ON LIMIT CYCLES FOR A CLASS OF DIFFERENTIAL SYSTEMS WITH POSITIVE DEFINITE POLYNOMIAL

In this paper, the nonexistence, existence and the number of limit cycles for a class of differential systems with positive definite polynomial are considered, and the results obtained generalize and supplement those of [1].     

EXISTENCE OF POSITIVE MULTIPLE SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR

In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point theorem on the cone.     

保护私有信息的一般线性方程组计算协议

作为科学计算的一个重要问题,保护私有信息的线性方程组的求解在金融、机械及通信等领域有着广泛的应用.在不经意传输的意义下,利用有限域上计算Moore-Penrose伪逆矩阵的概率算法,设计新的安全协议,解决了隐私保护的一般线性方程组在有限域上的安全两方计算问题,并利用模拟范例证明该协议在半诚实模型下是安全的.     

Wavelet operational matrix method for solving the Riccati differential equation

A Haar wavelet operational matrix method (HWOMM) was derived to solve the Riccati differential equations. As a result, the computation of the nonlinear term was simplified by using the Block pulse function to expand the Haar wavelet one. The proposed method can be used to solve not only the classical Riccati differential equations but also the fractional ones. The capability and the simplicity of the proposed method was demonstrated by some examples and comparison with other methods.     

基于不完全偏好信息的多阶段应急群决策方法

针对灾害事件的多阶段演化特征,研究多阶段应急群决策方法。在复杂的决策环境下,为了解决决策专家难以对应急方案进行准确评价的问题,允许专家以残缺精确数与残缺模糊数判断矩阵给出偏好信息;而且,多阶段应急群决策模型通过构建目标规划模型对决策专家进行分阶段赋权,并解得各决策阶段下群体的方案偏好,最后通过求解决策阶段权重,获取全局群体偏好最优解。应用于危险化学品液态苯泄漏的应急处置案例验证了该方法的可行性与有效性。     

一对四元数矩阵方程的共轭延拓解

定义广义四元数共轭延拓矩阵的概念,利用矩阵分块和四元数矩阵的实表示方法,分别给出四元数矩阵方程AX=C和XB=D存在列共轭延拓解和行共轭延拓解的必要充分条件及解的表达式.     

具有捕食正效应及Holling Ⅱ功能性反应的捕食-食饵系统

本文研究一类具有捕食正效应的Holling Ⅱ功能性反应的食饵-捕食者系统:dx/dt=rx(1-x/k+εy/k)-αxy/1+ωx,dy/dt=kαxy/1+ωx-dy,讨论其平衡点的性态.     

递推数列通项的矩阵解法

分情形讨论递推数列求通项的问题,介绍相应的矩阵解法,并借助实例说明其应用。     

Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control

This paper is concerned with the global exponential synchronization problem of two identical nonlinear time-delay Lur’e systems via delayed impulsive control. Some novel impulsive synchronization criteria are obtained by introducing a discontinuous Lyapunov function and by using the Lyapunov–Razumikhin technique, which are expressed in forms of linear matrix inequalities. The derived criteria reveal the effects of impulsive input delays and impulsive intervals on the stability of synchronization error systems. Then, sufficient conditions on the existence of a delayed impulsive controller are derived by employing these newly-obtained synchronization criteria. Additionally, some synchronization criteria for two identical time-delay Lur’e systems with impulsive effects are presented by using delayed continuous feedback control. The synchronization criteria via delayed continuous feedback control can deal with the case when the impulsive control strategy fails to synchronize two identical impulsive time-delay Lur’e systems. Three numerical examples are provided to illustrate the efficiency of the obtained results.     

Sampled-data nonlinear observer design for chaos synchronization: A Lyapunov-based approach

This paper considers sampled-data based chaos synchronization using observers in the presence of measurement noise for a large class of chaotic systems. We study discretized model of chaotic systems which are perturbed by white noise and employ Lyapunov-like theorems to come up with a simple yet effective observer design. For the choice of observer gain, a suboptimal criterion is obtained in terms of LMI. We present semiglobal as well as global results. The proposed scheme can also be extended for discrete-time chaotic systems. Numerical simulations have been carried out to verify the effectiveness of theoretical results.