global dynamics for a new high dimensional sir model with distributed delay abstract in this paper a new high dimensional sir epidemic model with double epidemic hypothesis and delays is proposed which is a high dimensional system of impulsive functional differential equations with time delays the linear chain trick technique is employed to prove the upper boundedness of solutions of the impulsive delay differential equations and scaling method techniques for inequalities and classification method are used to study the permanence of the high dimensional system we also prove that the infection free periodic solution of the system is globally attractive when r 1 1 and the system is permanent under r 2 1 moreover numerical simulation for impulsive and delayed system is presented to illustrate our main conclusions which shows that time delays and pulse vaccination have significant effects on the dynamics behaviors of the model the feature of the present paper is that the double epidemic hypothesis have different forms of delays to more realistically describe the spread of epidemic though which makes the high dimensional system more complex

intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators a theory of intrinsic fluctuations is developed of a phase ordering parameter for large populations of weakly and uniformly coupled limit cycle oscillators with distributed native frequencies in particular it is shown that the intensity as well as the correlation time of fluctuations exhibit power law divergence at the onset of mutual entrainment with critical exponents which depend on whether the coupling strength approaches the threshold from below or above this peculiar feature is demonstrated by numerical simulations mainly through finite size scaling analyses in the course of exploring its origin we encounter a new concept termed a correlation frequency which provides a natural interpretation of the finite size scaling laws a comment is given on a recent theory by kuramoto and nishikawa to clarify why it contradicts our results

oscillator death in populations of all to all coupled nonlinear oscillators abstract the behavior of finitely many and infinitely many coupled weakly nonlinear oscillators is studied and it is shown that the uniform rest state can become stable if the coupling is sufficiently strong and the frequencies are sufficiently disparate numerical results show that the phenomenon is robust and occurs when many of the hypotheses are relaxed

stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and levy jumps abstract in this paper a hybrid stochastic prey predator system with double time delays and commercial exploitation is established where combined dynamic effects of telephone noise and levy jumps on stochastic population dynamics are taken into accounts existence and uniqueness of globally positive solution to the proposed system are investigated by constructing appropriate stochastic lyapunov functions existence of an ergodic and unique stationary distribution of the positive solution is discussed sufficient conditions for permanence in mean and extinction of corresponding population are derived furthermore sufficient and necessary criteria for optimal exploitation strategy are studied numerical simulations are carried out to show consistency with theoretical analysis

a physicist s sandbox we discuss some recent results suggesting that certain spatially extended dynamical systems naturally evolve toward a state characterized by domains of all length scales the analogy with second order phase transitions has prompted the name self organized criticality specific results are available for cellular automaton models which can be thought of as caricatures of a sandpile undergoing avalances the potential generality of the results stems from the very simple nonlinear diffusion dynamics governing the system

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

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

threshold behavior of a stochastic lotka volterra food chain chemostat model with jumps abstract taking levy jumps into account a lotka volterra food chain chemostat model in random environment is proposed and investigated we first prove the existence and uniqueness of the global positive solution then conditions for extinction of the microorganisms are derived in two cases furthermore we establish sufficient conditions for persistence in the mean of the system theoretical analysis indicates that the dynamics of the considered model are determined by two threshold parameters r 0 s and r 1 s and both white noise and levy noise are disadvantageous to the system finally numerical simulations are given to illustrate the results

lower critical dimension for populations of oscillators with randomly distributed frequencies a renormalization group analysis it is argued by way of a renormalization group analysis that the lower critical dimension of macroscopic mutual entrainment in a class of populations of oscillators satisfies a certain inequality which is sensitive to the tail of the distribution of native frequencies this result is supported in part by numerical simulations as well as a proof of the absence of long range order in one dimension

stability analysis of a fractional order diffused prey predator model with prey refuges abstract in this paper a fractional order diffused prey predator model with prey refuges is considered the existence uniqueness non negativity and boundedness of the solutions for the model are proved moreover some sufficient conditions are given to ensure the existence and uniform asymptotic stability of the equilibrium point of the studied system finally numerical simulations are presented in order to support the theoretical results

