【作者】 冯玉玲；

【导师】 张喜和；

【作者基本信息】 长春理工大学 ， 光学， 2009， 博士

【摘要】 混沌控制和同步是非线性动力学领域的重要课题之一,近年来约瑟夫森结和光探测器以其广泛的应用受到国内外科技界普遍关注,因此对约瑟夫森结和光探测器混沌控制和混沌同步的研究成为前沿的热门课题,本文的结果更为其稳定地工作、约瑟夫森结在微波保密通讯领域的应用以及更好地利用和回避光探测器中的混沌现象都奠定了良好的理论和实验基础。本文主要研究了电阻电容电感分路的约瑟夫森结(resistive-capacitive-inductive-shunted Josephson junction(RCLSJJ))的混沌控制、混沌同步以及混沌反控制;然后对光探测器的混沌特征、混沌控制和混沌反控制作了一些研究。全文分为四大部分:RCLSJJ的混沌控制、RCLSJJ的混沌同步、RCLSJJ的混沌反控制、光探测器的混沌特征和混沌控制及混沌反控制的研究。第一部分,首先对RCLSJJ的动力学方程进行了深入研究,对其稳定性作了分析,通过李指数和分岔图等手段研究了RCLSJJ混沌产生的方式和过程,给出了系统处于周期状态和混沌状态的参数范围。然后提出四种控制RCLSJJ混沌的方案:延时线性反馈法、延时反馈法、周期信号控制法和外部周期信号参数调制法,对每种方案都给出了详细的数值研究过程,得到了有效的混沌控制结果,即:这些方案能将RCLSJJ中的混沌控制到不同的稳定周期状态。在第三种方案中首次分析了热噪声对RCLSJJ混沌控制的影响,并且将RCL.SJJ系统的动力学状态和该系统的Ⅰ-Ⅴ曲线相联系,使得其动力学状态更直观。第二部分,首先通过单向耦合方法首次研究了两个RCLSJJ间的广义混沌同步,利用辅助系统的方法验证了这两个RCLSJJ系统间广义混沌同步的存在。然后提出两种混沌精确同步的方案:用自治的混沌系统作为驱动系统实现RCLSJJ系统间混沌精确同步;用非自治的混沌系统作为驱动系统完成RCLSJJ系统间混沌精确同步。详细分析了实现混沌同步的具体过程,给出了被驱动系统的状态随驱动系统变化的规律。这里首次用不同于响应系统的系统作为驱动系统,实现了RCLSJJ系统间的混沌精确同步。第三部分,首次提出两种使RCLSJJ从周期状态转化为混沌状态的具体方案,即:用激光脉冲调制临界电流实现RCLSJJ中混沌的反控制;用附加的交变电流调制偏置电流实现RCLSJJ中混沌的反控制。数值结果表明:这些方案是有效的,并且通过适当选择调制幅值和调制频率能实现不同的混沌轨道重构。第四部分,首先对本征光导体分析了其混沌产生的过程,研究了混沌暂态时间的间隔和相关参数值的关系,结果表明:随陷阱浓度的减小,混沌暂态时间变长;随光激发产生载流子的速率的增加,混沌暂态时间也变长。然后对非本征光导体p-Ge讨论了其产生混沌的方式,提出了两种控制其混沌的方案,分别是周期信号控制法和对非自治系统混沌的位相控制法,数值研究证明了这两个方案的有效性。最后通过研究混沌激光和非本征光导体p-Ge的作用,实现了该光导体中混沌的反控制。最后,对本文的工作进行了总结,并根据RCLSJJ和光探测器的结构特性和应用情况,提出了进一步工作的展望。更多还原

【Abstract】 Controlling and synchronizing chaos are one of the most important problems in the field of nonlinear dynamics. Recently, Josephson junctions and photo-detectors have attracted much more attentions due to their extensive applications. Therefore, the investigations of control and synchronization of chaos in Josephson junctions and photo-detectors became a forward problem. The results of this dissertation establish good theoretical and experimental foundation for using their stable work states, utilizing Josephson junctions in the microwave secrecy communication, and applying and avoiding the chaos phenomena in the photo-detectors.This dissertation mainly investigates the control and synchronization as well as anti-control of chaos in resistive-capacitive-inductive-shunted Josephson junction (RCLSJJ). Then, for photo-detectors, its chaotic characters, chaos control, and chaos generation are also studied. The research work can been divided into four parts: controlling chaos in the RCLSJJ, synchronizing chaos in the RCLSJJ, anti-control of chaos in the RCLSJJ, and the investigation of chaotic features and chaos control as well as chaos generation in the photo-detectors.In part one, firstly, the dynamic equation of the RCLSJJ is deeply investigated, and the stability of its stable solutions is analyzed. Through the lyapunov exponent and the bifurcation diagram, the way and the process of generation chaos in the RCLSJJ are studied, and the parameter ranges of the periodic states and chaotic states are given. Secondly, four schemes of control chaos in the RCLSJJ are proposed, they are as follows: delayed linear feedback, delayed feedback, periodic signal control method and outer period signal parameter modulation method. For each scheme, the detailed numerical research process are given, good results are obtained, namely, these schemes all can effectively control chaos in the RCLSJJ into the different stable periodic states. In the third method, we analyze the influence of thermal noise on controlling chaos in the RCLSJJ for the first time, and the dynamical states of the RCLSJJ are contacted with its I-V curve so as to get its dynamical states directly.In part two, firstly, the generalized synchronization of chaos in two RCLSJJs is investigated by un-directionally coupling for the first time, and the auxiliary system approach has been used to detect the existence of this generalized synchronization state. Then, two schemes for completely synchronizing chaos in RCLSJJs are presented, which are taking autonomous chaotic system as driving system and taking non-autonomous chaotic system as driving system, respectively. We analyze in detail the process of realizing complete chaos synchronization, and give the law that the states of the driven systems vary with the driving system. For the first time, the complete chaos synchronization in RCLSJJs are realized by using the system that is different from response system as driving system.In part three, for the first time, two schemes are proposed for controlling the RCLSJJ from the periodic state into chaotic state, namely: modulating the critical current by using laser pulse and modulating bias current by using additive ac current realize anti-control of chaos in RCLSJJ, respectively. The numerical results show that these two schemes are effect, and the different chaotic orbits can been reconstructed by appropriately selecting the modulation amplitude and modulation frequency.In part four, firstly we analyze the process of generation chaos in the intrinsic photoconductor, and investigate the dependent relationship between the chaotic intermittent time interval and the relative parameter values. The result shows this time increases with reducing the concentration of traps; on the other hand, with increasing the rate of photo-excited charge carriers, this time can also been increased. Secondly, for the extrinsic photo-conductor p-Ge we discuss its manner of chaos generation, and present two schemes for controlling its chaos state, and they are controlling chaos by using periodic signal and controlling chaos in non-autonomous system by using the phase, respectively. The numerical investigations demonstrate the effect of these schemes. Finally, we realize anti-control of chaos in the extrinsic photo-conductor p-Ge by investigating the interaction between the chaotic laser and this photo-conductor.In the end, we briefly summarize our contributions, and discuss the future work according to the structural properties and applications of the RCLSJJ and photo-detector.更多还原