Existence of periodic solutions to a system with functional response on time scales

This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.     

Changes in Repetitive Firing Rate Related to Phase Response Curves for Andronov-Hopf Bifurcations

We study specific changes in repetitive firing in the two-dimensional Hindmarsh-Rose （2dHR） oscillatory sys- tem that undergoes a bifurcation transition from the supercritical Andronov-Hopf （All） type to the subcritical Andronov-Hopf （SAH） type. We identify dynamical mechanisms which are responsible for changes of the repeti- tive firing rate during the AH to SAH bifurcation transitions. These include frequency-shift functions in response to small perturbations of a timescale parameter, its multiplicative parameter, and an external input current in the 2dHR oscillatory system. The frequency-shift functions are explicitly represented as functions relating to the phase response curves （PRCs）. Then, we demonstrate that when the timescale is normal and relatively fast, the repetitive firing rate slightly increases and decreases respectively during the AH to SAH bifurcation transition with a change of the intrinsic parameter, whereas it decreases during the SAH to AH bifurcation transition with an increase in the timescale. By analyzing the three different frequency-shift functions, we show that such changes of the repetitive firing rate depend largely on changes of the PRC size. The PRC size for the SAH bifurcation shrinks to the PRC size for the AH bifurcation.     

Electromagnetic Bloch oscillation in one-dimensional multiple microcavities composed of metamaterials

We propose a photonic structure stacked sequentially by one-dimensional photonic crystals and cavities. The whole structure is composed of single-negative and double-negative materials. The optical Wannier-Stark ladder （WSL） can be obtained in a low frequency region by modulating the widths of the cavities in order. We simulate the dynamical behavior of the electromagnetic wave passing through the proposed photonic structure. Due to the dispersive characteristics of the metamaterials, a very narrow WSL can be obtained. The long-period electromagnetic Bloch oscillation is demonstrated theoretically to have a period on a microsecond time scale.     

质子交换膜燃料电池多时间尺度下的动态特性

目前对质子交换燃料电池动态性能的研究多针对于运行参数对系统的影响,未涉及多时间尺度下电池的动态特性和相应多时间尺度模型的研究.为探明质子交换膜燃料电池动态变化时系统内各因素在不同时间尺度下对输出性能的影响效力,利用质量扩散方程及理想气体状态方程求得氧气和氢气有效分压,根据能量守恒定律、热力学定律、电化学反应方程建立动态模型.通过设置载荷突变(大、中、小时间尺度动态时长分别为0.6 s, 165 s, 16 min)研究负载电流突变时电压立即突变的机理,从作用于动态性能时长的时间常数着手,控制变量分析双层电荷层效应的电容C、燃料氧化剂的延迟时间常数τe、热力学特性(温度T)对动态性能的影响(变量初值为C=4 F,τe=80 s, T=307.7 K),明确其在不同时间尺度下的作用强度,借助Matlab/Simulink平台仿真呈现研究结果并验证所建模型的正确性和有效性.仿真结果表明:负载突变时电压突变是由于开路电压和欧姆极化电阻的作用且欧姆电阻占主导(欧姆过电压变化值2 V,开路电压变化0.05 V),小时间尺度(ms)下C对动态性能起主导作用,中时间尺度(s)下τe对动态特性影响较大,...     

POSITIVE SOLUTIONS FOR p-LAPLACIAN DYNAMIC EQUATIONS ON TIME SCALES

The three-point boundary value problems of p-Laplacian dynamic equations on time scales are investigated. By using Krasnosel＇skii＇s fixed-point theorem and fixed-point index theorem, criteria are achieved for the existence of at least one, two or 2n positive solutions. Furthermore, some examples are included to illustrate the main theorems.     

黑洞的温度和熵变化是时间尺度变换的补偿效应

以史瓦西黑洞和Ｖａｉｄｙａ黑洞为例，研究了时间尺度变换的补偿效应．规范势就是仿射联络的缩并．黑洞的熵变化和Ｈａｗｋｉｎｇ温度都可看作补偿场的纯规范势 关键词：     

太阳系起源时间的最早科学推算

 一些读者可能记得曾经有过这样的报导:大约一九八二年四、五月间,九大行星都运行到太阳一侧,而且几乎全集中到大约九十度的一个角度内。这当然是相当罕见的事件。但鉴于九大行星以不同的速度绕太阳运行,这种事件迟早会出现的。如果知道了九大行星的运行周期及它们目前的位置,可以预测多少年以后会有这样的事件发生。 值得注意的是,早在两千年以前,我们的祖先就进行过类似的推算,并据此来计算太阳系的起源时间。 在西汉中期,有一本叫作《命历序》的纬书出现。纬书是一种讲迷信的书。     

EXISTENCE OF POSITIVE SOLUTIONS TO A THREE-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER DYNAMIC EQUATIONS WITH DERIVATIVE ON TIME SCALES

In this paper, we consider the existence of positive solutions to a three-point boundary value problem for second order dynamic equations with derivative on time scales.Applying Leggett-Williams fixed point theorem, we obtain at least three positive solutions to the problem. An example is also presented to illustrate the applications of the results obtained.     

时间尺度上二阶线性动力学方程的一般解与Ulam稳定性

本文利用参数变易法研究了时间尺度上二阶变系数线性动力学方程的解与Ulam稳定性问题. 特别地,在不同的系数情形下建立了二阶常系数线性动力学方程的Ulam稳定性理论.     

连续搅拌槽式反应器中自催化化学反应的延迟同步

讨论了由两个连续搅拌槽式反应器组成的化学反应系统的延迟同步问题.基于Lyapunov稳定性理论,通过选择适当的输出和同步信号得到了使反应实现延迟同步的控制函数,并用数值模拟验证了方法的有效性.最后指出延迟同步误差系统存在着两种不同的时间尺度. 关键词： 延迟同步 化学反应 连续搅拌槽式反应器 时间尺度