时标正弦动力学方程稳定性与分岔分析

Stabilities and bifurcations of sine dynamic equations on time scale

本文研究时标上正弦动力学方程的平衡点稳定性和分岔现象.研究表明随时标参数的变化,正弦动力学方程展现出完全不同的解,会产生n倍周期分岔和平衡点分裂等特有现象.同时,不增加系统参数,仅改变时标的复杂性就能扩展动力学方程处于混沌状态的参数空间,这为时标上动力学方程在混沌加密和雷达波形设计等领域的应用提供了潜在的优势.

A time scale is a nonempty closed subset of the real numbers R. Recently, the dynamic equations on time scale laave recewed mucla attention, which have the generalized forms of differential and differential dynamic equations. In this paper, we study the stabilities of fixed points and bifurcations of the sine dynamic equations on time scale. The results show that the solutions of the sine dynamic equations become different with the time scale parameter changing. And n-period-doubling bifurcations and splits of fixed points are observed. Moreover, the chaotic parameter spaces of the dynamic equations are expanded by the increase of complexity of time scale but without increasing the system parameter, thus providing a potential advantage for chaos encryption, radar waveform design and other application areas.