phase locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies abstract we study phase locking in a network of coupled nonlinear oscillators with local interactions and random intrinsic frequencies the oscillators are located at the vertices of a graph and interact along the edges they are coupled by sinusoidal functions of the phase differences across the edges and their intrinsic frequencies are independent and identically distributed with finite mean and variance we derive an exact expression for the probability of phase locking in a linear chain of such oscillators and prove that this probability tends to zero as the number of oscillators grows without bound however if the coupling strength increases as the square root of the number of oscillators the probability of phase locking tends to a limiting distribution the kolmogorov smirnov distribution this latter result is obtained by showing that the phase locking problem is equivalent to a discretization of pinned brownian motion the results on chains of oscillators are extended to more general graphs in particular for a hypercubic lattice of any dimension the probability of phase locking tends to zero exponentially fast as the number of oscillators grows without bound we also consider a less stringent type of synchronization characterized by large clusters of oscillators mutually entrained at the same average frequency it is shown that if such clusters exist they necessarily have a sponge like geometry

constructing free energy approximations and generalized belief propagation algorithms important inference problems in statistical physics computer vision error correcting coding theory and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs the belief propagation bp algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree but only approximate when the factor graph has cycles we show that bp fixed points correspond to the stationary points of the bethe approximation of the free energy for a factor graph we explain how to obtain region based free energy approximations that improve the bethe approximation and corresponding generalized belief propagation gbp algorithms we emphasize the conditions a free energy approximation must satisfy in order to be a valid or maxent normal approximation we describe the relationship between four different methods that can be used to generate valid approximations the bethe method the junction graph method the cluster variation method and the region graph method finally we explain how to tell whether a region based approximation and its corresponding gbp algorithm is likely to be accurate and describe empirical results showing that gbp can significantly outperform bp

periodic solution of a prey predator model with nonlinear state feedback control assume that when the number of pests reaches the certain threshold pest management strategy will be taken to control pests based on this assumption in this paper we propose a pest management model with nonlinear state feedback control we then analyze the dynamic behavior of the model more precisely we first investigate the singularity of the model by using method of qualitative analysis secondly the existence of periodic solution of the model is studied by using successor functions and poincare bendixson theorem and then it is followed by the study of the stability of periodic solution finally an example with numerical simulations is given to illustrate our conclusions

the dynamics of a stochastic vaccinated tuberculosis model with treatment abstract in this paper we study a stochastic model with vaccination and treatment to describe the transmission dynamics of tuberculosis firstly by using the stochastic lyapunov analysis method we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model then we obtain sufficient conditions for extinction of the diseases our work greatly improves the results of feng and qiu 2018 finally some examples and numerical simulations are introduced to illustrate our theoretical results

dynamics of a large system of coupled nonlinear oscillators abstract we consider the interaction of a large number of limit cycle oscillators with linear all to all coupling and a distribution of natural frequencies the system exhibits extremely rich dynamics as the coupling strength and the width of the frequency distribution are varied we find a variety of steady behaviors that can be described by a stationary distribution in phase space frequency locking amplitude death incoherence and partial locking an unexpected result is that the system can also exhibit unsteady behavior in which the phase space distribution evolves periodically quasiperiodically or even chaotically the simple form of the model allows us to derive several analytical results the stability boundaries of amplitude death and incoherence are found explicitly rigorous results on the existence and stability of frequency locking are also obtained

amplitude death in complex networks induced by environment we present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment like external system we develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death an important outcome of our study is a universal relation between the critical coupling strength and the largest nonzero eigenvalue of the coupling matrix our results are fully supported by the detailed numerical analysis for different network topologies

stationary distribution of a stochastic staged progression hiv model with imperfect vaccination abstract in this paper we study a stochastic staged progression hiv model with imperfect vaccination we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by using the stochastic lyapunov analysis method

