Keywords: 
• 正弦映射 /
• 分岔 /
• 混沌 /
• 时标动力学方程

Abstract: 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.