一个粘弹性振子的动力学与控制

本文详细分析了一个具有粘弹性项的非线性振子的动力学与控制.首先研究了系统平衡点的稳定性,表明系统存在复杂的无界动力学行为.然后引入时滞速度反馈对这个不稳定系统进行控制.研究结果表明速度反馈控制能镇定此不稳定的粘弹性系统.适当的选择控制增益和控制时滞,控制系统有稳定的平衡点,由Hopf分岔产生的周期解,拟周期解,并能展现出复杂的混沌解.数值模拟验证了结论的正确性.     

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.     

时滞控制神经网络的稳定性和Turing斑图结构

本文讨论了一类时滞反应扩散神经网络模型.利用时滞来控制系统的稳定性、分岔和Turing斑图.研究结果表明,在一定条件下,时滞不仅能影响系统的稳定性和周期震荡性,还能影响系统的Turing不稳定性.数值模拟验证了理论分析的正确性,同时还说明了时滞能改变斑图的结构.     

大规模超环神经网络分岔动力学

目前绝大多数神经网络分岔动力学局限于结构简单、低维少节点模型, 这与真实的大规模神经网络系统相去甚远. 因此, 研究大量神经元耦合的高维神经网络模型更具实际应用价值. 环状及辐射状结构在神经网络中普遍存在, 提出了一类大规模超环时滞神经网络模型, 结构包含一个大环和任意多个小环, 并且每个环上拥有任意多个神经元. 运用特征值法和分岔理论, 选取时滞为分岔参数, 给出了该超环神经网络模型的稳定性条件和Hopf分岔判据. 数值仿真结果, 验证该理论结果的正确性.     

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....     

基于RecurDyn的旋转弹发射出筒过程动力学仿真

针对某旋转弹筒弹分离试验时出现尾翼座与筒壁刮擦的问题,用Recur Dyn对弹体出筒过程进行动力学仿真.对筒弹分离试验进行故障复现,分析故障原因;根据故障分析结论对筒弹设计方案提出更改建议并再次仿真;第二次试验结果表明该分析结论和仿真结果正确.此外,还给出设计方案更改后正常发动机推力状况下的弹体出筒过程的重要总体仿真结果.该研究缩短产品设计周期、降低研制成本.     

分数阶计算机病毒模型的稳定性与分岔分析

随着有线和无线通信网络的普及,计算机病毒已经成为当代信息社会的一大威胁,单纯依靠杀毒软件已经无法彻底清除病毒,而通过对其在互联网上的传播机制的分析,以及对其模型的研究,可以找到有效的防范计算机病毒的对策。因此,基于非线性动力学与分数阶系统理论,建立了一类具有饱和发生率的分数阶时滞SIQR计算机病毒模型。计算出模型的平衡点,并通过分析相应的特征方程研究了时滞对平衡点稳定性的影响。选择时滞作为分岔参数,得到了发生Hopf分岔的时滞临界值。研究发现,系统的动力学行为依赖于分岔的临界值,同时给出了系统局部稳定和产生Hopf分岔的条件。在此基础上,研究了分数阶阶次的变化对分岔阈值的影响。最后,通过数值模拟验证了理论分析的正确性。     

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。     

一类旋转弹在高空中的锥形运动稳定性

为揭示弹箭在高空飞行过程中由于重力持续作用产生大攻角的物理本质,建立了弹道平面内时变参数的弹体运动数学模型,并推导了弹体在高空飞行段的攻角响应方程.同时,为了分析弹道顶点附近锥形运动的稳定性,综合考虑弹体姿态运动和位移运动建立了旋转弹锥形运动的动力学模型.针对大攻角引起显著气动非线性效应的情况,采用李雅普诺夫一级近似方法,给出了弹道顶点附近弹体锥形运动的稳定判据,并通过数值仿真验证了其正确性.     

分数阶时滞传染病模型的传播动力学

本文研究了一个具有时滞的分数阶SEIR传染病模型,并且着重研究了时滞的引入对模型的动力学行为的影响.首先,建立了分数阶SEIR传染病模型并给出了无时滞情况下地方病平衡点稳定的充分条件,以此来确保时滞的引入具有实际意义.其次,结合分岔理论求得了Hopf分岔发生的条件以及分岔阈值的表达式.研究发现,系统的动力学行为依赖于分...     

