对称耦合振子中同相解的稳定性

本文研究了一类耦合系统中同相解的稳定性,并给出了耦合Oregon振子中同相解 稳定性的充分条件.     

双水槽耦合孤波观察及其理论分析 *

最新实验发现,当两水槽底部连通构成耦合双槽时,这个耦合系统就支持一对同相或反相的耦合孤波.描述了这种耦合孤波对的动力学特性,包括处于不同槽中孤波间的相互作用.给出了支配这一过程的孤波耦合方程组,并由此给出了初步的理论解释,即几种稳态耦合孤波解.     

耦合Hodgkin-Huxley方程中同相解的稳定性

本文证明了耦合Ｈｏｄｇｋｉｎ－Ｈｕｘｌｅｙ方程中同相解的稳定性．     

二阶微分方程组的耦合积分边值问题

研究了二阶微分方程组的耦合积分边值问题.在一对上-下解和下-上解的条件下,利用一个新的比较原则和Fredholm定理给出了其极解的存在性.     

Banach空间非线性二阶微分积分方程初值问题的单调迭代方法

利用单调迭代方法及Mnch不动点定理,研究了Banach空间中混合单调二阶微分积分方程初值问题的耦合最小最大拟解及解的存在性,给出了耦合最小最大拟解及解的存在定理.     

一类广义非线性Schr(o)dinger扰动方程的泛函渐近解法

研究了一类非线性Schr(o)dinger扰动耦合系统.利用近似解相关联的特殊方法,首先讨论了对应的线性系统,并得到了其精确解.再利用泛函迭代的方法得到了非线性Schr(o)dinger扰动耦合系统的泛函渐近解析解.这个渐近解是一个解析式,还可对它进行解析运算.这对使用简单的模拟方法得到的近似解是达不到的.     

耦合Kaup-Kupershmidt方程显式行波解

主要利用tanh函数方法,对耦合Kaup-Kupershmidt方程进行了讨论,通过行波约化及Riccati方程,将两个五阶的非线性演化方程转化为两个包含若干参变量的代数系统,借助于Mathematica软件符号运算功能,最终得到了上述耦合方程的显式行波解,包括类孤子解,三角函数周期解以及有理解.     

含临界指数与Hardy项耦合椭圆系统的非平凡解

研究了一类含临界指数耦合非线性项的奇异椭圆方程组,通过对临界耦合非线性项的分析与精确的能量估计,利用环绕定理,得到了这类方程组非平凡解的存在性.     

Banach空间非线性发展方程的耦合周期解

本文利用上下解方法与正算子半群理论,讨论了Banach空间中具有混合单调（混拟单调）性质的非线性发展方程耦合周期解的存在性及周期解的存在唯一性,所得结果概括并推广了有关常微分方程和偏微分方程的若干结论．     

一类差分系统边值问题在渐近线性下的多解存在性

应用临界点理论,获得了一类差分系统边值问题在渐近线性下存在多个非平凡解的条件.     

Nonexistence theorem except the out-of-phase and in-phase solutions in the coupled van der Pol equation system

We consider a coupled van der Pol equation system. Our coupled system consists of two van der Pol equations that are connected with each other by linear terms. We assume that two distinctive solutions (out-of-phase and in-phase solutions) exist in the dynamical system of coupled equations and give answers to some problems.     

Quantification of synchronization phenomena in two reciprocally gap-junction coupled bursting pancreatic β-cells

This paper aims to discuss our research into synchronized transitions in two reciprocally gap-junction coupled bursting pancreatic β-cells. Numerical results revealed that propagations of synchronous states could be induced not only by changing the coupling strength, but also by varying the slow time constant. Firstly, these asynchronous and synchronous states such as out-of-phase, almost in-phase and in-phase synchronization were specifically demonstrated by phase portraits and time evolutions. By comparing interspike intervals (ISI) bifurcation diagrams of two coupled neurons with an individual neuron, we found that coupling strength played a critical role in tonic-to-bursting transitions. In particular, with the phase difference and ISI-distance being introduced, regions of various synchronous and asynchronous states were plotted in a two-dimensional parameter space. More interestingly, it was found that the coupled neurons could always realize complete synchronization as long as the coupling strength was appropriate.     

