一类恒化器竞争模型正解存在区域的刻画

刻画了一类带Ivlev型反应函数的非均匀恒化器竞争模型正解的存在域。利用不动点指数理论和上下解方法证明了在a 1λ？1且b 1σ？1的前提下,系统有正解的充要条件是a＆gt;r1（a＆#39;b）且b＆gt;r2（a＆#39;b）。结合单调方法和不动点指数理论,说明存在域Λ是R2＋中的一个无界连通区域,其边界由两条递增的曲线Γ1：a=F1（b）和Γ2：b=F2（a）构成。证明了系统在存在域Λ的某个子区域内至少有两个正解。     

Brusselator反应扩散模型共存态的定性分析

运用Poincaré不等式、Schwarz不等式以及Young不等式,通过积分方法分析了一类化学反应扩散模型--Brusselator模型的共存态解,给出了模型共存态的一些性质。     

带动态边界的非均匀Timoshenko梁的反馈镇定

对于一端具负载的非均质Timoshenko梁, 研究了其边界反馈镇定问题. 首先提出了一种边界反馈控制方案, 建立了相应的闭环系统的适定性. 然后利用乘子法证明了, 当两个边界反馈控制同时作用于梁的负载端时, 闭环系统是指数稳定的.     

具有非单调发生率的SIR传染病模型的稳定性

研究了一类具有非单调发生率的SIR传染病模型。给出了系统解的正性、一致有界性和全局吸引性,接着运用Hurwitz-Rouché判别法,讨论了对应系统无病平衡态和地方病平衡态的局部渐近稳定性。最后通过上下解方法和比较原理说明,当常数输入率足够大时,地方病平衡态是全局渐近稳定的;当常数输入率或者接触率足够小时,无病平衡态是全局渐近稳定的。     

基于高斯混合模型聚类的非均匀采样系统的多模型切换辨识

从概率统计方法出发,提出一种基于高斯混合模型聚类与递推最小二乘算法的非均匀采样系统的多模型建模方法.首先,采用高斯混合模型作为调度函数,使用最大期望(EM)算法迭代更新估计高斯混合模型中参数,从而通过每个子系统的高斯概率密度函数计算和比较来确定子系统的激活情况; 其次,采用递推最小二乘算法估计局部子系统参数;然后,使用鞅收敛定理对所提出的算法性能进行分析; 最后,通过非均匀采样系统的多模型建模来证明所提出方法的有效性.     

非均匀采样数据系统的新型模型描述方法

提升技术是处理非均匀采样数据（Non-uniformly sampled-data,NUSD）系统的标准工具.然而,提升状态空间模型存在因果约束问题,相应的提升传递函数模型结构复杂,且参数数目过多.因此,它们不便于非均匀采样数据系统的辨识与控制.通过引入时变后移算子,本文提出了一种输入输出表达的新型模型描述方法.该模型能够克服提升系统模型的缺点,使得传统单率系统的辨识和控制方法能够推广到非均匀采样数据系统中.仿真结果表明了新模型的优越性和有效性.     

带形状参数的指数均匀B样条模型

本文给出了k(k≥2)阶带形状参数指数多项式的均匀B样条模型.该类模型具有很多与B样条模型相同的性质,并且具有一个可调节的形状参数.由该模型构造的曲线,通过改变形状参数的取值,可以调整曲线接近其控制多边形的程度.该模型可以应用于CAD/CAM领域,作为几何造型一种新的有效模型.     

一类退缩扩散互惠模型的共存态和渐近性

对于一类两种群互惠模型,如果扩散项为[-upΔu]和[-vqΔv,]则在[p,][q]和反应函数的系数满足一定条件时该模型的解在有限时间爆破,而在另外的一些条件下存在整体解。证明：如果扩散项为[-Δum]和[-Δvn,]则解的动力学性态会完全不同。在适当的条件下,该时变问题存在唯一整体解,相应的平衡态问题存在正的最大和最小解。此外,这个时变解在一些初值条件下收敛到最大平衡解,而在另一些初值条件下收敛到最小平衡解。这种收敛性对反应函数的任意系数都成立。这意味着带不同退缩扩散项的互惠模型的动力学性态也可能不同。     

具有阶段结构及B-D功能反应的食饵-捕食模型

研究一类食饵具有阶段结构及Beddington-DeAngelis功能反应的食饵-捕食模型的稳定性,利用特征根法,讨论了捕食者灭绝平衡点及食饵和捕食者共存平衡点的局部稳定性;通过引入新的引理,利用微分方程比较定理及迭代法,得到了捕食者灭绝平衡点和食饵、捕食者共存平衡点全局稳定的充分条件;数值模拟验证了主要结果。     

含反应扩散项的时滞细胞神经网络模型的W1,2（Ω）-与X1,2（Ω）-稳定性

针对一类具反应扩散项的时滞细胞神经网络模型,利用Poincare不等式与辅助函数的方法,获得了该系统的W^1,2（Ω）-指数稳定性和X^1,2（Ω）-渐近稳定性条件;与以往文献结论不同,这些稳定性条件包含了扩散算子项,与以往结果比较,获得的指数稳定性条件更强.最后,通过实例说明该方法的可行性.     

