Analysis of a mutualism model with time-related coefficients in a stochastic environment

In this paper,a mutualism model with stochastic perturbations is considered and some of its coefficients are related to time.Under some assumptions,we make efforts to prove the existence and uniqueness of a positive solution,and the asymptotic behavior to the problem is discussed.Furthermore,we also prove the properties of stochtistic boundedness,uniform continuity and stochastic permanence of this system.At last,some numerical simulations are introduced to illustrate our main results.

GLOBAL ASYMPTOTICAL STABILITY OF AN OBLIGATE LOTKA-VOLTERRA MUTUALISM MODEL

By constructing a suitable Lyapunov function,sufficient conditions which ensure the global asymptotical stability of the positive equilibrium and boundary equilibrium of an obligate Lotka-Volterra mutualism model are obtained,respectively.It is shown that the conditions which ensure the local stability of the nonnegative equilibria is enough to ensure their global asymptotical stability.Our result supplements and complements some known result.

Analysis of a mutualism model with stochastic perturbations

This paper is concerned with a mutualism ecological model with stochastic perturba- tions. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied. Moreover, we show that the solution is stochastically bounded, uniformly continuous and stochastic perma- nence. The sufficient conditions for the system to be extinct are given and the conditionsfor the system to be persistent are also established. At last, some figures are presented to illustrate our main results.

Permanence and extinction of stochastic regime-switching mutualism model

This paper is concerned with the permanence and extinction of a stochastic regime-switching mutualism model.We aim to find the difference between the stochastic mutualism model with regime-switching and without regimc-switching.By studying ergodicity of regime-switching diffusion processes,we establish the sufficient conditions to estimate the permanence and extinction of a species in a random switching environment.Moreover,compared with the systerm without switching,the advantages of the stochastic regime-switching mutualism model are given.

New approach to calculating tree height at the regional scale

Background:Determining the spatial distribution of tree heights at the regional area scale is significant when performing forest above-ground biomass estimates in forest resource management research.The geometric-optical mutual shadowing(GOMS)model can be used to invert the forest canopy structural parameters at the regional scale.However,this method can obtain only the ratios among the horizontal canopy diameter(CD),tree height,clear height,and vertical CD.In this paper,we used a semi-variance model to calculate the CD using high spatial resolution images and expanded this method to the regional scale.We then combined the CD results with the forest canopy structural parameter inversion results from the GOMS model to calculate tree heights at the regional scale.Results:The semi-variance model can be used to calculate the CD at the regional scale that closely matches(mainly with in a range from-1 to 1 m)the CD derived from the canopy height model(CHM)data.The difference between tree heights calculated by the GOMS model and the tree heights derived from the CHM data was small,with a root mean square error(RMSE)of 1.96 for a 500-m area with high fractional vegetation cover(FVC)(i.e.,forest area coverage index values greater than 0.8).Both the inaccuracy of the tree height derived from the CHM data and the unmatched spatial resolution of different datasets will influence the accuracy of the inverted tree height.And the error caused by the unmatched spatial resolution is small in dense forest.Conclusions:The semi-variance model can be used to calculate the CD at the regional scale,together with the canopy structure parameters inverted by the GOMS model,the mean tree height at the regional scale can be obtained.Our study provides a new approach for calculating tree height and provides further directions for the application of the GOMS model.

Survival analysis of an impulsive stochastic facultative mutualism system with saturation effect

A system of impulsive stochastic differential equations is proposed as a two-species facultative mutualism model subject to impulsive and two coupling noise source perturbations,in which the saturation effect is taken into account.A set of sufficient criteria for extinction(exponential extinction and extinction)and permanence(permanence in time average and stochastic permanence)of the system are established.Extensive simulation figures are demonstrated to support the theoretical findings.Meanwhile,we look at the effects of coupling white noises,impulses,intrinsic growth rates,intra-specific competition rates and inter-specific mutualism rates on the survival of populations.

EXISTENCE OF POSITIVE PERIODIC SOLUTION OF A DISCRETE TIME MUTUALISM SYSTEM WITH DELAYS

Discrete-time analogue of mutualism model is introduced. The discrete-time analogues is considered to be numerical discretization of the continuous-time models and we study their dynamical characteristics. It is shown that the discrete-time analogues preserve the periodicity of the continuous-time models.

EXISTENCE OF POSITIVE PERIODIC SOLUTION OF MUTUALISM SYSTEM WITH INFINITE DELAYS

In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solution of a mutualism system with infinite delays. Our results generalize those of Yang etc. [8] and Gopalsamy and He [7].

Learning from context： a mutual reinforcement model for Chinese microblog opinion retrieval

This study addresses the problem of Chinese microblog opinion retrieval, which aims to retrieve opinionated Chinese microblog posts relevant to a target specified by a user query. Existing studies have shown that lexicon-based approaches employed online public sentiment resources to rank sentiment words relying on the document features. However, this approach could not be effectively applied to mi- croblogs that have typical user-generated content with valu- able contextual information： ＂user-user＂ interpersonal interactions and ＂user-post/comment＂ intrapersonal interactions. This contextual information is very helpful in estimating the strength of sentiment words more accurately. In this study, we integrate the social contextual relationships among users, posts/comments, and sentiment words into a mutual reinforcement model and propose a unified three-layer heterogeneous graph, on which a random walk sentiment word weighting algorithm is presented to measure the strength of opinion of the sentiment words. Furthermore, the weights of sentiment words are incorporated into a lexicon-based model for Chinese microblog opinion retrieval. Comparative experiments are conducted on a Chinese microblog corpus, and the results show that our proposed mutual reinforcement model achieves significant improvement over previous methods.

A natural communication system on genome evolution

The central dogma of molecular biology describes the flow of genetic information from DNA via RNA to protein and duplication from ancestral to descendent DNA（Crick,1958）.However,the genetic information could not be quantified and mathematically modeled.So it differs from the“information”formulated by Shannon and used in information and coding theories（Shannon,1949）.