Mathematical Sciences: Nonlinear Dynamics of Oscillator Arrays

数学科学：振荡器阵列的非线性动力学

• 批准号: 9500948
• 负责人: Steven Strogatz
• 金额: $ 18万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500948&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Dynamics; Oscillator

DMS_9500948 Strogatz The proposal is to study the nonlinear dynamics of oscillator arrays, using mathematical methods of dynamical systems theory, bifurcation theory, and perturbation theory, along with numerical simulation. One project concerns arrays of superconducting Josephson junctions, and will be carried out in collaboration with an experimental group at MIT. This work is aimed at understanding the phase-locking properties of series arrays; the propagation and instabilities of kinks in one-dimensional parallel arrays; and the behavior of vortices and row-switched states in two-dimensional arrays. A second project (in collaboration with an experimental group at Georgia Tech) will address the dynamics of laser arrays. Areas of investigation will include phase-locking in slightly detuned laser arrays; controlling chaos in laser arrays; and mutual synchronization of chaotic lasers, with possible applications to private communication. The Principal Investigator and his experimental collaborators will study the dynamics of superconducting Josephson arrays and laser arrays. Josephson arrays can be used as very sensitive detectors of magnetic fields (with biomedical and astronomical applications), voltage standards, power generators at submillimeter wavelengths (a part of the spectrum that is difficult to access by other technologies), and as ultrafast switching devices and transmission lines. All of these technologies would benefit from a deeper mathematical understanding of synchronization and vortex propagation in Josephson arrays. The goals of the laser array project are to find methods for improving the phase-locking characteristics of laser arrays (to increase their power output), and to develop novel encryption schemes for private communications, based on mutual synchronization of chaotic lasers.

该提案是研究振荡器阵列的非线性动力学，使用动力系统理论，分叉理论和扰动理论的数学方法，沿着数值模拟。其中一个项目涉及超导约瑟夫森结阵列，将与麻省理工学院的一个实验小组合作进行。 这项工作的目的是了解的相位锁定性能的串联阵列;在一维平行阵列的扭结的传播和不稳定性;以及在二维阵列的涡旋和行切换状态的行为。第二个项目（与格鲁吉亚理工学院的一个实验小组合作）将研究激光阵列的动力学。研究领域将包括微失谐激光器阵列的锁相;控制激光器阵列中的混沌;以及混沌激光器的相互同步，并可能应用于私人通信。 首席研究员和他的实验合作者将研究超导约瑟夫森阵列和激光阵列的动力学。约瑟夫森阵列可用作磁场（生物医学和天文学应用），电压标准，亚毫米波长（其他技术难以访问的光谱的一部分）的功率发生器的非常敏感的探测器，并作为超快开关器件和传输线。所有这些技术都将受益于对约瑟夫森阵列中的同步和涡旋传播的更深入的数学理解。激光器阵列项目的目标是找到改善激光器阵列锁相特性的方法（以增加其功率输出），并根据混沌激光器的相互同步开发新的私人通信加密方案。