Dynamical approach to complex regional economic growth based on Keynesian model for China

The paper addresses the problem of complex regional economic growth by using nonlinear Keynesian model with focusing on direct foreign investments effects. We investigate the dynamics of the model for the broad range of parameters which, in particular, contains the parameter values obtained recently by econometric analysis of the data for economic growth in China. For the single-region model we give conditions for which the dynamics of the model will be chaotic or regular. The parameters which prevent the economic stagnation are indicated. Further, we consider the model for two regions with a common trade as a coupling factor. The conditions are given for the two trading systems to exhibit chaotic synchronization, in-phase and out-of-phase behavior.     

Free vibration of embedded double-walled carbon nanotubes considering nonlinear interlayer van der Waals forces

In this article, nonlinear free vibration of embedded double-walled carbon nanotubes (DWCNTs) duo to the nonlinear interlayer van der Waals (vdW) force is studied based on the nonlocal Euler-Bernoulli beam theory. The interlayer vdW force is modeled as a nonlinear function of inner and outer tubes deflections considering the variation of the interlayer distance along the circumference of DWCNTs. The harmonic balance method is applied to analyze the relationship between the deflection amplitudes and the frequencies of in-phase and out-of-phase free vibrations for DWCNTs. Finally, the influences of the nonlocal parameter, surrounding elastic medium, nanotube length, end condition and vibrational mode on the nonlinear free vibration properties of DWCNTs are discussed in detail.     

Bifurcations and exact traveling wave solutions of the equivalent complex short-pulse equations

In this paper, we study the traveling wave solutions for a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrodinger (NLS) equation in the ultrashort-pulse regime. The corresponding traveling wave systems of the equivalent complex short-pulse equations are two singular planar dynamical systems with four singular straight lines. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.     

One-way and two-way couplings of CFD and structural models and application to the wake-body interaction

The current study focuses on the wake-body interaction of a circular cylinder, whose transverse free vibration is modeled by a mass-spring-damper system coupled to a computational fluid dynamics (CFD) model for the flow and wake. We first simulate the free vibration of the elastically-mounted cylinder and the wake, and analyze the transverse load it exerts on the cylinder and its phase with the vibration. We vary the damping by three orders of magnitude and examine the difference in the wake-body interaction for slightly-damped and highly-damped systems. We then use the spectral properties of the free vibration and use them to construct two different types of forced vibrations: one consists only of the fundamental component of the free vibration, and the other accounts for all spectral properties of it. We compare the wake load for each type to that corresponding to the free vibration. The forced vibrations correspond to a one-way coupling and the information is communicated from the CFD model to the structural model, whereas the free vibration corresponds to a two-way coupling of the models. By comparing the spectral properties of the wake load, including the phase relation of its components with the vibration, which we obtained for the free vibration and for the equivalent forced vibration, we identify the effects of the wake feedback. The findings show that a forced vibration does not reproduce exactly the wake load at small and intermediate levels of structural damping. As the damping increases, the vibration changes from being in-phase with the wake load to being 90° out-of-phase with it, corresponding to two different wake states, and the forced vibration gives wake load that is very close to the one occurring in the case of full wake-body interaction.     

r-循环线性系统求解的快速算法

本文给出r-循环线性系统求解的一种快速算法.当r-循环矩阵非奇异时,该快速算法求出该线性系统的唯一解;当r-循环矩阵奇异时,该快速算法求出该线性系统的通解.     

矩阵方程AXB=D解的研究

给出了矩阵方程AXB=D相容的又一充要条件,同时讨论它的极小范数解、最小二乘解和极小范数最小二乘解,推广了文献[1]和[3]的结论.