Existence of Equilibrium Solutions to a Size-Structured Predator-Prey System with Functional Response

In this paper, we consider a nonlinear size-structured population model with functional response, which describes the dynamics of a predator-prey system living in a common habitat. We present a kind of functional response for the prey being a plant or algae, and explain its biological meanings. When the vital rates depend both on the individual＇s size and on the total population or only depend on the former, we obtain the existence of equilibrium solutions.

Stability results for a nonlinear two-species competition model with size-structure

We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community,in which the mortality,fertility and growth are sizedependent.Existence and uniqueness of nonnegative solutions to the system are analyzed.The existence of the stationary size distributions is discussed,and the linear stability is investigated by means of the semigroup theory of operators and the characteristic equation technique.Some sufficient conditions for asymptotical stability/instability of steady states are obtained.The resulting conclusion extends some existing results involving age-independent and age-dependent population models.

The Chapman-Richards Distribution and its Relationship to the Generalized Beta

Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptions of the Chapman-Richards growth function, constant mortality and recruitment into the mathematical form of the distribution. Therefore, unlike 'assumed' distribution models, it is intrinsically linked with the underlying vital rates for the forest area under consideration. Methods: It is shown that the Chapman-Richards distribution can be recast as a subset of the generalized beta distribution of the first kind, a rich family of assumed probability distribution models with known properties. These known properties for the generalized beta are then immediately available for the Chapman-Richards distribution, such as the form of the compatible basal area-size distribution. A simple two-stage procedure is proposed for the estimation of the model parameters and simulation experiments are conducted to validate the procedure for four different possible distribution shapes. Results: The simulations explore the efficacy of the two-stage estimation procedure;these cover the estimation of the growth equation and mortality-recruitment derives from the equilibrium assumption. The parameter estimates are shown to depend on both the sample size and the amount of noise imparted to the synthetic measurements. The results vary somewhat by distribution shape, with the smaller, noisier samples providing less reliable estimates of the vital rates and final distribution forms. Conclusions: The Chapman-Richards distribution in its original form, or recast as a generalized beta form, presents a potentially useful model integrating vital rates and stand diameters into a flexible family of resultant distributions shapes. The data requirements are modest, and parameter estimation is straightforward provided the minimal recommended sample sizes are obtained.

炭黑补强丁苯橡胶的力学性能研究

丁苯橡胶不能结晶,所以它是非自补强的橡胶,未补强的纯胶强度低,难以制造出具有使用价值的橡胶制品。炭黑是橡胶工业上最重要的补强性填料,炭黑的性质对橡胶的加工性能和成品性能具有决定的影响。因此本实验选用了不同种类的炭黑,考察了炭黑的粒径及结构度对T2000R胶料的基本性能的影响。实验结果表明:随着炭黑粒径的增加,T2000R硫化胶的拉伸强度逐渐降低,撕裂强度降低。但是硫化胶的耐磨耗性能和定伸应力逐渐增大。

Stability and bifurcation analysis of a size-stage-structured cooperation model

In this paper,we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator.The primary feature of this model is to consider size structure,stage structure and obligate and facultative symbiosis at the same time in a cooperation system.We use the method of characteristic to show that this new model can be reduced to a threshold delay equations(TDEs)model,which can be further transformed into a functional differential equations(FDEs)model by a simple change of variables.Such simplification allows us to apply the classical theory of FDEs and establish a set of sufficient conditions to investigate the qualitative analysis of solutions of the FDEs model,including the global existence and uniqueness,positivity and boundedness.What's more,we use the geometric criteria to get the conclusions about stability and Hopf bifurcation of positive equilibrium because the coefficients of the characteristic equation depend on the bifurcation parameter.Finally,numerical simulations are carried out as supporting evidences of our analytical results.Our results show that the presence of size structure and stage structure plays an important role in the dynamic behavior of the model.

THE EQUILIBRIA OF THE SIZE STRUCTURED POPULATION MODEL

In this paper the existence and stability of the positive equilibrium of the size-structured population model are proved by Rabinowitz's theorem and the local linearization method.The result here shows that near the bifurcation point where a branch of positive equilibria appears,the stability of the positive equilibrium on the branch is dcpendent on the direction of the bifurcation.The argument for the model of age-structured population is generalized in this paper.