周期性轨道的稳定性条件──混沌的可控性

STABILITY CRITERION OF A PERIODIC ORBIT─CONTROLLABILITY OF CHAOS

研究了随时间周期运动态的稳定性条件，详细分析了在旋转生成矩阵作用下两互相耦的线性常微分方程组的行为，并用几何方法阐明在瞬时的生成矩阵始终保持本征值具有负实部的条件下，参考轨道可能失稳的机制和原因．这一分析澄清了在控制混沌研究中对可控制条件的一些含糊认识．

Stability conditions of time-dependent orbits are discussed.The dynamics of a simple set of two coupled linear ordinary differential equations with rotating generating matrix is analyzed in detail.It is shown that the traiectory may asymptotically run away from the reference state though the real parts of the two eigenvalues of the instant matrix are negative all the time.This analysis is used to clarify some ambiguous points in the discussion of controllability of chaos.