一类具有时滞和非线性发生率的SIRS传染病模型稳定性与Hopf分岔分析

研究了一类具有时滞及非线性特性发生率的SIRS传染病模型,首先利用特征值理论分析了无病平衡点和地方病平衡点的局部稳定性;并以时滞τ作为分岔参数,分析了模型的Hopf分岔行为,运用中心流形定理和规范型理论给出了分岔方向及分岔周期解稳定性的计算公式;最后,数值模拟验证了理论分析结果.     

传输时延环境下信息物理融合系统中恶意病毒传播的稳定性与分岔分析

本文考虑到恶意病毒在信息物理融合系统中的传播具有时延性,基于非线性动力学理论建立了一类更具一般性的含有时滞的恶意病毒传播模型.通过选取时滞作为分岔参数,并讨论相关的特征方程,研究了时滞对系统局部稳定性和Hopf分岔的影响.研究发现,系统的动力学行为依赖于分岔的临界值.此外,给出了保证系统稳定性和产生Hopf分岔的条件....     

一类具有标准发生率的SIRS传染病模型分岔分析

研究了一类具有脉冲生育和接种、垂直传染和标准发生率的SIRS传染病模型的动力学行为,通过利用Poincaré映射,讨论了平凡解和正周期-T解的存在和稳定性以及系统的跨临界分岔和flip分岔行为,并给出了能验证理论分析的数值结果.     

时滞和扩散驱动下信息物理融合系统恶意病毒传播动力学

本文提出了信息物理融合系统(CPS)中具有反应扩散效应的时滞恶意病毒传播模型, 研究了恶意病毒传播 的空间格局动态演化机制, 为恶意病毒在信息物理融合系统中预测和控制提供了战略指导. 给出了模型的基本再 生产数, 并分析了空间中无病毒平衡点和地方病毒平衡点的存在性. 在无时滞条件下建立了扩散引发的图灵不稳 定条件; 在有时滞条件下得到了时滞依赖的稳定性条件和Hopf分岔判据. 最后, 通过数值仿真验证了理论分析的正 确性.     

一类时滞网络病毒传播模型的Hopf分支

考虑到杀毒软件查杀病毒需要一定的时间周期,以及免疫主机对网络病毒的临时免疫力,本文基于SIQR网络病毒传播模型提出一类时滞SIQRS网络病毒传播模型。以杀毒软件查杀病毒需要一定的时间周期时滞为分支参数,通过分析相应特征方程根的分布,得到模型有病毒平衡点局部渐近稳定和产生Hopf分支的充分条件。给出一个仿真示例,对理论分析结果的正确性进行了验证。     

具有时滞和饱和接触率的SIRS模型的Hopf分支

应用微分方程分支理论,研究了具有时滞和饱和接触率的SIRS模型,以时滞[τ]为分支参数,运用Hopf分支理论,得到当时滞[τ]充分小时正平衡点是局部渐近稳定的,当[τ]经过一系列临界值时模型出现Hopf分支。用Matlab软件进行数值仿真验证了结论的正确性。     

一类具有非线性饱和执行器的不确定时滞系统鲁棒控制

研究一类具有非线笥饱和执行器朱确定线性时滞系统的鲁棒性镇定问题。所考虑的不确定时滞系统具有时变未知且有界的不确定参数和状态时滞。提出了新的鲁棒可镇定判据和相应的鲁棒无记忆状态反馈控制器设计方法。数值仿真例子说明了所提出方法的有效性。     

一类混沌系统的Hopf分岔控制

针对带参数的混沌系统,运用 Routh-Hurwitz判据及 Hopf分岔理论研究系统存在的动力学行为,设计状态反馈控制器对系统进行 Hopf分岔控制。分析系统参数及控制参数分别对系统稳定性与 Hopf分岔类型的影响,得到了系统稳定及不发生 Hopf分岔的系统参数条件。研究结果表明：控制器中的线性控制部分及非线性控制部分均能改变系统的分岔行为,使系统渐近稳定。数值仿真证明控制器设计的有效性。     

一类捕食型时滞无线传感网络蠕虫病毒传播模型

由于无线传感网络具有广泛的应用和易受恶意软件攻击的特点,其安全性问题受到了国内外研究学者的广泛关注.借助于Holling-Ⅱ类捕食模型,研究一类时滞易感-感染-重度感染-恢复-易感(susceptible-infected-terminally infected-recovered-susceptible,SITRS)...     

一类时滞分数阶SIR模型的动力学分析

为提高对传染病动力学模型分析的精确性,建立了一个新的带有时滞的分数阶传染病易感-感染-恢复(susceptible-infected-removed, SIR)模型,针对该模型进行稳定性分析并且讨论产生Hopf分岔的条件。首先,将整数阶系统转化为分数阶系统并求出正平衡点。然后,以时滞为分岔参数求出分岔点。研究发现,当时滞小于分岔点时,系统在正平衡点处是局部渐近稳定的;当时滞大于分岔点时,系统在正平衡点处发生Hopf分岔。同时,通过分析分数阶阶次对分岔点的影响发现,随着阶次的增加,系统的分岔点减小。最后,通过数值模拟验证了所得结论的准确性。     

Bifurcation and control of disease spreading networks model with two delays

In this paper, the dynamical behaviors are investigated for a complex network with two independent delays. Instead of taking time delays as bifurcation parameters, we choose probability $p$ and parameter $\mu$ as the control parameters to study their effects on local stability and Hopf bifurcation, respectively. Moreover, the conditions for generating Hopf bifurcation are given. Furthermore, we further discuss the effects of two time delays on the critical values of parameters $p$ and $\mu$. Finally, numerical simulations are used to illustrate the validity of the obtained results.     

