Oscillatory expression and variability in p53 regulatory network

The effect of delay, nonlinearity and noise on oscillatory motion is of permanent interest for theoretical and experimental research. Here we explore a negative feedback loop between p53 and Mdm2 with a time delay, which is a key circuit in the response of cells to damage. This circuit shows noisy sustained oscillations in individual human cells following DNA damage, and damped oscillations at the cell population level. We demonstrate the effect of delay on the oscillation, and the correlation in time course. In a multi-species system, the events at different time points which span a time delay are coupled even when the delay is large compared with the other characteristic times of the system. We also clarify that the dynamics at the single-cell level appears to be coherent resonance, and the origin of the damped oscillation at the macroscopic level out of the sustained ones at the single-cell level can be ascribed to the dephasing process which is induced by the interplay between nonlinearity and noise. The findings are consistent with experimental observations and advance our understanding of the dynamics of the p53 network.     

Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay

We propose a simple adaptive delayed feedback control algorithm for stabilization of unstable periodic orbits with unknown periods. The state dependent time delay is varied continuously towards the period of controlled orbit according to a gradient-descent method realized through three simple ordinary differential equations. We demonstrate the efficiency of the algorithm with the Rössler and Mackey-Glass chaotic systems. The stability of the controlled orbits is proven by computation of the Lyapunov exponents of linearized equations.     

Equivalent conditions on periodic feedback stabilization for linear periodic evolution equations

This paper studies the periodic feedback stabilization for a class of linear T  -periodic evolution equations. Several equivalent conditions on the linear periodic feedback stabilization are obtained. These conditions are related to the following subjects: the attainable subspace of the controlled evolution equation under consideration; the unstable subspace (of the evolution equation with the null control) provided by the Kato projection; the Poincaré map associated with the evolution equation with the null control; and two unique continuation properties for the dual equations on different time horizons [0,T]$[0,T]$ and [0,_n0T]$[0,n_{0}T]$ (where _n0$n_0$ is the sum of algebraic multiplicities of distinct unstable eigenvalues of the Poincaré map). It is also proved that a T-periodic controlled evolution equation is linear T-periodic feedback stabilizable if and only if it is linear T-periodic feedback stabilizable with respect to a finite-dimensional subspace. Some applications to heat equations with time-periodic potentials are presented.     

BIFURCATION ANALYSIS IN A GENERALIZED FRICTION MODEL WITH TIME-DELAYED FEEDBACK

In this paper, we consider a generalized model of the two friction models, both of which have two different types of control forces with time-delayed feedback proposed by Ashesh Sara et al. By taking the time delay as the bifurcation parameter, we discuss the local stability of the Hopf bifurcations. Under some condition, the generalized model harbors a phenomenon that the equilibrium may undergo finite switches from stability to instability to stability and finally become unstable. By applying the method introduced by Faria and Magalhaes, we compute the normal form on the center manifold to determine the direction and stability of the Hopf bifurcations. Numerical simulations are carried out and more than one periodic solutions may exist according to the bifurcation diagram given by BIFTOOL. Finally a brief conclusion is presented.     

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014     

考虑投资者心理预期的投资性商品价格运行稳定性识别与反馈控制机制设计

以投资性商品的价格运行系统为研究对象,引入反映投资者心理预期的变量,对传统的蛛网模型加以改进,并据此构建非均衡市场环境下投资性商品价格运行开环系统模型,对非均衡市场环境下投资性商品市场价格运行的稳定性进行识别,在此基础上对反馈控制机制进行设计.以我国的住宅市场的价格运行系统为实证研究对象,结合历史数据对所构模型的有效性进行验证,并对未来可能出现情况进行预测.实证研究主要结论如下:第一,我国住宅市场投资者对预期收益的敏感程度以及供应商对商品前期价格的敏感程度均较高,价格运行能自发实现稳定的区域较小;第二,现有调控政策不变的情况下,我国住宅市场价格正向偏离稳定区域的程度将减小;第三,若政府从影响投资者心理预期的角度入手对我国住宅市场价格波动进行干预,希望我国住宅市场的价格运行能以最快的速度趋于稳态,则设计反馈控制机制时,应重视投资者对商品价格未来的心理预期受商品历史价格的影响程度远高于受市场供需的影响程度这一现象.     

需求受库存水平影响的短生命周期物品延迟订货的库存管理

像计算机、电视机、空调等这类具有物理变质的可能性很小,但生命周期较短、不断更新换代、价值不断贬值的电子产品会发生无形变质的现象.在假设无形变质率与需求率负相关,同时在产品的存储过程中,考虑库存水平对销售量的影响情况下,研究需求受库存水平影响、且缺货时存在延迟订货的短生命周期物品的库存管理问题.创新之处在于考虑了产品的缺货问题;在允许缺货的条件下,建立了短生命周期物品的库存模型;运用数值算例进行了求解和验证;并对各参数进行了敏感性分析.     

几类最优避免冲突码

长度为n重量为w的避免冲突码C是群Z_n的w元子集族,满足对任意的x,y∈C,x≠y有d*(x)∩d*(y)=Φ,其中d*(x)={a-b(mod n):a,b∈x,a≠b}.避免冲突码适用于无反馈时隙同步多址冲突信道.C中的元素称为码字,C中所包含的码字的个数称为码的容量,它是系统中所支持的潜在用户的个数.利用已有的3种构造方法给出了重量在4到10之间的一些最优CAC(p,w)码类.     

一类不确定时变时滞系统的鲁棒自适应稳定控制

研究了一类不确定时变时滞系统的鲁棒自适应稳定控制问题.系统包含多变时滞非线性扰动.基于Lyapunov稳定性理论和Lyapunov-K rasovsk ii型泛函设计出了一种无记忆的自适应状态反馈控制器,并证明了满足一定条件时,此控制器使得闭环系统最终一致有界.