Volterra积分微分方程的稳定性

本文给出判定Ｖｏｌｔｅｒｒａ积分微分方程（Ⅰ）零解的稳定性、一致稳定性和渐近稳定性的准则。     

On the realization of nonlinear discrete-time systems

It is shown, on the basis of a compact expression of the kernels of the discrete Volterra series associated to a linear analytic discrete-time system, that the kernels satisfy a suitable property which enables their inductive characterization. We also give a first result on the realization of a given family of functions by a linear analytic discrete-time system with linear invertible drift term.     

Measuring a linear approximation to weakly nonlinear MIMO systems

The paper addresses the problem of preserving the same LTI approximation of a nonlinear MIMO (multiple-input multiple-output) system. It is shown that when a nonlinear MIMO system is modeled by a multidimensional Volterra series, periodic noise and random multisines are equivalent excitations to the classical Gaussian noise, in a sense that they yield in the limit, as the number of the harmonics M→∞, the same linear approximation to the nonlinear MIMO system. This result extends previous results derived for nonlinear SISO (single-input single-output) systems. Based upon the analysis of the variability of the measured FRF (frequency response function) due to the presence of the nonlinearities and the randomness of the excitations, a new class of equivalent input signals is proposed, allowing for a lower variance of the nonlinear FRF measurements, while the same linear approximation is retrieved.     

带化学反应的边界层流动问题中一类弱奇异Volterra积分方程的近似解

研究带化学表面反应的边界层流动问题导出的一类弱奇异Volterra积分方程的近似解。以一些化学反应的阶数为例求出解在零点的分数阶级数展开式及其■有理逼近。通过将发散积分解释为Hadamard有限部分积分,并借助数值积分方法导出解在无穷远点的带高阶对数项的渐近展开式。实际计算表明,给出的解在零点和无穷远点展开式的联合使用可以在整个半无限区间上高效地求解这类带化学表面反应的边界层流动问题。     

一类非线性隔振器振动传递特性分析

非线性输出频率响应函数是由Volterra级数发展而来的一个新概念.对一类具有反对称阻尼特性的隔振器,通过该概念推导出了振动传递性与系统非线性参数之间的显式解析关系；进而系统地研究了非线性阻尼参数对隔振器的力传递性能和位移传递性能的影响.研究结果表明,虽然非线性隔振器在受正弦信号激励下会出现高次倍频分量,但对于其传递性...     

Which games are growing bacterial populations playing?

Microbial communities display complex population dynamics, both in frequency and absolute density. Evolutionary game theory provides a natural approach to analyse and model this complexity by studying the detailed interactions among players, including competition and conflict, cooperation and coexistence. Classic evolutionary game theory models typically assume constant population size, which often does not hold for microbial populations. Here, we explicitly take into account population growth with frequency-dependent growth parameters, as observed in our experimental system. We study the in vitro population dynamics of the two commensal bacteria (Curvibacter sp. (AEP1.3) and Duganella sp. (C1.2)) that synergistically protect the metazoan host Hydra vulgaris (AEP) from fungal infection. The frequency-dependent, nonlinear growth rates observed in our experiments indicate that the interactions among bacteria in co-culture are beyond the simple case of direct competition or, equivalently, pairwise games. This is in agreement with the synergistic effect of anti-fungal activity observed in vivo. Our analysis provides new insight into the minimal degree of complexity needed to appropriately understand and predict coexistence or extinction events in this kind of microbial community dynamics. Our approach extends the understanding of microbial communities and points to novel experiments.     

水声信号的非线性建模与预测方法

对水声信号尤其是混响干扰和背景噪声的预测和滤波,是水下目标信号检测的基础,在非平稳、非高斯、非线性水声信号处理中具有重要应用.本文利用最小二乘估计和Volterra级数理论,分别对水声信号建立预测模型并进行一步及多步预测,通过分析预测结果,选取最优预测参数.仿真结果表明,基于奇异值分解的Volterra级数模型的预测相对误差较最小二乘估计小一个数量级,预测结果更加逼近真实值.     

PARAFAC-based channel estimation and data recovery in nonlinear MIMO spread spectrum communication systems

In this paper, a new tensorial modeling is first proposed for nonlinear multiple-input multiple-output (MIMO) direct sequence spread spectrum communication systems. The channel is modeled as an instantaneous MIMO Volterra system. Then, a direct data approach for joint blind channel estimation and data recovery is developed using the parallel factor (PARAFAC) decomposition of a third-order tensor composed of received signals, exploiting space, time and code diversities. A blind channel estimation method based on the PARAFAC decomposition of a fifth-order tensor composed of covariances of the received signals is also proposed, considering phase shift keying (PSK) modulated transmitted signals. The proposed estimation algorithms are evaluated by simulating a nonlinear uplink MIMO radio over fiber (ROF) communication system.     

基于分数阶小波的模拟电路参数估计* Deng Yong(邓勇)?, Zhang He(张禾)

Aiming at the problem of parameter estimation in analog circuits, a new approach is proposed. The approach is based on the fractional wavelet to derive the Volterra series model of the circuit under test(CUT). By the gradient search algorithm used in the Volterra model, the unknown parameters in the CUT are estimated and the Volterra model is identified. The simulations show that the parameter estimation results of the proposed method in the paper are better than those of other parameter estimation methods.     

基于DFP的二阶Volterra模型及其对Rössler混沌序列的预测

为克服最小二乘法或归一化最小二乘法在二阶Volterra建模时参数选择不当引起的问题,在最小二乘法基础上,应用一种基于后验误差假设的可变收敛因子技术,构建了一种基于Davidon-Fletcher-Powell算法的二阶Volterra模型（DFPSOVF）.给出参数估计中自相关逆矩阵估计的递归更新公式,并对其正定性、有界性和τ（n）的作用进行了研究.将DFPSOVF模型应用于Rössler混沌序列的单步预测,仿真结果表明其能够保证算法的稳定性和收敛性,不存在最小二乘法和归一化最小二乘法的发散问题.