复空间中变时滞复动力系统激光失谐性分析与复同步

Time delay is ubiquitous, which changes dynamically in the real world. Complex parameter is an important index to describe laser detuning. In order to reveal the essence of laser detuning, we focus on the characteristics and complex modified hybrid function projective synchronization of laser detuning complex dynamical system with both time-varying delay and complex parameter in complex space. The main contents are as follows. Firstly, we study the effect of both complex parameter and time-varying delay on formation mechanism of special chaotic attractors, and reveal the essential law of laser detuning. Secondly, we propose complex modified hybrid function projective synchronization on account of the characteristics that both the real and imaginary parts of the complex variable can be stretched evolving in the same or inverse directions and rotated evolving in different directions with a time-dependent intersection angle simultaneously. Therefore, it breaks the bottleneck of the previous function synchronization which only can stretch the real and imaginary parts of complex state variables evolving in the same or inverse directions. Finally, using physically measurable states in the real-world, combining error feedback and system identification, we design adaptive complex modified hybrid function projective synchronization controller to control the tuned states and restore the original resonant state, and finish physical simulation by digital circuit. As a application, we discuss complex modified hybrid function projective synchronization of laser detuning complex networks, and explain the physical mechanism and synchronization of laser detuning complex networks from a new perspective. The results will provide a direct theoretical basis and technical support to improve the performance of laser, increase output power and laser applications in military technology and science.

时滞在客观世界中无法避免，通常是动态改变的。复参数是刻画激光失谐物理特征的重要指标。为揭示激光失谐的本质，本项目利用变时滞复参数复动力系统，在复空间中研究激光失谐的特性及其复修正混杂函数投影同步，主要内容为：(1)刻画复参数和时变时滞因数对特殊混沌吸引子形成的影响机理，探究激光失谐的本质规律；(2)基于复变量的实虚部能够同时拉伸和旋转，并以相同相角同时旋转的特质，提出复修正混杂函数投影同步，打破了以前的函数同步只能实现状态变量实虚部拉伸的瓶颈；(3)基于可测物理量，结合误差反馈和系统辨识，设计自适应复修正混杂函数投影同步控制器，将激光失谐控制到调谐状态，利用数字电路实现物理仿真。作为推广应用，研究激光失谐复杂网络的复修正混杂函数投影同步，从一个新的视角解释激光失谐复杂网络的同步现象物理机理。该项目成果为改善激光器性能，提高激光输出功率及激光的科学技术和军事应用提供直接的理论基础和技术支撑。

时滞在真实世界中无法避免，复参数是刻画激光失谐的重要数字特征。在复空间中研究变时滞复参数复动力系统的动力学行为及其形成机理，有助于揭示激光失谐的物理特性和本质规律。本项目运用复动力系统理论、李雅普诺夫函数和不等式等技术方法，对几类激光系统的失谐特性和复同步进行深入研究，并设法将相关方法和结果推广应用到激光失谐复杂网络的动力学特性和同步问题。主要研究结果包括：(1) 利用变时滞复参数复动力系统，分析了激光失谐的动力学特性，得到了复参数和变时滞因数对特殊混沌吸引子形成的影响机理；对激光失谐的特殊吸引子，利用DSP实现了物理仿真。(2) 提出了复广义同步的概念，打破了以前的同步只能实现状态变量实虚部拉伸的局限。而且，复广义同步是一种比复修正混杂函数投影同步更广泛的同步，能够更好地描述各种同步现象。创新性地设计了简单易于物理实现的误差反馈控制器和复参数更新律，建立了复空间复参数复动力系统自适应复同步的新准则；提出了复向量线性无关的概念，给出了复参数辨识的充要条件。(3) 将激光系统的失谐特性应用于安全通信，设计了激光混沌保密通信方案，利用数值仿真验证通信方案的可行性、安全性和稳定性。 (4) 作为推广应用，研究了星形激光网络失谐的动力学特性，得到了激光失谐复杂网络的同步现象物理机理。所得结果丰富和完善了复动力系统理论体系，并为激光器性能的改善及激光输出功率的提高提供直接的理论基础和技术支撑。. 项目期间，参加了国内会议3次，国际会议5次，发表了32篇论文，其中27篇论文被SCI收录（2篇中科院JCR大类一区论文，2篇卓越期刊论文, 1篇ESI高被引论文)），4篇被EI收录，1篇被Web of Science Proceedings(ISTP)收录。