广义Chua电路簇发现象及其分岔机理

通过引入由电感和电阻组成的控制电路模块,并适当选定参数,建立了具有快慢效应的四阶广义Chua电路的模型.探讨了快子系统随慢变量变化产生fold分岔及Hopf分岔的条件,进而探讨了整个系统的动力学演化过程,重点分析了系统中存在的各种快慢效应,给出了两种典型的对称式fold/fold和fold/Hopf周期簇发现象及其相应的分岔机制,从分岔的角度,指出了两种簇发现象的本质区别.     

高维广义蔡氏电路中的快慢动力学行为及其分岔分析

讨论了四阶广义蔡氏电路在两时间尺度下的动力学行为. 由数值模拟得到了系统在不同参数条件下的周期簇发解和混沌吸引子. 通过引入快慢分析法,从分岔的角度,以周期解为例, 对系统动力学行为产生的机理及其演化规律进行了理论分析和解释, 其结论与数值计算的结果基本符合.     

铂族金属氧化过程中的簇发振荡及其诱发机理

铂族金属表面氧化过程是典型的多相催化反应之一, 具有广泛的应用背景及丰富的振荡行为, 因此深入研究铂族金属的氧化中的物理及化学过程具有重要的理论意义及工程应用前景. 通过对铂族金属CO的氧化过程中实测数据的回归分析, 建立了不同尺度耦合解析动力学理论模型. 通过对平衡态的稳定性分析, 指出在一定条件下稳态解会由鞍-结同宿轨道分岔导致周期振荡. 当快子系统产生Hopf分岔时, 该周期振荡会进一步演化为两尺度耦合的周期簇发振荡, 即N^k振荡, 并由加周期分岔使得系统处于激发态的时间显著增加.在此基础上, 利用分岔理论进一步分析了周期簇发及加周期分岔的产生机理, 揭示了周期簇发中沉寂态和激发态相互转化时的不同分岔模式.     

具有非线性控制的Chua电路的混沌同步

Chua电路是一个非光滑系统.本文通过广义哈密顿系统和观测器方法,将具有非线性控制的Chua电路的混沌同步问题转化成研究具有非线性控制的光滑系统的零解稳定性;进而利用滑模控制对该光滑系统的零解稳定性进行了研究,从而使得Chua电路达到了混沌同步.最后,将上述方法应用到具体系统,数值结果也表明其正确性.     

周期激励下Chen系统的簇发现象分析

对于周期激励下的Chen系统,当激励项的频率和原系统的固有频率存在量级上的差异时,系统表现出两个时间尺度下的动力学行为.首先,将激励项作为一个变量对系统进行了分岔分析.然后应用快慢分析法探讨了在不同的参数条件下,激励项周期变化时产生的对称式折叠簇发、对称式亚临界Hopf簇发、对称式Hopf-同宿簇发现象及其产生机制.同时还讨论了激励幅值和频率对系统不同簇发的影响.     

多分界面下四维蔡氏电路的张弛簇发及其机制研究

在经典蔡氏电路的基础上,引入反馈元件,建立了包含多个分界面的四维广义蔡氏电路.在适当的参数条件下,状态变量之间会存在量级上的差距,从而构成了包含两个时间尺度的快慢耦合系统.分析了快子系统的平衡点及其性质,进而利用微分包含理论,探讨了不同的非光滑分界面上的奇异性.给出了系统在两组参数条件下的不同周期簇发行为,应用快慢分析法探讨了系统轨迹在经过多个分界面时的特殊簇发现象,揭示了多吸引子共存时不同的簇发行为的形成机理以及非光滑分岔对簇发行为的影响.     

永磁同步电动机的簇发振荡分析及协同控制

以永磁同步电动机系统作为研究对象,当永磁同步电动机受到周期性外部负载扰动,且扰动频率与电机系统的固有频率之间存在量级差时,永磁同步电动机系统中存在快慢耦合效应,会产生复杂的簇发行为,严重影响电机的安全稳定运行.首先利用快慢动力学分析方法将负载扰动项作为系统的慢变参数,分析系统随慢变参数变化的动力学行为,揭示了系统"周期性对称式亚临界霍普夫(Hopf)簇发振荡"的演化机理.其次针对电机系统出现的簇发振荡,提出了基于协同控制的簇发振荡抑制策略.通过定义含有所有系统状态的宏变量来设计协同控制器,当宏变量在控制器作用下收敛到不变流形时,永磁同步电动机系统也稳定到平衡态.最后通过理论证明和实验验证该方法的有效性,仿真结果表明,协同控制策略在系统存在外部负载扰动时,具有连续的控制律,能够有效地快速抑制永磁同步电动机出现的簇发振荡现象,从而使系统稳定运行.     

多平衡态下簇发振荡产生机理及吸引子结构分析

以周期激励下受控Lorenz模型为例, 考察了多平衡态共存下激励频率与系统固有频率之间存在量级差距也即存在频域上的不同尺度时的耦合效应. 由于激励频率远小于系统的固有频率, 因此将整个激励项视为慢变参数, 分析随慢变参数变化下的各种分岔模式及其相应的分岔行为, 指出在一定条件下, 不同平衡点会产生Hopf分岔和fold分岔. 根据分岔条件的不同, 给出了两种典型情况下的簇发振荡, 并通过引入转换相图, 揭示了不同簇发的产生机理, 指出多平衡态和多种分岔共存不仅会导致沉寂态和激发态的多样性, 而且会使得不同沉寂态和激发态之间存在着不同的转换形式.     