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

analysis of a stochastic autonomous mutualism model abstract an autonomous lotka volterra mutualism system with random perturbations is investigated under some simple conditions it is shown that there is a decreasing sequence k which has the property that if 1 1 then all the populations go to extinction i e lim t x i t 0 1 i n if k 1 k 1 then lim t x j t 0 j k 1 n whilst the remaining k populations are stable in the mean i e lim t t 1 0 t x i s d s a positive constant i 1 k if n 1 then all the species are stable in the mean sufficient conditions for stochastic permanence and global asymptotic stability are also established

a fast learning algorithm for deep belief nets we show how to use complementary priors to eliminate the explaining away effects that make inference difficult in densely connected belief nets that have many hidden layers using complementary priors we derive a fast greedy algorithm that can learn deep directed belief networks one layer at a time provided the top two layers form an undirected associative memory the fast greedy algorithm is used to initialize a slower learning procedure that fine tunes the weights using a contrastive version of the wake sleep algorithm after fine tuning a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels this generative model gives better digit classification than the best discriminative learning algorithms the low dimensional manifolds on which the digits lie are modeled by long ravines in the free energy landscape of the top level associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind

reduced complexity iterative decoding of low density parity check codes based on belief propagation two simplified versions of the belief propagation algorithm for fast iterative decoding of low density parity check codes on the additive white gaussian noise channel are proposed both versions are implemented with real additions only which greatly simplifies the decoding complexity of belief propagation in which products of probabilities have to be computed also these two algorithms do not require any knowledge about the channel characteristics both algorithms yield a good performance complexity trade off and can be efficiently implemented in software as well as in hardware with possibly quantized received values

stability of incoherence in a population of coupled oscillators we analyze a mean field model of coupled oscillators with randomly distributed frequencies this system is known to exhibit a transition to collective oscillations for small coupling the system is incoherent with all the oscillators running at their natural frequencies but when the coupling exceeds a certain threshold the system spontaneously synchronizes we obtain the first rigorous stability results for this model by linearizing the fokker planck equation about the incoherent state an unexpected result is that the system has pathological stability properties the incoherent state is unstable above threshold butneutrally stable below threshold we also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise

asymptotic behavior of stochastic multi group epidemic models with distributed delays abstract in this paper we introduce stochasticity into multi group epidemic models with distributed delays and general kernel functions the stochasticity in the model is a standard technique in stochastic population modeling when the perturbations are small by using the method of stochastic lyapunov functions we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number r 0 if r 0 1 the solution of the stochastic system oscillates around the disease free equilibrium e 0 while if r 0 1 the solution of the stochastic model fluctuates around the endemic equilibrium e moreover we also establish sufficient conditions of these results

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

transitions to amplitude death in a regular array of nonlinear oscillators we investigate amplitude death in a regular array of nonlinear oscillators we find that the system undergoes three transitions during the road to complete amplitude death the first two are related to partial amplitude death one induces partial amplitude death and the other enhances it the last transition establishes complete amplitude death we also find that the first two belong to a second order transition and are universal while the last one is strongly dependent on the system parameters

from collective oscillations to collective chaos in a globally coupled oscillator system abstract various types of collective behaviors are discovered in globally coupled ginzburg landau oscillators when the coupling is sufficiently weak the oscillators are either in complete synchrony or their phases are scattered completely randomly for finite coupling new collective behaviors emerge such as splitting of the population into a small number of clusters or their fusion into a continuous stringlike distribution in the phase plane low dimensional chaotic dynamics arises from the coupled motion of 3 point clusters chaotic motion is also exhibited by fused clusters which is of extremely high dimension possibly proportional to the system size as is implied from its lyapunov analysis in the latter type of chaos the motion of the string is in some cases characterized by repeated stretching and foldings it is argued how this kind of coherent behavior seen on a collective level does not contradict the high dimensionality of the corresponding chaotic attractor

a stochastic sirs epidemic model with logistic growth and general nonlinear incidence rate abstract in this paper we consider a stochastic sirs epidemic model with logistic growth and general nonlinear incidence rate we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic lyapunov function which provides us a good description of persistence we find that the hypothetical conditions on the nonlinear function are relative weak and valid for many forms of incidence rate

