非线性自治系统中周期间的关系

Relations between periods in nonlinear autonomous systems

用数值模拟方法对三维非线性自治系统进行了分析,结果发现:随着系统中衰减项参量变化,在同一周期状态内,系统的周期基本不变;在不同的周期状态之间,系统的周期具有近似简单倍数关系,或者说系统的其他频率与基频有近似简单分数关系.

By analyzing numerically some three-dimensional nonlinear chaotic systems,it is found that the fundamental period and other period (stable and unstable)in these systems almost do not drift (within the same period)with the variety of damping parameters and the average period values of different periods almost have the simple approximate relationship,that is,there is a simple factional relationship between the fundamental frequency and other frequency.