Applications and Theory of Controlling Symbol Dynamics: Communicating with Chaos

小行星9704639 本项目主要解决控制混沌和控制符号的问题 小扰动下的动力学 最近的研究表明， 受控混沌轨道的符号动力学表示 用于与混沌信号发生器通信。的演变 一个混沌动力系统的轨迹等价于符号 在适当的符号空间中的动态。 最近出现的控制 使用OGY（Ott，Grebogi和Yorke）技术和各种 具有物理应用的目标定位算法已经证明， 混沌可以被控制，固有的不稳定性可以被用作 允许小的故意扰动引起大信号的优点 变化.混沌的小扰动耦合控制 学习相应符号动态的语法意味着 控制扰动实际上是对原始动态的编码方案。 使用符号的基于地图的描述来控制符号动态 动态需要解决以下问题：学习响应 映射迭代到控制参数的变化，学习半共轭，或编码函数，在映射的动态之间， 吸引子和相应符号动力学的语法，以及 找到依赖于适当选择的最小文法 相空间中的分区。特别是，扩展包括正在进行的 致力于在高维动力系统中进行通信。 调查包括实际噪声环境控制与 带宽权衡和遍历性问题，学习系统响应 控制和符号动力学的混沌动力系统， 只有通过实验数据的时间序列嵌入才知道，并且进一步 开发实用的语法学习算法。 非线性通信理论的这一新领域有望发展成为 提供通用信息传输技术的新范例， 对电子和光学介质都有用，这应该得到广泛的应用。 民用和军用通信基础设施。 一个伟大 最近在应用和理论动力系统方面的大量研究， 一直致力于利用混沌动力学 系统可以控制。 混沌的敏感依赖特性 实际上有利于建立一个高度敏捷的控制系统， 一个小的故意的系统变化可以引起大的响应;所以 所谓的“蝴蝶效应”使我们能够控制系统的反应， 非常小的动力控制。 遍历理论告诉我们， 系统可以被认为是一个无限的信息源; 混沌使我们能够用极低的控制来操纵这种信息流。 一个示例应用是高功率信号 发电机（例如，电子电路），其有意地在 混沌政权，使一个小规模的背负式控制器电路，对 微芯片规模，有能力准确地操纵高功率 信息承载信号该方法与标准线性 通信技术，其中高功率电子电路 需要同样大规模的开关设备来影响大功率 发送高功率消息所需的变化。 不仅 混沌控制通信 动力学，如前所述，但也适用于更广泛的 在自然界中发现的典型的高维混沌动力学。 通过控制混沌来进行交流， 应用，包括新的和简单的电子工程 通信设备，以及新的和简单的光通信 设备，以及生物学，化学和 认知科学

9704639 Bollt This project addresses problems in controlling chaos and controlling symbol dynamics with small perturbations. Recent work has demonstrated the utilization of symbolic dynamics representation of controlled chaotic orbits for communications with chaotic signal generators. The evolution of trajectories of a chaotic dynamical system is equivalent to symbolic dynamics in an appropriate symbol space. The recent advent of controlling chaos using the OGY (Ott, Grebogi, and Yorke) technique and a variety of targeting algorithms, with physical applications, has demonstrated that chaos can be mastered, and inherent instabilities can be used as an advantage in allowing small deliberate perturbations to cause large signal variations. Coupling control of chaos through small perturbations with learning the grammar of the corresponding symbol dynamics means that the control perturbations are actually a coding scheme on the original dynamics. Controlling symbol dynamics using a map based description of the dynamics requires resolution of the following issues: learning the response of map iterates to variations in the control parameters, learning the semi- conjugacy, or coding function, between the dynamics of the map on the attractor and the grammar of the corresponding symbol dynamics, and finding the minimal grammar which is dependent on the appropriate choice of the partition in phase space. In particular, extensions include on-going work on communicating in higher dimensional dynamical systems. Investigations include issues of practical noisy environment control versus bandwidth trade-off and issues of ergodicity, learning system response to controls, and symbol dynamics of a chaotic dynamical system which is known only by time-series embedding of experimental data, and the further development of practical grammar learning algorithms. This new field of nonlinear communication theory promises to develop into a new paradigm offe ring a general information transmission technique, useful to both electronic and optical media, which should find wide applications in civil and military communications infrastructures. A great deal of recent research in applied and theoretical dynamical systems has been focused on taking advantage of the fact that a chaotic dynamical system can be controlled. The sensitive dependence characteristic of chaos is actually advantageous to building a highly agile control system in which a small deliberate system variations can cause a large response; the so called ``butterfly effect" allows us to steer the system responses with extremely small powered controls. Ergodic theory tells us that a chaotic system can be considered as an unlimited information source; and control of chaos allows us to manipulate this information flow with extremely low-powered controls. An example application is a high-powered signal generator (e.g. an electronic circuit), which operates intentionally in the chaotic regime, so that a small-scaled piggy-back controller circuit, on the micro-chip scale, has the ability to accurately manipulate high-powered message bearing signals. This method is in contrast to standard linear communication techniques, in which a high powered electronic circuit requires an equally large-scaled switching device to affect the large power variations required to transmit a high powered message. Not only is communicating through control of chaos applicable to one-dimensional dynamics, as previously demonstrated, but also applies to the more widely typical class of higher dimensional chaotic dynamics found in nature. Communicating by control of chaos promises numerous practical applications including the engineering of new and simple electronic communications devices, and new and simple optical communications devices, as well as the modeling of phenomenon in biology, chemistry, and cognitive science.