amplitude death through a hopf bifurcation in coupled electrochemical oscillators experiments and simulations amplitude death was observed in experiments with two coupled periodic electrochemical oscillators without time delay simulation results confirmed that the observed amplitude death was obtained via a hopf bifurcation the two oscillators must have a minimum discrepancy and both be near their individual hopf bifurcations for amplitude death to occur phase drift coexisting with unstable asymmetric phase locked solutions amplitude death and in phase synchronization were observed in both the experiments and simulations as coupling strength was increased in addition the simulations showed that a stable asymmetric phase locked solution exists between the phase drift and amplitude death regions

rational solutions and lump solutions to the generalized 3 1 dimensional shallow water like equation abstract through symbolic computation with maple the rational solutions and the lump solutions of the generalized 3 1 dimensional shallow water like equation are presented by using the generalized bilinear operator when the parameter p 3 it is pointed that these rational solutions are classified into five classes because they are obtained mainly by depending on the polynomial solutions the resulting lump solutions which are rationally localized in all directions in the space are acquired by making use of the quadratic function however not every nonlinear partial differential equation has the lump solutions if any the quantity of the lump solutions is fewer than the rational solutions only one class of lump solutions of the generalized 3 1 dimensional shallow water like equation is gotten and three 3d plots with specific values of the involved parameters are plotted

a ratio dependent predator prey model with disease in the prey in this paper a ratio dependent predator prey system with disease in the prey is formulated and analyzed mathematical analyses of the model equations with regard to invariance of nonnegativity boundedness of solutions nature of equilibria permanence and global stability are analyzed specially we shall show that ratio dependent predator prey models are rich in boundary dynamics and most importantly we shall show that a periodic solution can occur whether the system is permanent or not that is there are solutions which tend to disease free equilibrium while bifurcating periodic solution exists

amplitude response of coupled oscillators abstract we investigate the interaction of a pair of weakly nonlinear oscillators eg each near a hopf bifurcation when the coupling strength is comparable to the attraction of the limit cycles changes in amplitude cannot then be ignored and there are new phenomena we show that even for simple forms of these equations there are parameter regimes in which the interaction causes the system to stop oscillating and the rest state at zero stabilized by the interaction is the only stable solution when the uncoupled oscillators have a local frequency that is independent of amplitude zero shear and the coupling is scalar we give a complete description of the behavior we then analyze more complicated equations to show the effects of amplitude dependent frequency in the uncoupled equations nonzero shear and nonscalar coupling for example when there is shear there can be bistability between a phase locked solution and an unlocked drift solution in which the oscillators go at different average frequencies there can also be bistability between a phase locked solution and an equilibrium nonoscillatory solution the equations for the zero shear case have a pair of degenerate bifurcation points and the new phenomena in the nonzero shear case arise from a partial unfolding of these singularities when the coupling is nonscalar there are a variety of new behaviors including bistability of an in phase and an anti phase solution for two identical oscillators parameters for which only the anti phase solution is stable and phase trapping i e nonlocked solutions in which the oscillators still have the same average frequency it is shown that whether the coupling is diffusive or direct has many effects on the behavior of the system

a new predator prey model with a profitless delay of digestion and impulsive perturbation on the prey abstract in this paper we formulate a robust prey dependent consumption predator prey model with a delay of digestion and impulsive perturbation on the prey using the discrete dynamical system determined by the stroboscopic map we obtain a predator eradication periodic solution and show that the predator eradication periodic solution is globally attractive when harvesting for the prey is over certain value using a new qualitative analysis method for impulsive and delay differential equations we prove the system is uniformly persistent when harvesting for the prey is under certain value further we show the delay of digestion is a profitless time delay moreover we show our theoretical results by numerical simulation in this paper the main feature is that we introduce a delay of digestion and impulsive effects into the predator prey model and exhibit a new mathematical method which is applied to investigate the system which is governed by both impulsive and delay differential equations

amplitude death in an array of limit cycle oscillators we analyze a large system of limit cycle oscillators with mean field coupling and randomly distributed natural frequencies we prove that when the coupling is sufficiently strong and the distribution of frequencies has sufficiently large variance the system undergoes amplitude death the oscillators pull each other off their limit cycles and into the origin which in this case is astable equilibrium point for the coupled system we determine the region in couplingvariance space for which amplitude death is stable and present the first proof that the infinite system provides an accurate picture of amplitude death in the large but finite system