离散捕食系统的持久性和全局稳定性

研究一类带有Beddington．DeAngelis功能性反应和时滞的多维离散食饵．捕食系统的持久性和全局稳定性。利用差分方程的比较原理,给出了系统持久性的充分条件;应用估值方法推导得到系统全局稳定性的充分条件;使用不动点理论,证明了系统周期解的存在性和全局稳定性。     

Attractivity of fractional functional differential equations

In this paper, some attractivity results for fractional functional differential equations are obtained by using the fixed point theorem. By constructing equivalent fractional integral equations, research on the attractivity of fractional functional and neutral differential equations is skillfully converted into a discussion about the existence of fixed points for equivalent fractional integral equations. Two examples are also provided to illustrate our main results.     

一类随机Harrison型捕食与被捕食系统的稳定性分析

研究了一种具有Harrison功能反应函数的随机捕食与被捕食系统模型,该模型中捕食者的死亡率和被捕食者的增长率受到独立同分布的两对称三值噪声的影响.文中运用线性化理论和Shapiro-Loginov方程给出了系统扰动的一阶矩和二阶矩方程,并用Routh-Hurwitz稳定性判据给出了系统稳定的条件.研究表明噪声强度σ和噪声自相关时间τ均对系统的稳定性有影响.当噪声强度充分大或噪声自相关时间足够小都能使系统失稳.最后通过数值方法,验证了分析结果的准确性.     

Chaos control and synchronization of a three-species food chain model via Holling functional response

Chaos control and synchronization problem of a three-species food chain model with Holling I-type functional response is investigated. By the linearization approach, a feedback control law is developed to stabilize the model system to equilibrium points. Based on the bidirectional coupled method, chaos synchronization of the model system is studied. Numerical simulations show that the feedback control law can suppress chaos to unstable equilibrium points successfully. Further, the numeric results show that when the coupling strength 0<k<0.012, synchronization of two model systems cannot be achieved; when the coupling strength 0.012≤k<2, synchronization of two model systems is always achieved, furthermore, the larger is the coupling strength k, the smaller are the synchronization errors, the better is the effect of chaos synchronization; when the coupling strength k≥2, synchronization of two model systems can also be achieved, but the synchronization errors are bigger than that of 0.012≤k<2.     

一类SISO系统的预测函数控制及其鲁棒稳定性分析

首先给出对象不确定性描述,基于阶跃响应模型提出单值预测函数控制和双值预测函数控制两类算法的设计．然后将系统控制结构归结为内模控制结构,利用多项式Jury主系数定理,分别给出基于两类预测函数控制算法设计的闭环控制系统鲁棒稳定的充分条件．最后通过仿真实验讨论了控制器的参数调节．     

A viral infection model with periodic immune response and nonlinear CTL response

This paper investigates a viral infection model with periodic immune response and nonlinear cytotoxic T lymphocyte (CTL) response. Using the periodic rhythms of human immune system, the model can avoid the unreasonable equilibrium in the basic viral model with nonlinear CTL response introduced by Nowak et al. We obtain the global stability of the infection-free equilibrium and the immune-exhausted equilibrium. Numerical simulations show that the oscillation of immune system can affect the pattern of the viral dynamical behaviors. Period doubling bifurcations of the system are observed via simulations. This can provide a possible interpretation for the viral oscillation behaviors, which were observed in chronic HBV and HCV infection patients.     

functional control of integrating process based on impulse response

The predictive model is built according to the characteristics of the impulse response of integrating process. In order to eliminate the permanent offset between the setpoint and the process output in the presence of the load disturbance, a novel error compensation method is proposed. Then predictive functional control of integrating process is designed. The method given generates a simple control structure, which can significantly reduce online coInputation. Furthermore, the tuning of the controller is fairly straightforward. Simulation results indicate that the designed control system is relatively robust to the parameters variation of the process.     

Design of robust model predictive control with input constraints

This article addresses the problem of designing a robust output feedback model predictive control (MPC) with input constraints, which ensures a parameter-dependent quadratic stability and guaranteed cost for the case of linear polytopic systems. A new heuristic method is introduced to guarantee input constraints for the MPC. To reject disturbances and maintain the process at the optimal operating conditions or setpoints, the integrator is added to the controller design procedure. Finally, some numerical examples are given to illustrate the effectiveness of the proposed method.