基于超混沌Chua电路的广义同步保密通信

利用状态反馈方法成功地实现了 6维超混沌Chua电路的广义同步建立速度的加快 ,极大地缩短了同步过渡时间。同时 ,在广义同步的基础上设计了一种超混沌保密通信方案 ,有效地提高了通信系统的保密性能。理论分析和数值仿真均取得了显著的效果。     

广义BVP电路系统的振荡行为及其非光滑分岔机理

探讨了具有分段线性特性的广义BVP电路系统随参数变化的复杂动力学演化过程. 其非光滑分界面将相空间划分成不同的区域, 分析了各区域中平衡点的稳定性, 得到其相应的简单分岔和Hopf分岔的临界条件. 给出了不同分界面处广义Jacobian矩阵特征值随辅助参数变化的分布情况, 讨论了分界面处系统可能存在的分岔行为, 指出当广义特征值穿越虚轴时可能引起Hopf分岔, 导致系统由周期振荡转变为概周期振荡, 而当出现零特征值时则导致系统的振荡在不同平衡点之间转换. 针对系统的两种典型振荡行为, 结合数值模拟验证了理论分析的结果.     

基于电流传输器的蔡氏混沌电路的设计和实现

针对传统的蔡氏混沌电路中的信号频率受限和电流信号波形不易测量的缺点,提出了用电流传输器实现的蔡氏电路.采用电流传输器实现了有源仿真电感和蔡氏分段线性电阻,使电路的性能更加稳定、工作频率提高.同时,不需要任何附加电路,就可以非常容易地测量和观察电路中的电流波形以及与电流有关的相图.对电路进行了设计、计算机仿真、硬件实现和实验测试.测试结果与计算机仿真结果一致,证明了电路的正确性和设计的有效性.本电路适用于保密通信.     

不确定Chua’s电路的参数辨识与自适应同步

针对含有不确定参数的Chua’s电路,提出一种仅需传递单路信号实现混沌自适应同步的方法. 基于Lyapunov稳定性理论证明了该方法可使得两个Chua系统——驱动系统和未知参数的响应系统渐近地达到同步,并且可以辨识出响应系统的未知参数. 数值计算结果表明了该方法的有效性. 关键词： 不确定Chua’s电路 混沌同步 参数辨识 Lyapunov函数     

一个超混沌六阶蔡氏电路及其硬件实现

文章构建了一个新的超混沌六阶蔡氏电路,计算了该系统的Lyapunov指数和维数,给出了系统的数值仿真相图.同时,设计了相应的电子电路并进行了硬件实现,实验结果与仿真结果完全吻合,由此证实了该系统不仅存在而且可物理实现. 关键词： 六阶蔡氏电路 超混沌 硬件实验 混沌发生器     

Homoclinic bifurcation in Chua’s circuit

We report our experimental observations of the Shil’nikov-type homoclinic chaos in asymmetry-induced Chua’s oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcations. The asymmetry is introduced in the circuit by forcing a DC voltage. For a selected asymmetry, when a system parameter is controlled, we observed transition from large amplitude limit cycle to homoclinic chaos via a sequence of periodic mixed-mode oscillations interspersed by chaotic states. Moreover, we observed two intermediate bursting regimes. Experimental evidences of homoclinic chaos are verified with PSPICE simulations.     

Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation

We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system.By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency.Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples,in which different types of bursting oscillations such as sub Hopf/sub Hopf burster, sub Hopf/fold-cycle burster, and doublefold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states(QSs) and the repetitive spiking states(SPs) may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically.     

Bursting and spiking due to additional direct and stochastic currents in neuron models

Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter $V_{\rm K}$ in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ``circle/homoclinic" bursting and the integer multiple ``fold/homoclinic" bursting with one spike per burst, as well as the transition from integer multiple bursting to period-1 ``circle/homoclinic" bursting and that from stochastic ``Hopf/homoclinic" bursting to ``Hopf/homoclinic" bursting, are investigated in detail.     

Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation

The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.     

Bursting phenomena as well as the bifurcation mechanism in controlled Lorenz oscillator with two time scales

A controlled Lorenz model with fast-slow effect has been established, in which there exist order gap between the variables associated with the controller and the original Lorenz oscillator, respectively. The conditions of fold bifurcation as well as Hopf bifurcation for the fast subsystem are derived to investigate the mechanism of the behaviors of the whole system. Two cases in which the equilibrium points of the fast subsystem behave in different characteristics have been considered, leading to different dynamical evolutions with the change of coupling strength. Several types of bursting phenomena, such as fold/fold burster, fold/Hopf burster, near-fold/Hopf burster, fold/near-Hopf buster have been observed. Theoretical analysis shows that the bifurcations points which connect the quiescent state and the repetitive spiking state agree well with the turning points of the trajectories of the bursters. Furthermore, the mechanism of the period-adding bifurcations, resulting in the rapid change of the period of the movements, is presented.