analytical study of coupled two state stochastic resonators the two state model of stochastic resonance is extended to a chain of coupled two state elements governed by the dynamics of glauber s stochastic ising model appropriate assumptions on the model parameters turn the chain into a prototype system of coupled stochastic resonators in a weak signal limit analytical expressions are derived for the spectral power amplification and the signal to noise ratio of a two state element embedded into the chain the effect of the coupling between the elements on both quantities is analysed and array enhanced stochastic resonance is established for pure as well as noisy periodic signals the coupling induced improvement of the snr compared to an uncoupled element is shown to be limited by a factor four which is only reached for vanishing input noise

analysis of a stochastic hiv 1 infection model with degenerate diffusion abstract this paper studies a stochastic hiv 1 infection model with degenerate diffusion the asymptotic dynamics of the stochastic model are shown to be governed by a threshold parameter when the parameter is negative the infection is predicted to go extinct exponentially while the level of healthy cells converges weakly to a unique invariant measure when the threshold parameter is positive the solution of the stochastic model converges polynomially to a unique invariant probability measure indicating that the system admits a unique ergodic stationary distribution numerical simulations are conducted to show the analytical results these results highlight the role of environmental noise in the spread of hiv 1 the method can also be applied to the non degenerate systems

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

a predator prey model with disease in the prey after the seminal models of vito volterra and alfred james lotka in the mid 1920s for predator prey interactions mutualist and competitive mechanisms have been studied extensively in the recent years by researchers there are so many references in this context we have just cited here some books e g see 14 16 18 and the refer ences therein similarly after the pioneering work of kermack mckendrick on sirs susceptible infective removal susceptible epidemiological models have also received much attention from scientists relevant references in this context are also vast and we shall again mention here some books see 1 2 4 to mention a few but little attention has been paid so far to merge these two important areas of research see 7 21 in this paper we shall put emphasis in such an eco epidemiological system we consider a three species eco epidemiological system namely sound prey suscep tible infected prey infective and predator we consider the case when the predator mainly eats the infected prey this is in accordance with a previous model by hadeler and freedman 7 which describes a predator prey model where the prey is infected by a parasite and the prey in turn infects the predator with that parasite the infec tion weakens the prey and increases its susceptibility to predation while no predator impairing elect is accounted for while the paper is mainly theoretical and does not address any specific situation the reader may and several examples in 7 we derive persistence and extinction conditions of the populations and we also determine conditions for which the system enters a hopf type bifurcation moreover we observe that the bifurcated branches are supercritical in some parametric region space in a special case when the predator response function is a holling type ii function

disorder can eliminate oscillator death we use an array of diffusively coupled limit cycle oscillators with a regular monotonic trend of natural frequencies to demonstrate that the disorder introduced in the form of random deviations from a linear trend of frequencies can weaken considerably desynchronization induced oscillator death and as a result increase oscillation intensity substantially there exist definite optimal levels of magnitude of spatial disorder at which maximal oscillatory energy is attained in the array

dynamics of a novel nonlinear stochastic sis epidemic model with double epidemic hypothesis abstract in this paper we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis then we dedicate to develop a method to obtain the threshold of the stochastic sis epidemic model to this end first we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases second we explore and obtain the threshold of a stochastic sis system for the extinction and the permanence in mean of two epidemic diseases the results show that a large stochastic disturbance can cause infectious diseases to go to extinction in other words the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance this implies that the stochastic disturbance is conducive to epidemic diseases control to illustrate the performance of the theoretical results we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients

asymptotic behavior of a three species eco epidemiological model perturbed by white noise abstract this paper considers a three species eco epidemiological model perturbed by white noise stochastic stability and long time behavior around the equilibrium of deterministic eco epidemiological model are analyzed by lyapunov methods numerical simulations for a set of parameter values are presented to illustrate the analytical findings

asymptotic behavior of a stochastic delayed seir epidemic model with nonlinear incidence abstract this paper is concerned with a stochastic delayed seir epidemic model with nonlinear incidence firstly we verify that there exists a unique global positive solution of the system then by constructing some suitable lyapunov functions we study the asymptotic behaviors of the disease free equilibrium and the endemic equilibrium respectively