Chaos control of a chemical chaotic system via time-delayed feedback control method

In this paper, the control of chemical chaotic dynamical system is investigated by time-delayed feedback control technique. The controllability and the stability of the equilibriums and local Hopf bifurcation of the system are verified. Some numerical simulations which show the effectiveness of the time-delayed feedback control method are provided.     

Bifurcation control of small‐world networks with delays VIA PID controller

In this paper, the problem of bifurcation control for a small‐world network model with time delay is studied. We first put forward a Proportional‐Integral‐Derivative (PID) feedback scheme to control the Hopf bifurcation of the network. The time delay is selected as the bifurcation parameter. The conditions of the stability and Hopf bifurcation are given for the controlled network. By using the center manifold theorem and the normal form theory, the direction and stability of bifurcating periodic solutions are confirmed. The feasible region of the parameters of the controller is determined. It is found that the bifurcation dynamics of the small‐world network are optimized by adjusting the parameters of the PID controller. Finally, a numerical example verifies the effectiveness of the designed PID controller, and the relationships between the onset of the Hopf bifurcation and the control parameters are obtained.     

一类二阶时延神经网络的分岔分析和控制

讨论了一类二阶时延网络系统的非线性特性,应用线性化稳定性和分岔理论,提出了该系统从稳定到分岔的条件.结论指出利用延迟时间可以进行分岔控制、极限环幅值控制等,并给出了仿真的具体实例.     

Coning motion stability and decoupling methods analysis of spinning missiles with angle-of-attack feedback autopilot

The angle-of-attack (AOA) three-loop feedback autopilot is an improved three-loop autopilot that has been widely employed in missile control systems. For spinning missiles, however, unstable coning motion can be induced by the cross-couple effect. For spinning missiles with an AOA feedback autopilot, this paper analyzes the coning motion stability with the consideration of the augmentation loop and the position of the accelerometer and compares the performance of three decoupling methods. First, a novel double-channel actuator AOA three-loop autopilot is established, and the sufficient and necessary condition of coning motion stability is proposed analytically on account of the complex system equations. The stability condition shows that the stable region of the design parameters for the autopilot shrinks as a result of the spinning condition. Moreover, methods associated with actuator dynamics, control coupling, static stability, and the decoupling method of setting the lead angle to the control system are presented to improve the stability of spinning missiles. Numerical simulations are implemented to demonstrate the accuracy of the proposed methods, whose results illustrate that the stability conditions can guide AOA autopilot design for the flight stabilization of spinning missiles.     

网络控制系统PI预测控制及稳定性分析

将PID反馈原理引入广义预测控制（GPC）思想,把GPC目标性能函数改造成具有PI的结构形式,根据反馈时延导出多步控制序列,通过时延补偿器对前向时延进行补偿,使控制性能在网络环境下得到极大改善。控制器结合了PID控制和预测控制的优点,具有较强的鲁棒性和工程意义。构造Lyapunov函数对闭环系统的稳定性进行分析,并通过仿真验证了该算法的有效性。     

Asymptotic stability analysis of nonlinear real-time networked control systems

The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound （MADB） for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.     

一类多延时多变量网络控制系统的建模及稳定性

针对一类多延时多变量网络控制系统（NCS）,讨论其建模和稳定性问题．首先假设传感器采用时间驱动、控制器和执行器采用事件驱动,建立了系统在连续时域~MIMO数学模型;然后根据Lyapunov稳定性原理和Razumikhin定理,构造系统的Lyapunov函数,并分析系统的渐近稳定性,进而得到了系统稳定的时延参数和稳定性条件;最后通过仿真实例验证了该类网络控制系统的稳定判据．     

Stability and bifurcation of genetic regulatory networks with small RNAs and multiple delays

In this paper, we study the stability, bifurcation and periodic oscillation of two-gene regulatory networks mediated by small RNAs (sRNAs) with multiple delays. We first show the effect of sRNAs on the stability and bifurcation of genetic regulatory networks. Then we present sufficient conditions for the local stability of two-gene genetic regulatory networks in the parameter space, and assess critical values of the Hopf bifurcation. Although such networks may have multiple delays, sRNAs, positive feedbacks and different connection strengths among two genes, their stability and bifurcation depend on the sum of all time delays among all elements (including both mRNAs and proteins). Furthermore, the period of oscillations increases with the time delay, and in the case of larger delay, the amplitude of oscillations is robust against the change in the delay. Two examples are employed to illustrate the theorems developed in this study.