disease can be eradicated almost surely whereas if r 0 s 1 it has a stationary distribution which leads to the stochastic persistence of the disease finally numerical simulations are presented to illustrate our theoretical results

qualitative study of a stochastic sis epidemic model with vertical transmission abstract in this paper we study a stochastic sis epidemic model with vertical infection by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of a stationary probability measure of the model in addition we also establish sufficient conditions for extinction and persistence of the disease

a stochastic sirs epidemic model with infectious force under intervention strategies abstract in this paper we extend a classical sirs epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation sde one through introducing random fluctuations the value of our study lies in two aspects mathematically by using the markov semigroups theory we prove that the reproduction number r 0 s can be used to govern the stochastic dynamics of sde model if r 0 s 1 under mild extra conditions the sde system has a disease free absorbing set which means the extinction of disease with probability one if r 0 s 1 under mild extra conditions it has an endemic stationary distribution which leads to the stochastical persistence of the disease epidemiologically we find that random fluctuations can suppress disease outbreak which can provide us some useful control strategies to regulate disease dynamics

deformed fuzzy automata for correcting imperfect strings of fuzzy symbols presents a fuzzy method for the recognition of strings of fuzzy symbols containing substitution deletion and insertion errors as a preliminary step we propose a fuzzy automaton to calculate a similarity value between strings the adequate selection of fuzzy operations for computing the transitions of the fuzzy automaton allows us to obtain different string similarity definitions including the levenshtein distance a deformed fuzzy automaton based on this fuzzy automaton is then introduced in order to handle strings of fuzzy symbols the deformed fuzzy automaton enables the classification of such strings having an undetermined number of insertion deletion and substitution errors the selection of the parameters determining the deformed fuzzy automaton behavior would allow to implement recognizers adapted to different problems the paper also presents algorithms that implement the deformed fuzzy automaton experimental results show good performance in correcting these kinds of errors

stationary distribution of a stochastic siqr epidemic model with saturated incidence and degenerate diffusion abstract the objective of this paper is to study stationary distribution of a stochastic siqr epidemic model with saturated incidence and degenerate diffusion since the diffusion matrix is degenerate the uniform ellipticity condition is not satisfied the markov semigroup theory will be used to obtain the existence of a unique stable stationary distribution a threshold dynamic determined by the basic reproduction number r 0 s is established the disease can be eradicated almost surely if r 0 s 1 whereas if r 0 s 1 it has an endemic stationary distribution which leads to the stochastic persistence of the disease

the relationship between a continuous time renewal model and a discrete markov chain model of precipitation occurrence a relationship between a continuous wet dry renewal model with gamma distributed dry intervals and a markov chain model for daily rainfall is derived the relationship requires numerical evaluation for the general case but closed form solutions are available for the markov process case in which dry intervals are exponentially distributed the markov process equations are equivalent to those derived by j r green 1964 for first order transition probabilities but are presented in a simplified nonrecursive form the markov process relationships are examined for convergence and accuracy with simulation studies and comparison to observed rainfall records the markov process model is shown to provide a good representation in certain parts of the united states in other areas where the markov property is inappropriate due to event clustering or other phenomena the gamma model provides an improved characterization of the relationship between continuous and discrete rainfall occurrence

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