周期激励下四维非线性系统的簇发共存现象

在一个周期激励的四维非自治系统中,当激励的频率远小于系统的固有频率时,系统表现出了两时间尺度的动力学行为.将激励项定义为慢变参数,激励系统可以转化为广义自治系统.分析了广义自治系统平衡点的稳定性及其分岔条件.应用快慢分析法和转换相图,探讨了系统对应于不同初始条件的簇发现象及其产生机制,并对其中多种簇发共存的形成机理进行了讨论.同时,由于慢过效应的存在,簇发振荡的激发态和沉寂态的连接点和理论分析中的分岔点相比存在一定的滞后现象.     

参数激励系统的主共振分岔控制

设计了非线性参数控制器来改变参数激励系统的稳态响应,消除了系统主共振时的鞍结分岔和减小了系统稳态响应的幅值.从而消除了系统特有的跳跃和滞后现象.首先由多尺度法得到系统的近似频响方程,再由奇异性理论来分析分岔特性,从而实现非线性控制的目标.由数值模拟来确定了非线性参数控制器的有效性和可行性.     

变滤波器参数的内模控制在炉内脱硫系统中的应用

基于内模控制、模糊控制,针对炉内脱硫过程对象的大迟延、大惯性、变参数的特点,设计了变滤波器参数的内模控制系统。该控制方案对工况变化具有较好的自适应能力且实现简单。对某300MW循环流化床机组炉内脱硫系统的3种典型工况进行模型辨识及控制仿真,结果表明,该控制方案,超调小,过渡时间短,动态性能好,控制效果优于PID控制与内模控制。     

具有修正的Lelie-Gower项Holling-III类时滞捕食系统的Hopf分支

研究了一类具有修正的Leslie-Gower项与Holling-III类功能性反应函数的时滞捕食系统. 以时滞为分支参数, 讨论系统正平衡点的局部稳定性, 给出系统产生Hopf分支的时滞关键值. 进一步, 确定系统Hopf分支的方向与分支周期解稳定性, 并对系统全局分支周期解的存在性进行讨论. 最后, 利用仿真实例验证理论分析结果的正确性.     

含时滞和Ih流的神经元的同步放电行为

本文研究了时滞和超极化激活的阳离子流Ih对抑制耦合的水蛭神经元的同步放电行为的调控.通过数值仿真揭示了时滞、耦合强度和Ih流都能诱发丰富的同步转迁行为,如从同步的周期-6簇放电到同步的周期-1簇放电.借助ISI分岔和快慢变量分离方法获得了Ih流诱导同步转迁行为的动力学原因.研究结果表明,时滞和Ih流都是影响水蛭神经元同步行为的重要因素.     

Chaos Control and Bifurcation Behavior for a Sprott E System with Distributed Delay Feedback

In this paper, the problem of controlling chaos in a Sprott E system with distributed delay feedback is considered. By analyzing the associated characteristic transcendental equation, we focus on the local stability and Hopf bifurcation nature of the Sprott E system with distributed delay feedback. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using the normal form theory and center manifold theory. Numerical simulations for justifying the theoretical analysis are provided.     

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.     

Crossed Synchronization of Multiple Subnets Complex Network System with Time‐Varying Delay

A dual‐time varying delay complex network system is formed by a plurality of sub‐networks. This paper discusses the crossed synchronization stability of such systems on the basis of crossed synchronization definition between the sub‐nets. By the Lyapunov stability theory with the Zero Theorem, we obtained a sufficient condition that a synchronization exponentially stable controller exists in the complex network system, with characteristic variable delay. The relationship between the complex network nodes are discussed, and the two nodes must be connected and can interact with each other so it has the actual coupling strength. Finally, combining the given conditions, a numerical simulation illustrates its effectiveness.     

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。     

Stability of Linear Systems With Time‐Varying Delay: a Generalized Discretized Lyapunov Functional Approach

This paper investigates the stability of linear uncertain systems with time‐varying delay. Stability criteria are derived based on a generalized discretized Lyapunov functional approach. The kernel of the functional, which is a function of two variables, is chosen as piecewise linear. The stability conditions are written in the form of linear matrix inequalities. Numerical examples indicate significant improvements over the existing results.     

Prediction‐based Adaptive Robust Tracking Control of an Uncertain First‐Order Time‐Delay System

This paper considers the tracking problem of a delayed uncertain first‐order system which is simultaneously subject to (possibly large) known input delay, unknown but bounded time‐varying disturbance, and unknown plant parameter. The proposed predictor adaptive robust controller (PARC) involves prediction‐based projection type adaptation laws with model compensation and prediction‐based continuous robust feedback such that the closed loop system has global exponential convergence with an ultimate bound proportional to delay, disturbance bound, and switching gain. Further, if there are only delay and parameter uncertainties after some finite time, then semi‐global asymptotic tracking is guaranteed. The proposed design is shown to have significant closed loop performance improvement over the baseline controller.