Sliding dynamics and optimal control of avian influenza model with saturated incidence rate

In this paper, we develop a susceptible-infective-susceptible-infected-recovered avian influenza model with saturated incidence rate and three control measures, which is proposed to evaluate the comprehensive effects of different control measures on the spread of avian influenza. Based on the threshold policy, the threshold level is used as the reference index of whether to take control measures. No control measures will be taken when the total number of infected birds and humans is less than the threshold level. Otherwise, the three control measures will be implemented simultaneously to mitigate the spread of the disease. Furthermore, by using the Utkin equivalent control method, the existence of sliding mode equation and its dynamics are investigated. Additionally, the method of dynamic programming is introduced to study the optimal control for the model. Through constructing and proving the existence of viscosity solution of the corresponding Hamilton–Jacobi–Bellman equation, the optimal control pair is further obtained. Finally, numerical simulations are performed to illustrate the corresponding theoretical analysis results.     

具有多时滞的无线通信网络功率和速率控制

现有的无线通信网络功率和速率控制方法没有考虑系统中存在的多时滞情况,为此,针对具有多时滞的无线通信网络进行建模及功率和速率控制方法的研究.首先,根据无线通信网络功率和速率控制的物理机制,建立新的具有多时滞的无线通信网络功率和速率控制系统的数学模型.该模型包含速率控制中的时滞、功率控制中的时滞、状态时滞和输入时滞.在此基础上,通过预测控制和线性矩阵不等式设计鲁棒功率和速率控制器.仿真结果验证了所设计的功率和速率控制器的有效性.     

Analytical decoupling control strategy using a unity feedback control structure for MIMO processes with time delays

An analytical decoupling control method is proposed for multiple-input–multiple-output (MIMO) processes with multiple time delays. The desired diagonal system transfer matrix is proposed first in terms of the H₂ optimal performance specification, resulting in the ideal desired decoupling controller matrix derived within the framework of a unity feedback control structure. It is demonstrated that dead-time compensators must be enclosed in the decoupling controller matrix to realize absolute decoupling for MIMO processes with multiple time delays. To alleviate the difficulties associated with the implementation, the ideal desired decoupling controller matrix is transformed into a practical form using an analytical approximation approach. Correspondingly, the stability of the resultant control system is assessed, together with its robust stability in the presence of process uncertainties. An on-line tuning rule for the single adjustable parameter of each column controllers in the decoupling controller matrix is given to cope with the process unmodeled dynamics. Finally, illustrative examples are given to show the superiority of the proposed method over the recently improved decoupling control methods.     

Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate

In this paper, an SEIR epidemic disease model with time delay and nonlinear incidence rate is studied, and the dynamical behavior of the model under pulse vaccination is analyzed. Using the discrete dynamical system determined by the stroboscopic map, we show that there exists an infection-free periodic solution. Further, we show that the infection-free periodic solution is globally attractive when the period of impulsive effect is less than some critical value. Using a new modelling method, we obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delay, pulse vaccination can bring different effects on the dynamic behavior of the model by numerical analysis. Our results also show the time delay is “profitless”. The main feature of this paper is to introduce time delay and impulse into the SEIR epidemic model and to give pulse vaccination strategies.     

State predictive model following control system for linear time delays

In this paper, we propose a new state predictive model following control system （MFCS）. The considered system has linear time delays. With the MFCS method, we obtain a simple input control law. The bounded property of the internal states for the control is given and the utility of this control design is guaranteed. Finally, an example is given to illustrate the effectiveness of the proposed method.     

Repetitive control of servo systems with time delays

In many industrial robotic servo applications there is a need to track periodic reference signals and/or reject periodic disturbances. Moreover, time-delays are usually unavoidable in control systems due to the sensoring and communication delays. This paper presents an alternative repetitive control design for systems with constant time-delays in both forward and feedback control channels, which are dedicated to track/reject periodic signals. An additional delay is introduced together with the plant delays to construct an internal model for periodic signals, and a simple compensator based on the plant model inverse is utilized to stabilize the closed-loop system. Sufficient stability conditions of the closed-loop system and the robustness analysis against modeling uncertainties are studied. The proposed idea is further extended for general time-delay systems with only a delay term in the forward control channel. The “plug-in” structure used in conventional repetitive control designs is avoided, so that it leads to a simpler control configuration, i.e. only a proportional parameter and the cutoff frequency of a low-pass filter are required to be selected. Simulations based on a hard disk drive system and practical experiments on a rotary robotic servo system are provided to evaluate the effectiveness of the proposed method.     

A model reference adaptive control system for discrete multivariable systems with time delays

This paper presents a new method for designing a model reference adaptive control system for multivariable plants with time delays in the input and output variables. An adaptive algorithm guarantees the asymptotic stability of the error between the plant output and the reference sequence using no anticipative value of the plant output and unknown plant parameter. The validity of the theoretical result is illustrated by a numerical example.