多种群生态竞争系统周期正解的存在性

利用重合度理论中的延拓定理和泛函方法讨论了一类具有多个滞量的多物种生态竞争系统周期正解的存在性和全局吸引性,得到了一些新的结果。     

一类多滞量周期扰动非线性系统的周期解

采用更精确的先验估计，利用拓扑度讨论了一类具有多滞量的周期扰动非线性系统的T-周期解，得到了系统存在T-周期解的充分条件．证明了具有滞后的单种群对数模型在一定条件下存在的正周期解．     

时滞函数种群模型正周期解的存在性

利用重合度理论中的连续定理,研究了一类时滞函数种群模型的周正解,获得了这类模型存在正周期解的充分条件。     

基于生态系统动力学模型的太湖藻类动态模拟

本文以生态系统动力学模型CAEDYM为建模框架,紧密结合太湖生态系统结构与功能特点,以河道流量及其物质含量、风场、太阳辐射等为外部函数,以藻类生消及其相关营养盐变化过程为建模核心,建立了考虑内源释放的各种形态氮、磷输移与转化的太湖整体三维生态系统动力学模型.在前人研究工作的基础上,应用太湖2000年实测数据对模型进行率定和验证,确定了模型各参数值,计算结果显示模拟值能较好地拟合实测值,表明所建藻类生态动力学模型能较好地描述藻类及各种营养盐的动态变化,这对揭示太湖藻类"水华"暴发机理有一定的意义.     

一种基于 LPTV 的开关电容模拟信息转换器设计

模拟信息转换器(analog-to-information converter, AIC)以低于Nyquist率的采样率成为下一代模拟数字转换器的核心技术。模拟信息转换器采用随机解调模块处理输入数据,系统存在典型的时变特性,从而导致理论模型与实际电路模型失配。针对该问题,以开关电容作为AIC的核心部件,利用线性周期时变(linear periodically time-variant, LPTV)理论将周期时变的AIC系统转换为线性时不变系统,推导其系统传输函数,从而建立了AIC理论模型的电路设计方法。实验证明,该电路设计方法使理论的系统传输函数与实际电路的系统传输函数很好的匹配,充分验证了该设计方案的有效性。重构结果表明该电路可以将采样速率降低到原有奈奎斯特率的25%,重构信号的信噪比最高可达39.7 dB。     

基于逆系统方法的并网逆变器自适应模糊滑模控制研究

风电系统三相PWM并网逆变器控制的主要目标是控制输出电流并保证直流侧电容电压的恒定。针对现有的三相PWM并网逆变器系统具有多变量、非线性、强耦合等特点,采用开关函数法建立其开关周期平均模型,在并网逆变器数学模型的基础上,使用非线性逆系统方法,推导出并网逆变器的逆系统模型,构造出伪线性系统,实现了反馈线性化和解耦。对伪线性系统设计滑模控制器,考虑实际中存在建模误差,利用自适应模糊方法进行调整,解决了建模误差未知或变化的问题。理论分析和仿真结果均表明,该控制策略能保证直流侧电压恒定且能控制并网逆变器的输出电流,具有良好的动态响应能力。     

基于逆系统方法的并网逆变器自适应模糊滑模控制研究

风电系统三相PWM并网逆变器控制的主要目标是控制输出电流并保证直流侧电容电压的恒定.针对现有的三相PWM并网逆变器系统具有多变量、非线性、强耦合等特点,采用开关函数法建立其开关周期平均模型,在并网逆变器数学模型的基础上,使用非线性逆系统方法,推导出并网逆变器的逆系统模型,构造出伪线性系统,实现了反馈线性化和解耦.对伪线性系统设计滑模控制器,考虑实际中存在建模误差,利用自适应模糊方法进行调整,解决了建模误差未知或变化的问题.理论分析和仿真结果均表明,该控制策略能保证直流侧电压恒定且能控制并网逆变器的输出电流,具有良好的动态响应能力.     

具有阶段结构和HollingⅢ型功能反应的捕食-食饵系统持久性和全局稳定性

研究一类具有HollingⅢ型功能反应函数的捕食-食饵系统模型,通过建立适当的Lyapunov泛函,对模型进行定性分析,给出了系统的持久性、全局渐近稳定性的充分条件.     

三相电压型四桥臂逆变器的线性化控制模型

为建立三相电压型四桥臂逆变器的线性化控制模型,将微分几何理论应用到该系统中。利用开关函数和开关周期平均算子建立系统动态数学模型,合理选取状态变量、输入变量和输出变量,得到其仿射非线性系统模型。根据非线性微分几何理论,验证了该模型满足线性化的条件,通过非线性坐标变换将原来的非线性系统转化为既能控制又能观测的线性系统,并推导出原非线性系统的控制规律模型。通过实验验证了其有效性。     

PWM DC-DC变换器混杂动态系统的能控性和能观性

在PWM DC-DC变换器研究中引入混杂动态系统和切换线性系统的概念和相关理论,研究PWM DC-DC变换器的能控性和能观性.首先将PWM DC-DC变换器建立为周期型切换线性系统模型,然后根据周期型切换线性系统的一个周期之后和多周期的能控性和能观性定义及定理,以Buck PWM变换器为例,分析变换器一个周期之后和多周期的能控性和能观性,最后对Buck PWM变换器进行能控性实验验证.实验结果表明,在负载阶跃变化的情况下,变换器输出完全可以控制并且稳定在设计值,这和Buck PWM变换器作为周期型切换线性系统模型的能控性分析结果是一致的.本文的研究还表明,研究方法也适应于其他功率变换器能控性和能观性的研究.     