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

the stationary distribution and ergodicity of a stochastic phytoplankton zooplankton model with toxin producing phytoplankton under regime switching abstract this paper addresses a stochastic phytoplankton zooplankton model with toxin producing phytoplankton under regime switching the stochastic model in this paper includes white and colored noises for the model we first prove the existence of the global positive solution of the model and then by using khasminskii s method and lyapunov function we derive sufficient conditions for the existence of a unique ergodic stationary distribution finally numerical simulations are carried out to support our results

optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching abstract in this paper we stochastically perturb the harvesting mutualism system into stochastic system in a polluted environment by white noise telegraph noise and levy jump we first prove the existence and uniqueness of the global positive solution of the stochastic system and establish the sufficient condition for persistence in mean of the two cooperative species then using aggregation and ergodic methods the explicit forms of optimal harvesting strategy and the maximum of sustainable yield are obtained we also give some examples and numerical simulations to illustrate the theoretical results the impacts of toxicant in organism telegraph noise and levy jump on the persistence in mean and optimal harvesting strategy are revealed

a delayed vaccinated epidemic model with nonlinear incidence rate and levy jumps abstract a stochastic susceptible infectious recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity vaccination and le vy jumps on the transmission of diseases we first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable lyapunov functions based on the analysis we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system

theory of self synchronization in the presence of native frequency distribution and external noises abstract a general scheme is presented for the theoretical treatment of self synchronization of many body oscillators with variable amplitudes close to harmonic ones with small nonlinearity and dissipative interactions in the presence of external noises and a native frequency distribution applications of the theory are given to interacting van der pol oscillators with various frequency distributions the critical condition which leads to a nonvanishing order parameter is studied in detail it turns out that the synchronization is described in terms of two kinds of bifurcation mechanism mechanical and thermal ones new strong slaving emerges in the case of the mechanical bifurcation multifarious dependences of the order parameter on the width of native frequency distribution appears in some cases because of the presence of these two bifurcation mechanisms however only one bifurcation of landau type is observable since hybridization occurs when the two mechanisms coexist

mean field behavior for long and finite range ising model percolation and self avoiding walk we consider self avoiding walk percolation and the ising model with long and flnite range by means of the lace expansion we prove mean fleld behavior for these models if d 2 fi 2 for self avoiding walk and the ising model and d 3 fi 2 for percolation where d denotes the dimension and fi the power law decay exponent of the coupling function we provide a simplifled analysis of the lace expansion based on the trigonometric approach in borgs et al 13

applicability of n vicinity method for calculation of free energy of ising model abstract here we apply the n vicinity method of approximate calculation of the partition function to an ising model with the nearest neighbor interaction on d dimensional hypercube lattice we solve the equation of state for an arbitrary dimension d and analyze the behavior of the free energy as expected for large dimensions d 3 the system demonstrates a phase transition of the second kind in this case we obtain a simple analytical expression for the critical value of the inverse temperature when 3 d 7 this expression is in a very good agreement with the results of computer simulations in the case of small dimensions d 1 2 there is a noticeable discrepancy with the known exact results

lace expansion for the ising model the lace expansion has been a powerful tool for investigating mean field behavior for various stochastic geometrical models such as self avoiding walk and percolation above their respective upper critical dimension in this paper we prove the lace expansion for the ising model that is valid for any spin spin coupling for the ferromagnetic case we also prove that the expansion coefficients obey certain diagrammatic bounds that are similar to the diagrammatic bounds on the lace expansion coefficients for self avoiding walk as a result we obtain gaussian asymptotics of the critical two point function for the nearest neighbor model with d gg 4 and for the spread out model with d 4 and l gg 1 without assuming reflection positivity

