线性自调频系统动力学行为分析

Dynamic behavior analysis of linear self-FM system

摘要:

为重点研究线性自调频系统的动力学行为，根据锁相环的结构提出了一种新的线性自反馈调频系统，通过对线性自调频系统数学模型的分析，其动力学行为可以用简单的正弦映射描述。文章通过相空间轨迹、分岔图和Lyapunov指数研究正弦映射中的动力学行为和混沌现象，发现其动力学行为具有周期性和对称性的特点。同时分析对比了自调频混沌系统在不同状态下的频谱，为进一步研究自调频混沌信号源的设计和应用提供理论依据和数值参考。

Abstract:

According to the structure of phase locked loop, a new linear since feedback FM system is proposed，and its dynamic behaviors are studied. Based on the analysis of mathematical model of linear system since FM, the dynamic behavior can be described by using simple sine mapping. The dynamic behaviors and chaos phenomena of sine mapping are studied through phase space trajectory，bifurcation and Lyapunov exponent. It is discovered that the system bears the characteristics of periodic and symmetry on its dynamic behaviors. The frequency spectra under different conditions are compared for the chaos system of since FM，which may provide theoretical basis and numerical reference for the design of the self-FM chaos signal source.