具复杂偏差变元的Rayleigh方程的周期解

利用k-集压缩算子拓扑度抽象连续定理,研究了一类具复杂偏差变元的Rayleigh方程周期解的存在性,并获得了此类方程周期解存在的充分条件。本文的结果推广并改进了已有的结果。     

铁磁谐振过电压混沌振荡的理论研究

在中性点直接接地电力系统中,建立铁磁谐振过电压的数学模型,对该模型的异宿轨道进行计算,在此基础上运用Melnikov方法计算该系统的混沌阈值,即铁磁谐振过电压振荡发生的参数区域及混沌产生的条件,并深入探讨其周期解的存在性,为有效控制和消除过电压,抑制过电压中的混沌现象提供理论依据.     

一类高阶时滞微分方程的周期解

基于重合度理论，采用更精确的先验估计，研究了高阶时滞微分方程的周期解，得到了该方程存在周期解的充分条件。     

Multimode oscillator analysis via integral manifolds part I: Non-resonant case

This article represents Part I of a two-part paper which provides a rigorous mathematical foundation of the modeanalysis method for analysing the periodic and quasi-periodic oscillations observed in various types of coupled oscillators. Although the results predicted by this method had been confirmed by experiments to some extent, the crucial assumptions used to derive the averaged equations are based on engineering intuition. Moreover, while it is intuitively reasonable to associate an equilibrium solution of the averaged equations whose eigenvalues have negative real parts with that of a stable periodic or quasi-periodic solution of the original equation, the relationship between the solution of the averaged equations and that of the original equations as t tends to infinity, is not clear in a mathematical sense. This paper resolves the theoretical ambiguities of the mode analysis method by using the theory of integral manifolds. In particular, we recalculate the averaged equations in a rigorous way, and show that they coincide with those obtained before. Therefore, the theory of integral manifolds guarantees the existence of an integral manifold in the original system which corresponds to a steady-state periodic or quasi-periodic solution, provided the equilibrium point of the averaged equation has no eigenvalues with a zero real part (i.e. hyberbolic). This rigorous analysis proved that all our previous results obtained from the mode analysis method, i.e. averaged equations and stability analysis were correct.     

Multimode oscillator analysis via integral manifolds part II: Resonant case

This article represents Part II of a two-part paper which provides a rigorous mathematical foundation of the modeanalysis method for analysing the periodic and quasi-periodic oscillation observed in various types of coupled oscillators. Although the results predicted by this method had been confirmed by experiments to some extent, the crucial assumptions used to derive the averaged equations are based on engineering intuition. Moreover, while it is intuitively reasonable to associate an equilibrium solution of the averaged equations whose eigenvalues have negative real parts with that of a stable periodic or quasi-periodic solution of the original equation, the relationship between the solution of the averaged equations and that of the original equations as t tends to infinity, is not clear in a mathematical sense. This paper resolves the theoretical ambiguities of the mode analysis method by using the theory of integral manifolds. In particular, we recalculate the averaged equations in a rigorous way, and show that they coincide with those obtained before. Thereore, the theory of integral manifolds guarantees the existence of an integral manifold in the original system which corresponds to a steady-state periodic or quasi-periodic solution, provided the equilibrium point of the averaged equation has no eigenvalues with a zero real part (i.e. hyperbolic. This rigorous analysis proved that all our previous results obtained from the mode analysis method, i.e. averaged equations and the analysis were correct.     

Study of the periodic ferroresonance in the electrical power networks by bifurcation diagrams

The principal contribution of this article is to determine the existence zones of the various periodic ferroresonant modes (fundamental, harmonic and subharmonic) intervening in the electrical power network. The bifurcation diagrams are used for this purpose. To be able to plot a bifurcation diagram of a particular solution, it is initially necessary to locate this solution and then to follow it according to a bifurcation parameter. The developed computation code, resulting from the implementation of the Galerkin method jointly with the pseudo-arclength continuation method, has proved to be a powerful and reliable tool to construct these bifurcation diagrams. Indeed, it enables the electrical power network operators to better understand the problems of the phenomenon which had been observed in its network and to foresee new ferroresonance cases.Applied to the single-phase ferroresonant circuits, both series and parallel, we have been able to easily calculate the existence zones of these modes, as well as the stability limits of the system on ranges of broad variation of the parameters.Several results obtained numerically by software MATLAB, as from the real cases, are presented and commented upon.     

二阶半线性椭圆型方程组正整体解的存在性

在这篇文章中,我们讨论二阶半线性椭圆型方程组正整体解.利用不动点理解,单调方法和上下解技巧,由Lp估计和Schauder正则理论以及对角线方法,我们得到二阶椭圆型弱藕合组正整体解的存在性;我们还进一步讨论了广泛的一类二阶半线性椭圆型方程组,并利用正整体解的存在性结论,证明了这类椭圆型方程组有无穷多个有界,且其界异于零的整体解.     

Theoretical and experimental analysis of a simple PWM‐1 controlled interrupted electric circuit

In this paper, we analyze a simple PWM‐1 controlled interrupted electric circuit in order to essentially understand the circuit fundamental characteristics. First, we explain the circuit dynamics, and then we define the return map by using the exact solution. Next, we focus on the existence region of the solution (invariant interval) and bifurcation phenomena in the circuit. In particular, we find the circuit has three types of the invariant interval depending on the parameter. We also clarify that the period‐doubling bifurcation and the border‐collision bifurcation effect in the existence region of the periodic solution in a wide parameter plane. Finally, the mathematical results are verified by the laboratory experiment. Copyright © 2012 John Wiley & Sons, Ltd.