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

analytical expressions for energies degeneracies and critical temperatures of the 2d square and 3d cubic ising models abstract this paper revisits the fundamental statistical properties of the crucial model in critical phenomena i e the ising model guided by our knowledge of the energy values of the ising hamiltonian and aided by numerical estimation techniques we have obtained exact energies in 2d and 3d and nearly exact analytical forms for the degeneracies of the distinct eigenvalues the formulae we obtained both for energies and degeneracies have an exceedingly simple analytical form and are easy to use the resultant partition functions were utilised to determine the critical behaviour of the ising system on cubic lattices in 2d and 3d we obtained a logarithmic divergence of the specific heat in the 2d case and the critical temperature estimates provided additional confirmation of the correctness of our approach

asymptotic properties of hybrid diffusion systems in response to the increasing needs for control and optimization of hybrid systems this work is concerned with such asymptotic properties as recurrence also known as weak stochastic stability in the literature and ergodicity of regime switching diffusions using liapunov functions necessary and sufficient conditions for positive recurrence are developed then ergodicity of positive recurrent regime switching diffusions is obtained by constructing cycles using the associated discrete time markov chains

dynamical behavior of a stochastic multigroup sir epidemic model abstract in this paper we study a multigroup sir epidemic model in a stochastic environment by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model then we establish sufficient conditions for extinction of the diseases the results reveal that the smaller white noise can ensure the persistence of the diseases while the larger white noise can lead to the extinction of the diseases finally some examples and numerical simulations are provided to illustrate the theoretical results

dynamical behaviors of a stochastic malaria model a case study for yunnan china abstract in this paper we investigate dynamical behaviors for a stochastic malaria model by introducing the effect of environmental white noise on transmission dynamics of malaria firstly the distance between stochastic solutions and the disease free equilibrium of the corresponding deterministic model is estimated in the time mean sense by constructing stochastic lyapunov functions particularly by the comparison theorem of stochastic differential equations and the law of large numbers sufficient conditions for the extinction of the disease are obtained in the special case next the existence of the unique ergodic stationary distribution is proved by constructing a suitable lyapunov function finally the model is used to simulate the human malaria data in yunnan province and predict the trend of malaria in yunnan

global analysis and numerical simulations of a novel stochastic eco epidemiological model with time delay abstract in this paper a new stochastic eco epidemiological model is proposed and investigated and the high dimensional model includes time delay and a general incidence rate which make the study more complex first the existence and uniqueness of the global positive solution with any positive initial value are verified second using stochastic analysis methods and some differential inequality techniques we explore the long time asymptotic properties of the stochastic delayed system furthermore we prove that the solution of the stochastic delayed system has a unique stationary distribution and it has ergodic property third the sufficient conditions of permanence in mean or extinction for the ecological populations are obtained finally we introduce a series of computer simulations to show the performance of the theoretical results

collective synchronisation in lattices of nonlinear oscillators with randomness the authors study mutual synchronisation in a model of interacting limit cycle oscillators with random intrinsic frequencies it is shown rigorously that the model exhibits no long range order in one dimension and that in higher dimensional lattices large clusters of synchronised oscillators necessarily have a sponge like structure surprisingly the phase locking behaviour of the mean field model is completely different from that of any finite dimensional lattice indicating that d infinity is the upper critical dimension for phase locking

a new class of upper bounds on the log partition function we introduce a new class of upper bounds on the log partition function of a markov random field mrf this quantity plays an important role in various contexts including approximating marginal distributions parameter estimation combinatorial enumeration statistical decision theory and large deviations bounds our derivation is based on concepts from convex duality and information geometry in particular it exploits mixtures of distributions in the exponential domain and the legendre mapping between exponential and mean parameters in the special case of convex combinations of tree structured distributions we obtain a family of variational problems similar to the bethe variational problem but distinguished by the following desirable properties i they are convex and have a unique global optimum and ii the optimum gives an upper bound on the log partition function this optimum is defined by stationary conditions very similar to those defining fixed points of the sum product algorithm or more generally any local optimum of the bethe variational problem as with sum product fixed points the elements of the optimizing argument can be used as approximations to the marginals of the original model the analysis extends naturally to convex combinations of hypertree structured distributions thereby establishing links to kikuchi approximations and variants