时滞Logistic方程周期解的存在性与渐近性

利用Ｍａｗｈｉｎ重合度与李雅普洛夫泛函讨论了一类时滞Ｌｏｇｉｓｔｉｃ方程周期解的存在性及解的渐近性．     

时滞周期Logistic方程的周期解的稳定性

该文应用周期解的线性化稳定性的Ｆｌｏｑｕｅｔ理论研究了一类含时滞的周期Ｌｏｇｉｓｔｉｃ方程的周期解的稳定性．     

Logistic模型参数估计及预测实例

本文提出了对Ｌｏｇｉｓｔｉｃ模型中的参数进行迭代估计的新算法，通过比较分析，说明了本文算法的有效性。     

具扰动项的时滞Logistic方程的周期解

本文首先讨论一类时滞微分方程的周期解的存在性，然后将本文结果应用到具扰动项的 时滞Ｌｏｇｉｓｔｉｃ方程得出其正周期解的存在性，本文结果推广和改进了「１」和「６」的相应结果。     

关于Logistic方程的几种推导方法

Ｌｏｇｉｓｔｉｃ方程ｄｐｄｔ＝ａｐ－ｂｐ２，ｐ（ｔ０）＝ｐ０（１）是种群动态研究中最基本、最重要的方程之一．此外，它也是数模教学中一个极有价值的教学案例．文［４］中，作者曾以Ｌｏｇｉｓｔｉｃ方程在几种不同领域中的应用为例，讨论了在建模实践中如何利用已...     

Logistic方程的紊动现象

对于单参数二维映射ｆ（ｘ，ｙ）＝（ｙ，μｙ（１－ｘ）），本文给出使ｆ存在Ｓｍａｌｅ马蹄的两个参数区间，从而对Ｌｏｇｉｓｔｉｃ方程的一些数值计算结果作出理论上的解释。     

相关系数在贝类生长研究中的应用

在贝类生长理论与应用研究中，经常要用到生长方程，以往很多采用ＶｏｎＢｅｒｔａｌａｎｆｆｙ方程来描述，近来越来越多采用了Ｌｏｇｉｓｔｉｃ方程，用什么去衡量，哪一种方程好。本文认为用相关系数Ｒ作为衡量数据与方程拟合度的数量指标是合适的，即对同一批数据，分别求出这两个方程，然后选择相关系数较大的方程，本文对贝类的几种数据进行了处理，说明本文所涉及的贝类，用Ｌｏｇｉｓｔｉｃ方程去拟合更好一些。     

Logistic模型中参数的估计

本文得到Ｌｏｇｉｓｔｉｃ模型中参数ａｉ、ｂｉ 的一种便于使用的估计公式,在样本容量较小及精度要求不高时用作试题参数的估计是合适的,也可作为联合极大似然估计中的初始值     

Lotka-Volterra型泛函微分方程零解的全局吸引性

本文研究 Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ型泛函微分方程零解的全局吸引性,在情况下,获得了３／２－全局吸引性结果,应用所获结果于单种群增长模型──平方Ｌｏｇｉｓｔｉｃ方程改进了已有文献中的相应结果．     

两类记录值之和的中心极限定理

该文给出了Ｌｏｇｉｓｔｉｃ分布纪录值序列部分和的中心极限定理；对于Ｐａｒｅｔｏ分布纪录值序列的部分和T_n，获得了ｌｎT_n的中心极限定理．这一工作不仅具有概率论的极限理论方面的研究价值，而且在金融、保险等领域也具有相当重要的应用前景．     

Symmetry-Breaking Bifurcation for Free Elastic Shell of Biological Cluster,Part 2.

We will be concerned with a two-dimensional mathematical model for a free elastic shell of biological cluster. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of the shell of biological cluster may be found as solutions of a certain nonlinear functional-differential equation with several physical parameters. For each multiparameter this equation has a radially symmetric solution. Our goal is to study the bifurcation which breaks symmetry. In order to establish critical values of bifurcation parameter and buckling modes we will investigate an appropriate linear problem. Our main result on the existence of symmetrybreaking bifurcation will be proved by the use of a variational version of the Crandall-Rabinowitz theorem.     

Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a seventh degree Lyapunov system

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of seventh degree system are investigated. With the help of computer algebra system MATHEMATICA, the first 12 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 12 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for seventh degree Lyapunov systems.     

能源价格系统在随机干扰作用下的分岔研究

采用Khasminskii极限定理,随机平均法和FPK方程,研究了能源价格系统在随机干扰作用下的Hopf分岔特性,得到了分岔参数,并讨论了分岔参数对系统性态的影响.进而得出能源经济系统的相关结论.     

Logistic阻滞增长模型的稳定性与混沌

将Logistic阻滞增长模型的差分形式简化，讨论了它的稳定性，用计算机进行迭代求解。模拟了这一简单差分方程从收敛，分叉，2^n倍周期收敛进入混沌现象的过程。直观地展示了序列{yk}收敛，2倍周期，4倍周期……直至混沌的现象，这对Logistic阻滞增长模型的应用和混沌现象的模拟有很好的参考价值。     

Asymptotic Behavior of the Density in a Parabolic SPDE

Consider the density of the solution X(t, x) of a stochastic heat equation with small noise at a fixed t[0, T], x[0, 1]. In this paper we study the asymptotics of this density as the noise vanishes. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients and the residue of the expansion are explicitly calculated. In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximating process and the limit one is proved. Also a suitable iterative local integration by parts formula is developed.     

Bifurcations of limit cycles in a quintic Lyapunov system with eleven parameters

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 12 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 12 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems, the result of Jiang et al. (2009) [18] was improved.     

Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay

In this paper, we investigated Hopf bifurcation by analyzing the distributed ranges of eigenvalues of characteristic linearized equation. Using communication delay as the bifurcation parameter, linear stability criteria dependent on communication delay have also been derived, and, furthermore, the direction of Hopf bifurcation as well as stability of periodic solution for the exponential RED algorithm with communication delay is studied. We find that the Hopf bifurcation occurs when the communication delay passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical simulation is presented to verify the theoretical results.     

Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a cubic Lyapunov system

In the present paper, for the three-order nilpotent critical point of a cubic Lyapunov system, the center problem and bifurcation of limit cycles are investigated. With the help of computer algebra system-MATHEMATICA, the first 7 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact of there exist 7 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for cubic Lyapunov systems.     

Existence of periodic travelling waves solutions in predator prey model with diffusion

This paper deals with the qualitative analysis of the travelling waves solutions of a reaction diffusion model that refers to the competition between the predator and prey with modified Leslie–Gower and Holling type II schemes. The well posedeness of the problem is proved. We establish sufficient conditions for the asymptotic stability of the unique nontrivial positive steady state of the model by analyzing roots of the forth degree exponential polynomial characteristic equation. We also prove the existence of a Hopf bifurcation which leads to periodic oscillating travelling waves by considering the diffusion coefficient as a parameter of bifurcation. Numerical simulations are given to illustrate the analytical study.     

Linear stability and Hopf bifurcation analysis for exponential RED algorithm with heterogeneous delays

In this paper, the exponential RED algorithm with heterogeneous delays is considered. Local stability of the equilibrium solution of this algorithm is investigated based on analyzing the corresponding transcendental characteristic equation. Some general stability criteria involving the delays and the system parameters are derived by using generalized Nyquist criteria. In particular, using one of the delays as the bifurcation parameter, when the delays exceed a critical value, the exponential RED system undergoes a supercritical Hopf bifurcation. The explicit formulas determining the stability and the direction of periodic solutions bifurcating from the equilibrium are obtained by applying Hassard et al’s approaches. Finally, some numerical simulations are performed to verify the theoretical results.